Multi-planar material interfaces

1 Objective

Verify that internal material-cell boundaries do not materially change the response of a homogeneous trimmed solid, including where multiple planar interface faces meet along longitudinal edges or at cross-section corners. Six partitioned square cross-sections are compared with an unpartitioned monolithic beam using identical elastic properties in every material definition. The quantities of interest are the relative differences in tip displacement and in displacement and stress profiles sampled along the beam and across its section.

2 Geometry

The specimen is a prismatic cantilever with square cross-section \(b \times b\) and length \(L\). Every internal cross-section boundary is extruded through the full beam length, producing planar material-interface faces parallel to the beam axis. Figure 1 shows the monolithic reference and the six partition patterns.

Figure 1: Normalized cross-sections used by the homogeneous material-interface study. Each color denotes a distinct retained cell and material definition; all material properties are identical.
Table 1: Geometric parameters.
Quantity Symbol Value
Cross-section width \(b\) 10
Cross-section height \(b\) 10
Beam length \(L\) 100

The first three partitions exercise rectangular inclusions that respectively touch one exterior face, touch two exterior faces, or remain completely enclosed. The zig-zag and nested-L partitions divide the square into equal-area cells and introduce non-collinear interface planes. The Tetris partition uses a \(3 \times 3\) construction: two equal four-square L cells surround a one-square central cell, so three materials meet at the central square’s corners.

3 Material

The partitioned models use distinct Abaqus material and solid-section definitions for each colored cell: two definitions in the first five cases and three in the Tetris case. Every definition has the same isotropic, linear-elastic properties, so the internal boundaries are physically invisible in the continuum problem.

Table 2: Properties assigned independently to every material definition.
Property Symbol Value
Young’s modulus \(E\) \(100 \times 10^{9}\)
Poisson’s ratio \(\nu\) 0.3

4 Loading & boundary conditions

The \(z=0\) end face is pinned in all three translational directions. A uniform surface traction of magnitude \(t_y\) acts in the negative \(y\) direction over every cell face at \(z=L\). Applying the same traction to the full partitioned end face produces resultant shear force \(P=t_y b^2\) and exercises bending and transverse shear without introducing density as another material parameter.

Table 3: Applied loading.
Quantity Symbol Value
End shear traction \(t_y\) \(10.0 \times 10^{-3}\)
Resultant force \(P\) \(1\)
Direction — Negative \(y\)

5 Mesh & discretization

Each model uses the same immersed rectilinear background grid, outer geometry, grid origin, and \(h/p\) coordinates. The background element sizes are \((5,5,10)/2^k\) in \((x,y,z)\) for \(k=0,\ldots,3\), at degrees \(p=1\), \(2\), and \(3\) with maximum continuity \(C^{p-1}\). Only the retained internal cell topology changes between the monolithic and partitioned models. The complete study contains 84 independently schedulable simulations: seven cross-sections, four refinement levels, and three degrees. The following views look along the beam axis and use the \(p=2\) results databases. Retained cells are colored categorically by part_id using the Coreform primary palette in index order; each 2-by-2 figure progresses from the coarsest to the finest cross-sectional background mesh.

5.1 Monolithic reference

(a) \(h_{xy}=5\)
(b) \(h_{xy}=2.5\)
(c) \(h_{xy}=1.25\)
(d) \(h_{xy}=0.625\)
Figure 2: Monolithic reference cross-section meshes.

5.2 Bottom-centered one-third square

(a) \(h_{xy}=5\)
(b) \(h_{xy}=2.5\)
(c) \(h_{xy}=1.25\)
(d) \(h_{xy}=0.625\)
Figure 3: Bottom-centered one-third-square partition meshes.

5.3 Bottom-left one-half square

(a) \(h_{xy}=5\)
(b) \(h_{xy}=2.5\)
(c) \(h_{xy}=1.25\)
(d) \(h_{xy}=0.625\)
Figure 4: Bottom-left one-half-square partition meshes.

5.4 Centered one-third square

(a) \(h_{xy}=5\)
(b) \(h_{xy}=2.5\)
(c) \(h_{xy}=1.25\)
(d) \(h_{xy}=0.625\)
Figure 5: Centered one-third-square partition meshes.

5.5 Zig-zag interface

(a) \(h_{xy}=5\)
(b) \(h_{xy}=2.5\)
(c) \(h_{xy}=1.25\)
(d) \(h_{xy}=0.625\)
Figure 6: Zig-zag partition meshes.

5.6 Nested L interface

(a) \(h_{xy}=5\)
(b) \(h_{xy}=2.5\)
(c) \(h_{xy}=1.25\)
(d) \(h_{xy}=0.625\)
Figure 7: Nested-L partition meshes.

5.7 Tetris partition

(a) \(h_{xy}=5\)
(b) \(h_{xy}=2.5\)
(c) \(h_{xy}=1.25\)
(d) \(h_{xy}=0.625\)
Figure 8: Three-cell Tetris partition meshes.

6 Reference & accepted solutions

The primary numerical reference for every partitioned result is the monolithic beam at the identical degree, refinement level, background-grid placement, loading, and material properties. This same-\(h\), same-\(p\) pairing removes ordinary discretization error from the comparison and isolates the effect of creating and coupling retained material cells.

Six response differences are recorded for every pairing: tip \(u_y\); relative \(L^2\) differences in \(u_y\) along an axial line; and relative \(L^2\) differences in \(\sigma_{zz}\) and \(\tau_{yz}\) along vertical and horizontal midspan probes. The study-level CTest takes the maximum of those six quantities at the finest level and enforces the calibrated acceptance tolerance. The homogeneous Euler–Bernoulli cantilever solution [1] is also recorded by each simulation as a secondary, record-only diagnostic; it is not used to judge interface invariance because it carries independent beam-theory modeling error.

7 Results

Each partition geometry below is presented independently. The case-tabbed table reports the measured partitioned response, the same-\(h\), same-\(p\) monolithic reference response, and their relative difference for every mesh size and degree. For the tip displacement these are scalar values. For each line probe the measured and reference values are the profile \(L^2\) norms, while the relative difference is the \(L^2\) norm of the pointwise profile difference normalized by the reference norm. The three probe figures use one subfigure per degree and overlay every partitioned mesh size against the finest matching-degree monolithic result; the final figure tracks the maximum same-mesh relative difference across all six verification quantities under refinement.

7.1 Bottom-centered one-third square

Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-1.89 \times 10^{-9}\) \(-2.09 \times 10^{-9}\) \(9.44\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(9.28 \times 10^{-9}\) \(10.2 \times 10^{-9}\) \(9.26\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.25\) \(0.279\) \(10.4\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(31.8 \times 10^{-3}\) \(31.3 \times 10^{-3}\) \(11.9\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(48.4 \times 10^{-3}\) \(53.6 \times 10^{-3}\) \(9.76\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(38.9 \times 10^{-3}\) \(36.1 \times 10^{-3}\) \(8.09\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-3.32 \times 10^{-9}\) \(-3.41 \times 10^{-9}\) \(2.67\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(16.2 \times 10^{-9}\) \(16.6 \times 10^{-9}\) \(2.63\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.457\) \(0.471\) \(2.96\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(30.9 \times 10^{-3}\) \(30.6 \times 10^{-3}\) \(6.39\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(91.0 \times 10^{-3}\) \(94.4 \times 10^{-3}\) \(3.64\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(43.9 \times 10^{-3}\) \(43.9 \times 10^{-3}\) \(0.967\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-3.87 \times 10^{-9}\) \(-3.88 \times 10^{-9}\) \(0.238\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(18.8 \times 10^{-9}\) \(18.8 \times 10^{-9}\) \(0.236\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.531\) \(0.533\) \(0.46\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(31.8 \times 10^{-3}\) \(31.8 \times 10^{-3}\) \(1.08\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.108\) \(0.108\) \(0.292\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(46.6 \times 10^{-3}\) \(46.8 \times 10^{-3}\) \(0.375\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-3.97 \times 10^{-9}\) \(-3.97 \times 10^{-9}\) \(0.036\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.3 \times 10^{-9}\) \(19.3 \times 10^{-9}\) \(0.0361\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.544\) \(0.544\) \(0.219\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.1 \times 10^{-3}\) \(32.1 \times 10^{-3}\) \(0.936\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(90.1 \times 10^{-3}\) \(90.1 \times 10^{-3}\) \(0.0398\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(46.7 \times 10^{-3}\) \(46.7 \times 10^{-3}\) \(0.0783\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-3.99 \times 10^{-9}\) \(-3.99 \times 10^{-9}\) \(0.00453\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.0079\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.162\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(26.5 \times 10^{-3}\) \(26.7 \times 10^{-3}\) \(2.69\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(95.6 \times 10^{-3}\) \(95.0 \times 10^{-3}\) \(0.83\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(37.5 \times 10^{-3}\) \(37.5 \times 10^{-3}\) \(0.291\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(0.00549\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.00672\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.0237\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(30.8 \times 10^{-3}\) \(30.8 \times 10^{-3}\) \(2.64\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(94.7 \times 10^{-3}\) \(94.8 \times 10^{-3}\) \(0.0817\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(45.2 \times 10^{-3}\) \(45.2 \times 10^{-3}\) \(0.0854\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(341 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(427 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.00854\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(31.8 \times 10^{-3}\) \(31.8 \times 10^{-3}\) \(0.223\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(94.8 \times 10^{-3}\) \(94.8 \times 10^{-3}\) \(0.0278\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(46.9 \times 10^{-3}\) \(46.9 \times 10^{-3}\) \(0.133\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(335 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(403 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.00519\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.1 \times 10^{-3}\) \(32.1 \times 10^{-3}\) \(0.228\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(395 \times 10^{-6}\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(46.9 \times 10^{-3}\) \(46.9 \times 10^{-3}\) \(0.00364\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(0.00555\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.00642\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.147\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.0 \times 10^{-3}\) \(32.0 \times 10^{-3}\) \(2.41\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(94.7 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.248\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(46.4 \times 10^{-3}\) \(47.0 \times 10^{-3}\) \(1.53\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(86.9 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(121 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.0153\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.2 \times 10^{-3}\) \(32.2 \times 10^{-3}\) \(0.0333\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.00664\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(47.0 \times 10^{-3}\) \(47.0 \times 10^{-3}\) \(0.147\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(903 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.00107\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.00818\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.2 \times 10^{-3}\) \(32.2 \times 10^{-3}\) \(0.146\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.0246\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(47.0 \times 10^{-3}\) \(47.1 \times 10^{-3}\) \(0.0148\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(274 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(328 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(198 \times 10^{-6}\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.2 \times 10^{-3}\) \(32.2 \times 10^{-3}\) \(0.0455\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.00405\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(47.1 \times 10^{-3}\) \(47.1 \times 10^{-3}\) \(0.00211\%\)

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7.1.1 Centerline displacement profile

(a) \(p=1\)
(b) \(p=2\)
(c) \(p=3\)
Figure 9: Bottom-centered one-third square: centerline displacement profiles under mesh refinement.

7.1.2 Transverse normal-stress profile

(a) \(p=1\)
(b) \(p=2\)
(c) \(p=3\)
Figure 10: Bottom-centered one-third square: transverse normal-stress profiles under mesh refinement.

7.1.3 Transverse shear-stress profile

(a) \(p=1\)
(b) \(p=2\)
(c) \(p=3\)
Figure 11: Bottom-centered one-third square: transverse shear-stress profiles under mesh refinement.

7.1.4 Relative differences under refinement

Figure 12: Bottom-centered one-third square: maximum homogeneous-response difference under refinement.

7.2 Bottom-left one-half square

Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-1.95 \times 10^{-9}\) \(-2.09 \times 10^{-9}\) \(6.52\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(9.59 \times 10^{-9}\) \(10.2 \times 10^{-9}\) \(6.26\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.256\) \(0.279\) \(8.35\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.0 \times 10^{-3}\) \(31.3 \times 10^{-3}\) \(7.75\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(45.4 \times 10^{-3}\) \(53.6 \times 10^{-3}\) \(18.6\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(37.9 \times 10^{-3}\) \(36.1 \times 10^{-3}\) \(5.92\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-3.34 \times 10^{-9}\) \(-3.41 \times 10^{-9}\) \(2.13\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(16.2 \times 10^{-9}\) \(16.6 \times 10^{-9}\) \(2.1\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.459\) \(0.471\) \(2.74\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(31.1 \times 10^{-3}\) \(30.6 \times 10^{-3}\) \(8.78\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(87.2 \times 10^{-3}\) \(94.4 \times 10^{-3}\) \(10.2\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(43.7 \times 10^{-3}\) \(43.9 \times 10^{-3}\) \(2.8\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-3.87 \times 10^{-9}\) \(-3.88 \times 10^{-9}\) \(0.186\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(18.8 \times 10^{-9}\) \(18.8 \times 10^{-9}\) \(0.184\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.531\) \(0.533\) \(0.429\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(31.8 \times 10^{-3}\) \(31.8 \times 10^{-3}\) \(0.828\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.104\) \(0.108\) \(6.01\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(46.7 \times 10^{-3}\) \(46.8 \times 10^{-3}\) \(0.698\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-3.97 \times 10^{-9}\) \(-3.97 \times 10^{-9}\) \(0.0198\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.3 \times 10^{-9}\) \(19.3 \times 10^{-9}\) \(0.0197\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.544\) \(0.544\) \(0.119\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.1 \times 10^{-3}\) \(32.1 \times 10^{-3}\) \(0.48\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(88.6 \times 10^{-3}\) \(90.1 \times 10^{-3}\) \(2.29\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(46.6 \times 10^{-3}\) \(46.7 \times 10^{-3}\) \(0.43\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-3.99 \times 10^{-9}\) \(-3.99 \times 10^{-9}\) \(0.0227\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.0278\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.0297\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(26.6 \times 10^{-3}\) \(26.7 \times 10^{-3}\) \(4.83\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(94.5 \times 10^{-3}\) \(95.0 \times 10^{-3}\) \(0.793\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(38.2 \times 10^{-3}\) \(37.5 \times 10^{-3}\) \(5.28\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(0.00958\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.0116\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.0357\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(30.8 \times 10^{-3}\) \(30.8 \times 10^{-3}\) \(2.17\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(95.0 \times 10^{-3}\) \(94.8 \times 10^{-3}\) \(0.306\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(45.3 \times 10^{-3}\) \(45.2 \times 10^{-3}\) \(0.663\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(750 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(915 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.0309\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(31.8 \times 10^{-3}\) \(31.8 \times 10^{-3}\) \(0.357\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(94.9 \times 10^{-3}\) \(94.8 \times 10^{-3}\) \(0.079\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(46.9 \times 10^{-3}\) \(46.9 \times 10^{-3}\) \(0.261\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(177 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(210 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.00386\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.1 \times 10^{-3}\) \(32.1 \times 10^{-3}\) \(0.149\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.00786\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(46.9 \times 10^{-3}\) \(46.9 \times 10^{-3}\) \(0.124\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(0.00183\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.0021\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.201\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.0 \times 10^{-3}\) \(32.0 \times 10^{-3}\) \(0.802\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(94.6 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.602\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(46.6 \times 10^{-3}\) \(47.0 \times 10^{-3}\) \(1.35\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(0.00134\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.00157\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.028\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.2 \times 10^{-3}\) \(32.2 \times 10^{-3}\) \(0.0406\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.135\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(47.0 \times 10^{-3}\) \(47.0 \times 10^{-3}\) \(0.0564\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(227 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(269 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.00916\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.2 \times 10^{-3}\) \(32.2 \times 10^{-3}\) \(0.114\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.0458\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(47.1 \times 10^{-3}\) \(47.1 \times 10^{-3}\) \(0.0515\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(317 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(378 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(651 \times 10^{-6}\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.2 \times 10^{-3}\) \(32.2 \times 10^{-3}\) \(0.0171\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.0092\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(47.1 \times 10^{-3}\) \(47.1 \times 10^{-3}\) \(0.00986\%\)

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7.2.1 Centerline displacement profile

(a) \(p=1\)
(b) \(p=2\)
(c) \(p=3\)
Figure 13: Bottom-left one-half square: centerline displacement profiles under mesh refinement.

7.2.2 Transverse normal-stress profile

(a) \(p=1\)
(b) \(p=2\)
(c) \(p=3\)
Figure 14: Bottom-left one-half square: transverse normal-stress profiles under mesh refinement.

7.2.3 Transverse shear-stress profile

(a) \(p=1\)
(b) \(p=2\)
(c) \(p=3\)
Figure 15: Bottom-left one-half square: transverse shear-stress profiles under mesh refinement.

7.2.4 Relative differences under refinement

Figure 16: Bottom-left one-half square: maximum homogeneous-response difference under refinement.

7.3 Centered one-third square

Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-1.92 \times 10^{-9}\) \(-2.09 \times 10^{-9}\) \(7.89\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(9.46 \times 10^{-9}\) \(10.2 \times 10^{-9}\) \(7.57\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.251\) \(0.279\) \(10.2\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.0 \times 10^{-3}\) \(31.3 \times 10^{-3}\) \(11\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(48.2 \times 10^{-3}\) \(53.6 \times 10^{-3}\) \(10.2\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(39.0 \times 10^{-3}\) \(36.1 \times 10^{-3}\) \(8.45\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-3.17 \times 10^{-9}\) \(-3.41 \times 10^{-9}\) \(7.06\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(15.4 \times 10^{-9}\) \(16.6 \times 10^{-9}\) \(6.99\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.434\) \(0.471\) \(7.85\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(31.0 \times 10^{-3}\) \(30.6 \times 10^{-3}\) \(3.11\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(87.2 \times 10^{-3}\) \(94.4 \times 10^{-3}\) \(7.72\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(44.1 \times 10^{-3}\) \(43.9 \times 10^{-3}\) \(1.8\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-3.87 \times 10^{-9}\) \(-3.88 \times 10^{-9}\) \(0.293\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(18.8 \times 10^{-9}\) \(18.8 \times 10^{-9}\) \(0.291\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.531\) \(0.533\) \(0.424\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(31.8 \times 10^{-3}\) \(31.8 \times 10^{-3}\) \(1.59\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.108\) \(0.108\) \(0.561\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(46.8 \times 10^{-3}\) \(46.8 \times 10^{-3}\) \(0.401\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-3.97 \times 10^{-9}\) \(-3.97 \times 10^{-9}\) \(0.0566\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.3 \times 10^{-9}\) \(19.3 \times 10^{-9}\) \(0.0567\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.544\) \(0.544\) \(0.306\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.1 \times 10^{-3}\) \(32.1 \times 10^{-3}\) \(1.13\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(90.1 \times 10^{-3}\) \(90.1 \times 10^{-3}\) \(0.161\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(46.7 \times 10^{-3}\) \(46.7 \times 10^{-3}\) \(0.101\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-3.99 \times 10^{-9}\) \(-3.99 \times 10^{-9}\) \(569 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.0039\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.108\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(26.7 \times 10^{-3}\) \(26.7 \times 10^{-3}\) \(1.27\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(95.3 \times 10^{-3}\) \(95.0 \times 10^{-3}\) \(0.558\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(37.6 \times 10^{-3}\) \(37.5 \times 10^{-3}\) \(0.615\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(0.00213\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.00275\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.0171\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(30.8 \times 10^{-3}\) \(30.8 \times 10^{-3}\) \(0.782\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(95.1 \times 10^{-3}\) \(94.8 \times 10^{-3}\) \(0.422\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(45.2 \times 10^{-3}\) \(45.2 \times 10^{-3}\) \(0.792\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(126 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(144 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.016\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(31.8 \times 10^{-3}\) \(31.8 \times 10^{-3}\) \(0.364\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(94.8 \times 10^{-3}\) \(94.8 \times 10^{-3}\) \(0.0359\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(46.9 \times 10^{-3}\) \(46.9 \times 10^{-3}\) \(0.281\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(87.5 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(107 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.00561\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.1 \times 10^{-3}\) \(32.1 \times 10^{-3}\) \(0.329\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.0216\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(46.9 \times 10^{-3}\) \(46.9 \times 10^{-3}\) \(0.0618\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(0.00235\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(527 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.129\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.1 \times 10^{-3}\) \(32.0 \times 10^{-3}\) \(4.42\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(94.5 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.898\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(46.5 \times 10^{-3}\) \(47.0 \times 10^{-3}\) \(1.79\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(554 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(647 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.0285\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.2 \times 10^{-3}\) \(32.2 \times 10^{-3}\) \(0.112\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(95.0 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.175\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(47.0 \times 10^{-3}\) \(47.0 \times 10^{-3}\) \(0.183\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(120 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(134 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.0157\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.2 \times 10^{-3}\) \(32.2 \times 10^{-3}\) \(0.226\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.0879\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(47.0 \times 10^{-3}\) \(47.1 \times 10^{-3}\) \(0.0327\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(83.5 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(101 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.00336\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.2 \times 10^{-3}\) \(32.2 \times 10^{-3}\) \(0.0211\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.00912\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(47.1 \times 10^{-3}\) \(47.1 \times 10^{-3}\) \(0.0118\%\)

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7.3.1 Centerline displacement profile

(a) \(p=1\)
(b) \(p=2\)
(c) \(p=3\)
Figure 17: Centered one-third square: centerline displacement profiles under mesh refinement.

7.3.2 Transverse normal-stress profile

(a) \(p=1\)
(b) \(p=2\)
(c) \(p=3\)
Figure 18: Centered one-third square: transverse normal-stress profiles under mesh refinement.

7.3.3 Transverse shear-stress profile

(a) \(p=1\)
(b) \(p=2\)
(c) \(p=3\)
Figure 19: Centered one-third square: transverse shear-stress profiles under mesh refinement.

7.3.4 Relative differences under refinement

Figure 20: Centered one-third square: maximum homogeneous-response difference under refinement.

7.4 Zig-zag interface

Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-1.99 \times 10^{-9}\) \(-2.09 \times 10^{-9}\) \(4.56\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(9.79 \times 10^{-9}\) \(10.2 \times 10^{-9}\) \(4.33\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.264\) \(0.279\) \(5.48\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(31.6 \times 10^{-3}\) \(31.3 \times 10^{-3}\) \(4.29\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(50.7 \times 10^{-3}\) \(53.6 \times 10^{-3}\) \(6.81\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(37.2 \times 10^{-3}\) \(36.1 \times 10^{-3}\) \(3.22\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-3.34 \times 10^{-9}\) \(-3.41 \times 10^{-9}\) \(2.18\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(16.2 \times 10^{-9}\) \(16.6 \times 10^{-9}\) \(2.14\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.459\) \(0.471\) \(2.75\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(30.9 \times 10^{-3}\) \(30.6 \times 10^{-3}\) \(6.14\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(92.8 \times 10^{-3}\) \(94.4 \times 10^{-3}\) \(3.48\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(44.6 \times 10^{-3}\) \(43.9 \times 10^{-3}\) \(4.02\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-3.87 \times 10^{-9}\) \(-3.88 \times 10^{-9}\) \(0.192\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(18.8 \times 10^{-9}\) \(18.8 \times 10^{-9}\) \(0.19\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.532\) \(0.533\) \(0.295\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(31.8 \times 10^{-3}\) \(31.8 \times 10^{-3}\) \(1.13\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.107\) \(0.108\) \(2.02\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(46.6 \times 10^{-3}\) \(46.8 \times 10^{-3}\) \(0.627\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-3.97 \times 10^{-9}\) \(-3.97 \times 10^{-9}\) \(0.0271\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.3 \times 10^{-9}\) \(19.3 \times 10^{-9}\) \(0.0269\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.544\) \(0.544\) \(0.133\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.1 \times 10^{-3}\) \(32.1 \times 10^{-3}\) \(1.16\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(90.1 \times 10^{-3}\) \(90.1 \times 10^{-3}\) \(0.838\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(46.6 \times 10^{-3}\) \(46.7 \times 10^{-3}\) \(0.499\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-3.99 \times 10^{-9}\) \(-3.99 \times 10^{-9}\) \(0.0283\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.0335\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.0635\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(26.2 \times 10^{-3}\) \(26.7 \times 10^{-3}\) \(7.17\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(95.3 \times 10^{-3}\) \(95.0 \times 10^{-3}\) \(1.14\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(37.3 \times 10^{-3}\) \(37.5 \times 10^{-3}\) \(2.15\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(0.00223\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.00296\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.00625\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(30.8 \times 10^{-3}\) \(30.8 \times 10^{-3}\) \(1.22\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(95.0 \times 10^{-3}\) \(94.8 \times 10^{-3}\) \(0.294\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(45.0 \times 10^{-3}\) \(45.2 \times 10^{-3}\) \(0.807\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(645 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(751 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.0114\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(31.8 \times 10^{-3}\) \(31.8 \times 10^{-3}\) \(0.139\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(94.9 \times 10^{-3}\) \(94.8 \times 10^{-3}\) \(0.0528\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(46.8 \times 10^{-3}\) \(46.9 \times 10^{-3}\) \(0.561\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(456 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(543 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.00128\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.1 \times 10^{-3}\) \(32.1 \times 10^{-3}\) \(0.142\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.044\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(46.9 \times 10^{-3}\) \(46.9 \times 10^{-3}\) \(0.0546\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(0.00743\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.00885\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.0519\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.1 \times 10^{-3}\) \(32.0 \times 10^{-3}\) \(1.15\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(95.0 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.254\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(47.2 \times 10^{-3}\) \(47.0 \times 10^{-3}\) \(1.44\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(0.00261\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.00306\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.0168\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.2 \times 10^{-3}\) \(32.2 \times 10^{-3}\) \(0.415\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(94.8 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.147\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(47.0 \times 10^{-3}\) \(47.0 \times 10^{-3}\) \(0.459\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(422 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(506 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.0063\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.2 \times 10^{-3}\) \(32.2 \times 10^{-3}\) \(0.193\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.058\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(47.0 \times 10^{-3}\) \(47.1 \times 10^{-3}\) \(0.269\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(217 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(256 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(620 \times 10^{-6}\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.2 \times 10^{-3}\) \(32.2 \times 10^{-3}\) \(0.46\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.00508\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(47.1 \times 10^{-3}\) \(47.1 \times 10^{-3}\) \(0.265\%\)

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7.4.1 Centerline displacement profile

(a) \(p=1\)
(b) \(p=2\)
(c) \(p=3\)
Figure 21: Zig-zag interface: centerline displacement profiles under mesh refinement.

7.4.2 Transverse normal-stress profile

(a) \(p=1\)
(b) \(p=2\)
(c) \(p=3\)
Figure 22: Zig-zag interface: transverse normal-stress profiles under mesh refinement.

7.4.3 Transverse shear-stress profile

(a) \(p=1\)
(b) \(p=2\)
(c) \(p=3\)
Figure 23: Zig-zag interface: transverse shear-stress profiles under mesh refinement.

7.4.4 Relative differences under refinement

Figure 24: Zig-zag interface: maximum homogeneous-response difference under refinement.

7.5 Nested L interface

Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-1.97 \times 10^{-9}\) \(-2.09 \times 10^{-9}\) \(5.7\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(9.67 \times 10^{-9}\) \(10.2 \times 10^{-9}\) \(5.46\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.259\) \(0.279\) \(7.17\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(31.7 \times 10^{-3}\) \(31.3 \times 10^{-3}\) \(6.61\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(49.8 \times 10^{-3}\) \(53.6 \times 10^{-3}\) \(8.16\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(37.9 \times 10^{-3}\) \(36.1 \times 10^{-3}\) \(5.33\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-3.27 \times 10^{-9}\) \(-3.41 \times 10^{-9}\) \(4.25\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(15.9 \times 10^{-9}\) \(16.6 \times 10^{-9}\) \(4.2\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.451\) \(0.471\) \(4.5\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(31.1 \times 10^{-3}\) \(30.6 \times 10^{-3}\) \(2.72\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(91.7 \times 10^{-3}\) \(94.4 \times 10^{-3}\) \(5.81\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(44.2 \times 10^{-3}\) \(43.9 \times 10^{-3}\) \(3.01\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-3.87 \times 10^{-9}\) \(-3.88 \times 10^{-9}\) \(0.236\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(18.8 \times 10^{-9}\) \(18.8 \times 10^{-9}\) \(0.235\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.531\) \(0.533\) \(0.268\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(31.8 \times 10^{-3}\) \(31.8 \times 10^{-3}\) \(2.08\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.108\) \(0.108\) \(1.21\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(46.6 \times 10^{-3}\) \(46.8 \times 10^{-3}\) \(0.705\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-3.97 \times 10^{-9}\) \(-3.97 \times 10^{-9}\) \(0.042\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.3 \times 10^{-9}\) \(19.3 \times 10^{-9}\) \(0.0421\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.544\) \(0.544\) \(0.153\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.1 \times 10^{-3}\) \(32.1 \times 10^{-3}\) \(0.394\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(90.1 \times 10^{-3}\) \(90.1 \times 10^{-3}\) \(0.22\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(46.7 \times 10^{-3}\) \(46.7 \times 10^{-3}\) \(0.145\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-3.99 \times 10^{-9}\) \(-3.99 \times 10^{-9}\) \(0.0061\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.00721\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.106\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(26.4 \times 10^{-3}\) \(26.7 \times 10^{-3}\) \(5.02\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(95.4 \times 10^{-3}\) \(95.0 \times 10^{-3}\) \(0.896\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(39.1 \times 10^{-3}\) \(37.5 \times 10^{-3}\) \(8.02\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(0.00741\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.00917\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.11\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(30.8 \times 10^{-3}\) \(30.8 \times 10^{-3}\) \(3.45\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(95.1 \times 10^{-3}\) \(94.8 \times 10^{-3}\) \(0.459\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(45.2 \times 10^{-3}\) \(45.2 \times 10^{-3}\) \(0.832\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(348 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(361 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.0146\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(31.8 \times 10^{-3}\) \(31.8 \times 10^{-3}\) \(1.01\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(94.9 \times 10^{-3}\) \(94.8 \times 10^{-3}\) \(0.0821\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(46.8 \times 10^{-3}\) \(46.9 \times 10^{-3}\) \(0.546\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(174 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(198 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.00781\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.1 \times 10^{-3}\) \(32.1 \times 10^{-3}\) \(0.147\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.0388\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(46.9 \times 10^{-3}\) \(46.9 \times 10^{-3}\) \(0.0578\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(0.00109\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.00126\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.0291\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.1 \times 10^{-3}\) \(32.0 \times 10^{-3}\) \(0.992\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(95.0 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.433\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(46.9 \times 10^{-3}\) \(47.0 \times 10^{-3}\) \(1.38\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(0.00197\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.00234\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.0299\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.2 \times 10^{-3}\) \(32.2 \times 10^{-3}\) \(0.229\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(94.8 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.191\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(47.0 \times 10^{-3}\) \(47.0 \times 10^{-3}\) \(0.392\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(499 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(597 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.00985\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.2 \times 10^{-3}\) \(32.2 \times 10^{-3}\) \(0.0595\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.1\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(47.1 \times 10^{-3}\) \(47.1 \times 10^{-3}\) \(0.0749\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(230 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(271 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.00192\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.2 \times 10^{-3}\) \(32.2 \times 10^{-3}\) \(0.0289\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.0136\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(47.1 \times 10^{-3}\) \(47.1 \times 10^{-3}\) \(0.0194\%\)

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7.5.1 Centerline displacement profile

(a) \(p=1\)
(b) \(p=2\)
(c) \(p=3\)
Figure 25: Nested L interface: centerline displacement profiles under mesh refinement.

7.5.2 Transverse normal-stress profile

(a) \(p=1\)
(b) \(p=2\)
(c) \(p=3\)
Figure 26: Nested L interface: transverse normal-stress profiles under mesh refinement.

7.5.3 Transverse shear-stress profile

(a) \(p=1\)
(b) \(p=2\)
(c) \(p=3\)
Figure 27: Nested L interface: transverse shear-stress profiles under mesh refinement.

7.5.4 Relative differences under refinement

Figure 28: Nested L interface: maximum homogeneous-response difference under refinement.

7.6 Tetris partition

Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-1.93 \times 10^{-9}\) \(-2.09 \times 10^{-9}\) \(7.82\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(9.46 \times 10^{-9}\) \(10.2 \times 10^{-9}\) \(7.6\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.254\) \(0.279\) \(9.19\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(31.7 \times 10^{-3}\) \(31.3 \times 10^{-3}\) \(12.3\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(48.7 \times 10^{-3}\) \(53.6 \times 10^{-3}\) \(9.33\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(39.0 \times 10^{-3}\) \(36.1 \times 10^{-3}\) \(8.45\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-3.17 \times 10^{-9}\) \(-3.41 \times 10^{-9}\) \(7.15\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(15.4 \times 10^{-9}\) \(16.6 \times 10^{-9}\) \(7.08\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.435\) \(0.471\) \(7.83\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(31.2 \times 10^{-3}\) \(30.6 \times 10^{-3}\) \(4.9\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(87.0 \times 10^{-3}\) \(94.4 \times 10^{-3}\) \(8.27\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(43.8 \times 10^{-3}\) \(43.9 \times 10^{-3}\) \(1.5\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-3.86 \times 10^{-9}\) \(-3.88 \times 10^{-9}\) \(0.394\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(18.8 \times 10^{-9}\) \(18.8 \times 10^{-9}\) \(0.392\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.531\) \(0.533\) \(0.616\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(31.8 \times 10^{-3}\) \(31.8 \times 10^{-3}\) \(1.35\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.107\) \(0.108\) \(1.1\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(46.8 \times 10^{-3}\) \(46.8 \times 10^{-3}\) \(0.0943\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-3.97 \times 10^{-9}\) \(-3.97 \times 10^{-9}\) \(0.0768\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.3 \times 10^{-9}\) \(19.3 \times 10^{-9}\) \(0.077\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.544\) \(0.544\) \(0.311\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.1 \times 10^{-3}\) \(32.1 \times 10^{-3}\) \(1.13\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(90.1 \times 10^{-3}\) \(90.1 \times 10^{-3}\) \(0.223\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(46.7 \times 10^{-3}\) \(46.7 \times 10^{-3}\) \(0.107\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-3.99 \times 10^{-9}\) \(-3.99 \times 10^{-9}\) \(0.0152\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.0173\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.0549\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(26.6 \times 10^{-3}\) \(26.7 \times 10^{-3}\) \(4.89\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(95.0 \times 10^{-3}\) \(95.0 \times 10^{-3}\) \(0.585\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(36.8 \times 10^{-3}\) \(37.5 \times 10^{-3}\) \(2.69\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(0.00511\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.00635\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.0158\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(30.8 \times 10^{-3}\) \(30.8 \times 10^{-3}\) \(0.922\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(94.6 \times 10^{-3}\) \(94.8 \times 10^{-3}\) \(0.348\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(45.4 \times 10^{-3}\) \(45.2 \times 10^{-3}\) \(0.666\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(139 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(194 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.0138\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(31.8 \times 10^{-3}\) \(31.8 \times 10^{-3}\) \(0.349\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(94.8 \times 10^{-3}\) \(94.8 \times 10^{-3}\) \(0.0555\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(46.9 \times 10^{-3}\) \(46.9 \times 10^{-3}\) \(0.155\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(447 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(538 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.00531\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.1 \times 10^{-3}\) \(32.1 \times 10^{-3}\) \(0.335\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.0253\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(46.9 \times 10^{-3}\) \(46.9 \times 10^{-3}\) \(0.0473\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(0.00862\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.0102\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.13\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.1 \times 10^{-3}\) \(32.0 \times 10^{-3}\) \(1.6\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(94.8 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.468\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(47.1 \times 10^{-3}\) \(47.0 \times 10^{-3}\) \(0.799\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(0.00187\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.00225\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.0112\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.2 \times 10^{-3}\) \(32.2 \times 10^{-3}\) \(0.175\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.102\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(47.0 \times 10^{-3}\) \(47.0 \times 10^{-3}\) \(0.0945\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(788 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(936 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.0184\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.2 \times 10^{-3}\) \(32.2 \times 10^{-3}\) \(0.366\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.0806\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(47.1 \times 10^{-3}\) \(47.1 \times 10^{-3}\) \(0.017\%\)
Quantity Measured value Reference value Relative difference
Tip displacement \(u_y\) \(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(267 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\) \(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(320 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(0.548\) \(0.548\) \(0.0033\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(32.2 \times 10^{-3}\) \(32.2 \times 10^{-3}\) \(0.0264\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\) \(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.011\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\) \(47.1 \times 10^{-3}\) \(47.1 \times 10^{-3}\) \(0.0148\%\)

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7.6.1 Centerline displacement profile

(a) \(p=1\)
(b) \(p=2\)
(c) \(p=3\)
Figure 29: Tetris partition: centerline displacement profiles under mesh refinement.

7.6.2 Transverse normal-stress profile

(a) \(p=1\)
(b) \(p=2\)
(c) \(p=3\)
Figure 30: Tetris partition: transverse normal-stress profiles under mesh refinement.

7.6.3 Transverse shear-stress profile

(a) \(p=1\)
(b) \(p=2\)
(c) \(p=3\)
Figure 31: Tetris partition: transverse shear-stress profiles under mesh refinement.

7.6.4 Relative differences under refinement

Figure 32: Tetris partition: maximum homogeneous-response difference under refinement.

8 Performance

Trimming and Abaqus solve statistics are reported for every mesh level and degree, grouped by geometry. Abaqus problem size, timing, completion, and actual thread topology come from a sanitized JSON record generated from abaqus summarize -detail advanced and the solver message file. The raw summary files can contain host, user, and absolute-path data, so they are not published.

8.1 Monolithic reference

Coreform IGA Mesh

\(h_z\) Background Active Trimmed CPUs Wall-time [s]
\(10\) \(325\) \(99\) \(90\) \(1\) \(4.0\)
\(5\) \(1{,}127\) \(525\) \(354\) \(2\) \(9.8\)
\(2.5\) \(5{,}203\) \(3{,}321\) \(1{,}410\) \(4\) \(33.0\)
\(1.25\) \(29{,}963\) \(23{,}409\) \(5{,}634\) \(8\) \(152.5\)
\(h_z\) Background Active Trimmed CPUs Wall-time [s]
\(10\) \(735\) \(99\) \(90\) \(1\) \(4.2\)
\(5\) \(2{,}025\) \(525\) \(354\) \(2\) \(10.3\)
\(2.5\) \(7{,}605\) \(3{,}321\) \(1{,}410\) \(4\) \(37.2\)
\(1.25\) \(37{,}485\) \(23{,}409\) \(5{,}634\) \(8\) \(164.4\)
\(h_z\) Background Active Trimmed CPUs Wall-time [s]
\(10\) \(1{,}377\) \(99\) \(90\) \(1\) \(6.6\)
\(5\) \(3{,}267\) \(525\) \(354\) \(2\) \(11.8\)
\(2.5\) \(10{,}575\) \(3{,}321\) \(1{,}410\) \(4\) \(41.3\)
\(1.25\) \(46{,}023\) \(23{,}409\) \(5{,}634\) \(8\) \(170.7\)

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Coreform IGA for Abaqus solve

\(h_z\) Elements Nodes DOFs Threads Wall-time [s]
\(10\) \(579\) \(482\) \(1{,}446\) \(1\) \(1.0\)
\(5\) \(1{,}137\) \(1{,}152\) \(3{,}456\) \(2\) \(1.0\)
\(2.5\) \(4{,}345\) \(4{,}778\) \(14{,}334\) \(4\) \(1.0\)
\(1.25\) \(26{,}605\) \(28{,}296\) \(84{,}888\) \(8\) \(6.0\)
\(h_z\) Elements Nodes DOFs Threads Wall-time [s]
\(10\) \(575\) \(613\) \(1{,}839\) \(1\) \(1.0\)
\(5\) \(1{,}137\) \(1{,}487\) \(4{,}461\) \(2\) \(1.0\)
\(2.5\) \(4{,}345\) \(5{,}781\) \(17{,}343\) \(4\) \(3.0\)
\(1.25\) \(27{,}055\) \(31{,}916\) \(95{,}748\) \(8\) \(19.0\)
\(h_z\) Elements Nodes DOFs Threads Wall-time [s]
\(10\) \(571\) \(786\) \(2{,}358\) \(1\) \(2.0\)
\(5\) \(1{,}137\) \(1{,}896\) \(5{,}688\) \(2\) \(5.0\)
\(2.5\) \(4{,}993\) \(7{,}274\) \(21{,}822\) \(4\) \(18.0\)
\(1.25\) \(29{,}817\) \(37{,}002\) \(111{,}006\) \(8\) \(82.0\)

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8.2 Bottom-centered one-third square

Coreform IGA Mesh

\(h_z\) Background Active Trimmed CPUs Wall-time [s]
\(10\) \(325\) \(132\) \(110\) \(1\) \(5.4\)
\(5\) \(1{,}127\) \(630\) \(390\) \(2\) \(14.2\)
\(2.5\) \(5{,}203\) \(3{,}690\) \(1{,}638\) \(4\) \(46.1\)
\(1.25\) \(29{,}963\) \(24{,}786\) \(6{,}374\) \(8\) \(214.9\)
\(h_z\) Background Active Trimmed CPUs Wall-time [s]
\(10\) \(735\) \(132\) \(110\) \(1\) \(5.9\)
\(5\) \(2{,}025\) \(630\) \(390\) \(2\) \(15.2\)
\(2.5\) \(7{,}605\) \(3{,}690\) \(1{,}638\) \(4\) \(51.6\)
\(1.25\) \(37{,}485\) \(24{,}786\) \(6{,}374\) \(8\) \(236.1\)
\(h_z\) Background Active Trimmed CPUs Wall-time [s]
\(10\) \(1{,}377\) \(132\) \(110\) \(1\) \(9.4\)
\(5\) \(3{,}267\) \(630\) \(390\) \(2\) \(16.8\)
\(2.5\) \(10{,}575\) \(3{,}690\) \(1{,}638\) \(4\) \(57.4\)
\(1.25\) \(46{,}023\) \(24{,}786\) \(6{,}374\) \(8\) \(252.8\)

Download data (CSV)

Coreform IGA for Abaqus solve

\(h_z\) Elements Nodes DOFs Threads Wall-time [s]
\(10\) \(5{,}556\) \(3{,}696\) \(11{,}088\) \(1\) \(2.0\)
\(5\) \(7{,}062\) \(4{,}974\) \(14{,}922\) \(2\) \(2.0\)
\(2.5\) \(12{,}406\) \(10{,}172\) \(30{,}516\) \(4\) \(3.0\)
\(1.25\) \(48{,}538\) \(42{,}586\) \(127{,}758\) \(8\) \(8.0\)
\(h_z\) Elements Nodes DOFs Threads Wall-time [s]
\(10\) \(5{,}648\) \(3{,}982\) \(11{,}946\) \(1\) \(4.0\)
\(5\) \(7{,}302\) \(5{,}654\) \(16{,}962\) \(2\) \(4.0\)
\(2.5\) \(12{,}406\) \(11{,}750\) \(35{,}250\) \(4\) \(6.0\)
\(1.25\) \(50{,}212\) \(48{,}647\) \(145{,}941\) \(8\) \(21.0\)
\(h_z\) Elements Nodes DOFs Threads Wall-time [s]
\(10\) \(5{,}644\) \(4{,}299\) \(12{,}897\) \(1\) \(5.0\)
\(5\) \(7{,}366\) \(6{,}380\) \(19{,}140\) \(2\) \(9.0\)
\(2.5\) \(15{,}158\) \(15{,}020\) \(45{,}060\) \(4\) \(22.0\)
\(1.25\) \(64{,}942\) \(62{,}052\) \(186{,}156\) \(8\) \(107.0\)

Download data (CSV)

8.3 Bottom-left one-half square

Coreform IGA Mesh

\(h_z\) Background Active Trimmed CPUs Wall-time [s]
\(10\) \(325\) \(132\) \(88\) \(1\) \(5.6\)
\(5\) \(1{,}127\) \(630\) \(346\) \(2\) \(14.2\)
\(2.5\) \(5{,}203\) \(3{,}690\) \(1{,}378\) \(4\) \(45.0\)
\(1.25\) \(29{,}963\) \(24{,}786\) \(5{,}506\) \(8\) \(219.5\)
\(h_z\) Background Active Trimmed CPUs Wall-time [s]
\(10\) \(735\) \(132\) \(88\) \(1\) \(6.0\)
\(5\) \(2{,}025\) \(630\) \(346\) \(2\) \(14.8\)
\(2.5\) \(7{,}605\) \(3{,}690\) \(1{,}378\) \(4\) \(54.5\)
\(1.25\) \(37{,}485\) \(24{,}786\) \(5{,}506\) \(8\) \(223.6\)
\(h_z\) Background Active Trimmed CPUs Wall-time [s]
\(10\) \(1{,}377\) \(132\) \(88\) \(1\) \(8.8\)
\(5\) \(3{,}267\) \(630\) \(346\) \(2\) \(15.9\)
\(2.5\) \(10{,}575\) \(3{,}690\) \(1{,}378\) \(4\) \(56.6\)
\(1.25\) \(46{,}023\) \(24{,}786\) \(5{,}506\) \(8\) \(244.4\)

Download data (CSV)

Coreform IGA for Abaqus solve

\(h_z\) Elements Nodes DOFs Threads Wall-time [s]
\(10\) \(5{,}534\) \(3{,}505\) \(10{,}515\) \(1\) \(1.0\)
\(5\) \(6{,}918\) \(4{,}738\) \(14{,}214\) \(2\) \(3.0\)
\(2.5\) \(11{,}522\) \(9{,}576\) \(28{,}728\) \(4\) \(4.0\)
\(1.25\) \(47{,}298\) \(41{,}780\) \(125{,}340\) \(8\) \(8.0\)
\(h_z\) Elements Nodes DOFs Threads Wall-time [s]
\(10\) \(5{,}634\) \(3{,}795\) \(11{,}385\) \(1\) \(2.0\)
\(5\) \(7{,}078\) \(5{,}380\) \(16{,}140\) \(2\) \(4.0\)
\(2.5\) \(11{,}522\) \(11{,}158\) \(33{,}474\) \(4\) \(6.0\)
\(1.25\) \(48{,}870\) \(47{,}776\) \(143{,}328\) \(8\) \(21.0\)
\(h_z\) Elements Nodes DOFs Threads Wall-time [s]
\(10\) \(5{,}580\) \(4{,}090\) \(12{,}270\) \(1\) \(5.0\)
\(5\) \(7{,}158\) \(6{,}118\) \(18{,}354\) \(2\) \(8.0\)
\(2.5\) \(14{,}494\) \(14{,}548\) \(43{,}644\) \(4\) \(22.0\)
\(1.25\) \(63{,}590\) \(61{,}092\) \(183{,}276\) \(8\) \(126.0\)

Download data (CSV)

8.4 Centered one-third square

Coreform IGA Mesh

\(h_z\) Background Active Trimmed CPUs Wall-time [s]
\(10\) \(325\) \(110\) \(99\) \(1\) \(5.2\)
\(5\) \(1{,}127\) \(693\) \(504\) \(2\) \(18.7\)
\(2.5\) \(5{,}203\) \(3{,}649\) \(1{,}720\) \(4\) \(48.2\)
\(1.25\) \(29{,}963\) \(25{,}353\) \(7{,}480\) \(8\) \(245.4\)
\(h_z\) Background Active Trimmed CPUs Wall-time [s]
\(10\) \(735\) \(110\) \(99\) \(1\) \(5.6\)
\(5\) \(2{,}025\) \(693\) \(504\) \(2\) \(19.3\)
\(2.5\) \(7{,}605\) \(3{,}649\) \(1{,}720\) \(4\) \(49.4\)
\(1.25\) \(37{,}485\) \(25{,}353\) \(7{,}480\) \(8\) \(261.7\)
\(h_z\) Background Active Trimmed CPUs Wall-time [s]
\(10\) \(1{,}377\) \(110\) \(99\) \(1\) \(8.2\)
\(5\) \(3{,}267\) \(693\) \(504\) \(2\) \(22.1\)
\(2.5\) \(10{,}575\) \(3{,}649\) \(1{,}720\) \(4\) \(59.8\)
\(1.25\) \(46{,}023\) \(25{,}353\) \(7{,}480\) \(8\) \(291.2\)

Download data (CSV)

Coreform IGA for Abaqus solve

\(h_z\) Elements Nodes DOFs Threads Wall-time [s]
\(10\) \(6{,}518\) \(4{,}334\) \(13{,}002\) \(1\) \(4.0\)
\(5\) \(9{,}993\) \(6{,}672\) \(20{,}016\) \(2\) \(3.0\)
\(2.5\) \(14{,}513\) \(11{,}442\) \(34{,}326\) \(4\) \(2.0\)
\(1.25\) \(57{,}941\) \(48{,}232\) \(144{,}696\) \(8\) \(12.0\)
\(h_z\) Elements Nodes DOFs Threads Wall-time [s]
\(10\) \(6{,}642\) \(4{,}614\) \(13{,}842\) \(1\) \(3.0\)
\(5\) \(10{,}249\) \(7{,}362\) \(22{,}086\) \(2\) \(3.0\)
\(2.5\) \(14{,}513\) \(12{,}848\) \(38{,}544\) \(4\) \(6.0\)
\(1.25\) \(60{,}119\) \(54{,}816\) \(164{,}448\) \(8\) \(27.0\)
\(h_z\) Elements Nodes DOFs Threads Wall-time [s]
\(10\) \(6{,}344\) \(4{,}743\) \(14{,}229\) \(1\) \(7.0\)
\(5\) \(10{,}377\) \(8{,}120\) \(24{,}360\) \(2\) \(13.0\)
\(2.5\) \(17{,}609\) \(16{,}122\) \(48{,}366\) \(4\) \(23.0\)
\(1.25\) \(78{,}465\) \(70{,}226\) \(210{,}678\) \(8\) \(166.0\)

Download data (CSV)

8.5 Zig-zag interface

Coreform IGA Mesh

\(h_z\) Background Active Trimmed CPUs Wall-time [s]
\(10\) \(325\) \(132\) \(66\) \(1\) \(5.8\)
\(5\) \(1{,}127\) \(630\) \(258\) \(2\) \(14.4\)
\(2.5\) \(5{,}203\) \(3{,}690\) \(1{,}026\) \(4\) \(48.4\)
\(1.25\) \(29{,}963\) \(24{,}786\) \(4{,}098\) \(8\) \(211.0\)
\(h_z\) Background Active Trimmed CPUs Wall-time [s]
\(10\) \(735\) \(132\) \(66\) \(1\) \(6.0\)
\(5\) \(2{,}025\) \(630\) \(258\) \(2\) \(15.2\)
\(2.5\) \(7{,}605\) \(3{,}690\) \(1{,}026\) \(4\) \(49.8\)
\(1.25\) \(37{,}485\) \(24{,}786\) \(4{,}098\) \(8\) \(223.7\)
\(h_z\) Background Active Trimmed CPUs Wall-time [s]
\(10\) \(1{,}377\) \(132\) \(66\) \(1\) \(9.3\)
\(5\) \(3{,}267\) \(630\) \(258\) \(2\) \(16.0\)
\(2.5\) \(10{,}575\) \(3{,}690\) \(1{,}026\) \(4\) \(57.2\)
\(1.25\) \(46{,}023\) \(24{,}786\) \(4{,}098\) \(8\) \(257.8\)

Download data (CSV)

Coreform IGA for Abaqus solve

\(h_z\) Elements Nodes DOFs Threads Wall-time [s]
\(10\) \(6{,}200\) \(4{,}026\) \(12{,}078\) \(1\) \(3.0\)
\(5\) \(7{,}442\) \(5{,}212\) \(15{,}636\) \(2\) \(1.0\)
\(2.5\) \(13{,}514\) \(10{,}830\) \(32{,}490\) \(4\) \(4.0\)
\(1.25\) \(51{,}154\) \(44{,}414\) \(133{,}242\) \(8\) \(10.0\)
\(h_z\) Elements Nodes DOFs Threads Wall-time [s]
\(10\) \(6{,}310\) \(4{,}323\) \(12{,}969\) \(1\) \(2.0\)
\(5\) \(7{,}610\) \(5{,}904\) \(17{,}712\) \(2\) \(4.0\)
\(2.5\) \(13{,}514\) \(12{,}498\) \(37{,}494\) \(4\) \(5.0\)
\(1.25\) \(53{,}138\) \(51{,}132\) \(153{,}396\) \(8\) \(29.0\)
\(h_z\) Elements Nodes DOFs Threads Wall-time [s]
\(10\) \(6{,}278\) \(4{,}629\) \(13{,}887\) \(1\) \(5.0\)
\(5\) \(8{,}038\) \(6{,}868\) \(20{,}604\) \(2\) \(10.0\)
\(2.5\) \(16{,}002\) \(15{,}734\) \(47{,}202\) \(4\) \(25.0\)
\(1.25\) \(69{,}778\) \(66{,}026\) \(198{,}078\) \(8\) \(150.0\)

Download data (CSV)

8.6 Nested L interface

Coreform IGA Mesh

\(h_z\) Background Active Trimmed CPUs Wall-time [s]
\(10\) \(325\) \(132\) \(66\) \(1\) \(5.4\)
\(5\) \(1{,}127\) \(672\) \(298\) \(2\) \(16.8\)
\(2.5\) \(5{,}203\) \(3{,}772\) \(1{,}106\) \(4\) \(49.9\)
\(1.25\) \(29{,}963\) \(25{,}272\) \(4{,}578\) \(8\) \(247.6\)
\(h_z\) Background Active Trimmed CPUs Wall-time [s]
\(10\) \(735\) \(132\) \(66\) \(1\) \(5.8\)
\(5\) \(2{,}025\) \(672\) \(298\) \(2\) \(17.3\)
\(2.5\) \(7{,}605\) \(3{,}772\) \(1{,}106\) \(4\) \(55.1\)
\(1.25\) \(37{,}485\) \(25{,}272\) \(4{,}578\) \(8\) \(259.4\)
\(h_z\) Background Active Trimmed CPUs Wall-time [s]
\(10\) \(1{,}377\) \(132\) \(66\) \(1\) \(8.8\)
\(5\) \(3{,}267\) \(672\) \(298\) \(2\) \(18.7\)
\(2.5\) \(10{,}575\) \(3{,}772\) \(1{,}106\) \(4\) \(62.8\)
\(1.25\) \(46{,}023\) \(25{,}272\) \(4{,}578\) \(8\) \(282.4\)

Download data (CSV)

Coreform IGA for Abaqus solve

\(h_z\) Elements Nodes DOFs Threads Wall-time [s]
\(10\) \(7{,}202\) \(4{,}539\) \(13{,}617\) \(1\) \(4.0\)
\(5\) \(9{,}148\) \(6{,}056\) \(18{,}168\) \(2\) \(3.0\)
\(2.5\) \(14{,}108\) \(11{,}170\) \(33{,}510\) \(4\) \(3.0\)
\(1.25\) \(55{,}176\) \(46{,}522\) \(139{,}566\) \(8\) \(11.0\)
\(h_z\) Elements Nodes DOFs Threads Wall-time [s]
\(10\) \(7{,}336\) \(4{,}848\) \(14{,}544\) \(1\) \(3.0\)
\(5\) \(9{,}372\) \(6{,}776\) \(20{,}328\) \(2\) \(3.0\)
\(2.5\) \(14{,}108\) \(12{,}840\) \(38{,}520\) \(4\) \(7.0\)
\(1.25\) \(57{,}200\) \(53{,}264\) \(159{,}792\) \(8\) \(34.0\)
\(h_z\) Elements Nodes DOFs Threads Wall-time [s]
\(10\) \(7{,}204\) \(5{,}104\) \(15{,}312\) \(1\) \(6.0\)
\(5\) \(9{,}484\) \(7{,}578\) \(22{,}734\) \(2\) \(11.0\)
\(2.5\) \(17{,}944\) \(16{,}764\) \(50{,}292\) \(4\) \(25.0\)
\(1.25\) \(75{,}792\) \(69{,}142\) \(207{,}426\) \(8\) \(137.0\)

Download data (CSV)

8.7 Tetris partition

Coreform IGA Mesh

\(h_z\) Background Active Trimmed CPUs Wall-time [s]
\(10\) \(325\) \(143\) \(66\) \(1\) \(5.9\)
\(5\) \(1{,}127\) \(777\) \(294\) \(2\) \(20.4\)
\(2.5\) \(5{,}203\) \(3{,}977\) \(1{,}102\) \(4\) \(59.1\)
\(1.25\) \(29{,}963\) \(26{,}325\) \(4{,}542\) \(8\) \(297.7\)
\(h_z\) Background Active Trimmed CPUs Wall-time [s]
\(10\) \(735\) \(143\) \(66\) \(1\) \(6.3\)
\(5\) \(2{,}025\) \(777\) \(294\) \(2\) \(21.6\)
\(2.5\) \(7{,}605\) \(3{,}977\) \(1{,}102\) \(4\) \(62.6\)
\(1.25\) \(37{,}485\) \(26{,}325\) \(4{,}542\) \(8\) \(347.4\)
\(h_z\) Background Active Trimmed CPUs Wall-time [s]
\(10\) \(1{,}377\) \(143\) \(66\) \(1\) \(9.6\)
\(5\) \(3{,}267\) \(777\) \(294\) \(2\) \(23.4\)
\(2.5\) \(10{,}575\) \(3{,}977\) \(1{,}102\) \(4\) \(68.8\)
\(1.25\) \(46{,}023\) \(26{,}325\) \(4{,}542\) \(8\) \(413.7\)

Download data (CSV)

Coreform IGA for Abaqus solve

\(h_z\) Elements Nodes DOFs Threads Wall-time [s]
\(10\) \(10{,}513\) \(6{,}895\) \(20{,}685\) \(1\) \(3.0\)
\(5\) \(13{,}721\) \(9{,}176\) \(27{,}528\) \(2\) \(2.0\)
\(2.5\) \(20{,}069\) \(15{,}330\) \(45{,}990\) \(4\) \(4.0\)
\(1.25\) \(72{,}117\) \(57{,}780\) \(173{,}340\) \(8\) \(17.0\)
\(h_z\) Elements Nodes DOFs Threads Wall-time [s]
\(10\) \(10{,}707\) \(7{,}315\) \(21{,}945\) \(1\) \(5.0\)
\(5\) \(14{,}113\) \(10{,}201\) \(30{,}603\) \(2\) \(4.0\)
\(2.5\) \(20{,}069\) \(17{,}399\) \(52{,}197\) \(4\) \(7.0\)
\(1.25\) \(75{,}087\) \(66{,}478\) \(199{,}434\) \(8\) \(37.0\)
\(h_z\) Elements Nodes DOFs Threads Wall-time [s]
\(10\) \(10{,}483\) \(7{,}638\) \(22{,}914\) \(1\) \(9.0\)
\(5\) \(14{,}285\) \(11{,}314\) \(33{,}942\) \(2\) \(17.0\)
\(2.5\) \(24{,}797\) \(22{,}294\) \(66{,}882\) \(4\) \(28.0\)
\(1.25\) \(101{,}505\) \(88{,}218\) \(264{,}654\) \(8\) \(118.0\)

Download data (CSV)

9 Discussion

Because all material definitions are identical, the exact continuum response is independent of the internal cell decomposition. Differences from the monolithic result therefore measure numerical sensitivity to retained interfaces, including closed inclusions, re-entrant partition corners, diagonal interfaces, and three-material junctions. The full refinement history is retained so that a passing finest-level result can be distinguished from a coarse-grid coincidence and so regressions at individual interface topologies remain visible.

References

[1]
J. M. Gere and S. P. Timoshenko, Mechanics of materials, 4th ed. Boston: PWS Publishing Company, 1997.

Appendix

9.1 Capabilities exercised

The table is generated from current passing simulation and study artifacts. Each row must satisfy the linked capability card’s evidence contract; declaring a capability in a test does not, by itself, create evidence.

Table 4: Capabilities exercised by the current verification artifacts.
Capability Evidence level Official verification test
Linear static analysis Exercised Test_abaqus_verification_multiplanar_material_interfaces_nested_l_h2p2
Pinned boundary condition Exercised Test_abaqus_verification_multiplanar_material_interfaces_nested_l_h2p2
Threaded Abaqus/Standard execution Exercised Test_abaqus_verification_multiplanar_material_interfaces_nested_l_h2p2
Parallel Coreform IGA mesh generation Exercised Test_abaqus_verification_multiplanar_material_interfaces_nested_l_h2p2
Surface traction loading Exercised Test_abaqus_verification_multiplanar_material_interfaces_nested_l_h2p2
Cell-based material section assignment Exercised Test_abaqus_verification_multiplanar_material_interfaces_nested_l_h2p2
Multi-cell material interfaces Numerically validated Test_abaqus_verification_study_multiplanar_material_interfaces_nested_l_p2
Linear elastic material behavior Exercised Test_abaqus_verification_multiplanar_material_interfaces_nested_l_h2p2
Linear C0 spline basis Exercised Test_abaqus_verification_multiplanar_material_interfaces_nested_l_h2p1
Quadratic C1 spline basis Exercised Test_abaqus_verification_multiplanar_material_interfaces_nested_l_h2p2
Cubic C2 spline basis Exercised Test_abaqus_verification_multiplanar_material_interfaces_nested_l_h2p3
Immersed rectilinear meshes Exercised Test_abaqus_verification_multiplanar_material_interfaces_nested_l_h2p2
Explicit field-output selection Exercised Test_abaqus_verification_multiplanar_material_interfaces_nested_l_h2p2
Stress field output (S) Exercised Test_abaqus_verification_multiplanar_material_interfaces_nested_l_h2p2
Displacement field output (U) Exercised Test_abaqus_verification_multiplanar_material_interfaces_nested_l_h2p2
Line probes Exercised Test_abaqus_verification_multiplanar_material_interfaces_nested_l_h2p2
Boolean merge with retained boundaries Exercised Test_abaqus_verification_multiplanar_material_interfaces_nested_l_h2p2
Dependent part instances Exercised Test_abaqus_verification_multiplanar_material_interfaces_nested_l_h2p2

9.2 Download artifacts

Download all verification artifacts (ZIP)

9.2.1 Geometry CAD files

No separate CAD file is required for this problem; the geometry is fully defined in the Abaqus/CAE journal files.

9.2.2 Abaqus/CAE journal files

84 generated Abaqus/CAE journals are available.

Show 84 individual journals
Official verification test Journal download
Test_abaqus_verification_multiplanar_material_interfaces_bottom_center_third_h0p1 bottom_center_third_h0p1–multiplanar_material_interfaces_bottom_center_third_h0_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_bottom_center_third_h0p2 bottom_center_third_h0p2–multiplanar_material_interfaces_bottom_center_third_h0_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_bottom_center_third_h0p3 bottom_center_third_h0p3–multiplanar_material_interfaces_bottom_center_third_h0_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_bottom_center_third_h1p1 bottom_center_third_h1p1–multiplanar_material_interfaces_bottom_center_third_h1_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_bottom_center_third_h1p2 bottom_center_third_h1p2–multiplanar_material_interfaces_bottom_center_third_h1_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_bottom_center_third_h1p3 bottom_center_third_h1p3–multiplanar_material_interfaces_bottom_center_third_h1_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_bottom_center_third_h2p1 bottom_center_third_h2p1–multiplanar_material_interfaces_bottom_center_third_h2_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_bottom_center_third_h2p2 bottom_center_third_h2p2–multiplanar_material_interfaces_bottom_center_third_h2_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_bottom_center_third_h2p3 bottom_center_third_h2p3–multiplanar_material_interfaces_bottom_center_third_h2_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_bottom_center_third_h3p1 bottom_center_third_h3p1–multiplanar_material_interfaces_bottom_center_third_h3_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_bottom_center_third_h3p2 bottom_center_third_h3p2–multiplanar_material_interfaces_bottom_center_third_h3_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_bottom_center_third_h3p3 bottom_center_third_h3p3–multiplanar_material_interfaces_bottom_center_third_h3_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_bottom_left_half_h0p1 bottom_left_half_h0p1–multiplanar_material_interfaces_bottom_left_half_h0_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_bottom_left_half_h0p2 bottom_left_half_h0p2–multiplanar_material_interfaces_bottom_left_half_h0_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_bottom_left_half_h0p3 bottom_left_half_h0p3–multiplanar_material_interfaces_bottom_left_half_h0_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_bottom_left_half_h1p1 bottom_left_half_h1p1–multiplanar_material_interfaces_bottom_left_half_h1_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_bottom_left_half_h1p2 bottom_left_half_h1p2–multiplanar_material_interfaces_bottom_left_half_h1_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_bottom_left_half_h1p3 bottom_left_half_h1p3–multiplanar_material_interfaces_bottom_left_half_h1_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_bottom_left_half_h2p1 bottom_left_half_h2p1–multiplanar_material_interfaces_bottom_left_half_h2_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_bottom_left_half_h2p2 bottom_left_half_h2p2–multiplanar_material_interfaces_bottom_left_half_h2_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_bottom_left_half_h2p3 bottom_left_half_h2p3–multiplanar_material_interfaces_bottom_left_half_h2_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_bottom_left_half_h3p1 bottom_left_half_h3p1–multiplanar_material_interfaces_bottom_left_half_h3_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_bottom_left_half_h3p2 bottom_left_half_h3p2–multiplanar_material_interfaces_bottom_left_half_h3_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_bottom_left_half_h3p3 bottom_left_half_h3p3–multiplanar_material_interfaces_bottom_left_half_h3_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_centered_third_h0p1 centered_third_h0p1–multiplanar_material_interfaces_centered_third_h0_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_centered_third_h0p2 centered_third_h0p2–multiplanar_material_interfaces_centered_third_h0_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_centered_third_h0p3 centered_third_h0p3–multiplanar_material_interfaces_centered_third_h0_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_centered_third_h1p1 centered_third_h1p1–multiplanar_material_interfaces_centered_third_h1_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_centered_third_h1p2 centered_third_h1p2–multiplanar_material_interfaces_centered_third_h1_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_centered_third_h1p3 centered_third_h1p3–multiplanar_material_interfaces_centered_third_h1_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_centered_third_h2p1 centered_third_h2p1–multiplanar_material_interfaces_centered_third_h2_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_centered_third_h2p2 centered_third_h2p2–multiplanar_material_interfaces_centered_third_h2_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_centered_third_h2p3 centered_third_h2p3–multiplanar_material_interfaces_centered_third_h2_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_centered_third_h3p1 centered_third_h3p1–multiplanar_material_interfaces_centered_third_h3_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_centered_third_h3p2 centered_third_h3p2–multiplanar_material_interfaces_centered_third_h3_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_centered_third_h3p3 centered_third_h3p3–multiplanar_material_interfaces_centered_third_h3_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_monolithic_h0p1 monolithic_h0p1–multiplanar_material_interfaces_monolithic_h0_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_monolithic_h0p2 monolithic_h0p2–multiplanar_material_interfaces_monolithic_h0_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_monolithic_h0p3 monolithic_h0p3–multiplanar_material_interfaces_monolithic_h0_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_monolithic_h1p1 monolithic_h1p1–multiplanar_material_interfaces_monolithic_h1_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_monolithic_h1p2 monolithic_h1p2–multiplanar_material_interfaces_monolithic_h1_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_monolithic_h1p3 monolithic_h1p3–multiplanar_material_interfaces_monolithic_h1_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_monolithic_h2p1 monolithic_h2p1–multiplanar_material_interfaces_monolithic_h2_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_monolithic_h2p2 monolithic_h2p2–multiplanar_material_interfaces_monolithic_h2_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_monolithic_h2p3 monolithic_h2p3–multiplanar_material_interfaces_monolithic_h2_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_monolithic_h3p1 monolithic_h3p1–multiplanar_material_interfaces_monolithic_h3_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_monolithic_h3p2 monolithic_h3p2–multiplanar_material_interfaces_monolithic_h3_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_monolithic_h3p3 monolithic_h3p3–multiplanar_material_interfaces_monolithic_h3_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_nested_l_h0p1 nested_l_h0p1–multiplanar_material_interfaces_nested_l_h0_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_nested_l_h0p2 nested_l_h0p2–multiplanar_material_interfaces_nested_l_h0_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_nested_l_h0p3 nested_l_h0p3–multiplanar_material_interfaces_nested_l_h0_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_nested_l_h1p1 nested_l_h1p1–multiplanar_material_interfaces_nested_l_h1_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_nested_l_h1p2 nested_l_h1p2–multiplanar_material_interfaces_nested_l_h1_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_nested_l_h1p3 nested_l_h1p3–multiplanar_material_interfaces_nested_l_h1_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_nested_l_h2p1 nested_l_h2p1–multiplanar_material_interfaces_nested_l_h2_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_nested_l_h2p2 nested_l_h2p2–multiplanar_material_interfaces_nested_l_h2_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_nested_l_h2p3 nested_l_h2p3–multiplanar_material_interfaces_nested_l_h2_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_nested_l_h3p1 nested_l_h3p1–multiplanar_material_interfaces_nested_l_h3_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_nested_l_h3p2 nested_l_h3p2–multiplanar_material_interfaces_nested_l_h3_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_nested_l_h3p3 nested_l_h3p3–multiplanar_material_interfaces_nested_l_h3_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_tetris_h0p1 tetris_h0p1–multiplanar_material_interfaces_tetris_h0_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_tetris_h0p2 tetris_h0p2–multiplanar_material_interfaces_tetris_h0_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_tetris_h0p3 tetris_h0p3–multiplanar_material_interfaces_tetris_h0_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_tetris_h1p1 tetris_h1p1–multiplanar_material_interfaces_tetris_h1_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_tetris_h1p2 tetris_h1p2–multiplanar_material_interfaces_tetris_h1_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_tetris_h1p3 tetris_h1p3–multiplanar_material_interfaces_tetris_h1_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_tetris_h2p1 tetris_h2p1–multiplanar_material_interfaces_tetris_h2_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_tetris_h2p2 tetris_h2p2–multiplanar_material_interfaces_tetris_h2_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_tetris_h2p3 tetris_h2p3–multiplanar_material_interfaces_tetris_h2_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_tetris_h3p1 tetris_h3p1–multiplanar_material_interfaces_tetris_h3_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_tetris_h3p2 tetris_h3p2–multiplanar_material_interfaces_tetris_h3_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_tetris_h3p3 tetris_h3p3–multiplanar_material_interfaces_tetris_h3_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_zig_zag_h0p1 zig_zag_h0p1–multiplanar_material_interfaces_zig_zag_h0_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_zig_zag_h0p2 zig_zag_h0p2–multiplanar_material_interfaces_zig_zag_h0_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_zig_zag_h0p3 zig_zag_h0p3–multiplanar_material_interfaces_zig_zag_h0_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_zig_zag_h1p1 zig_zag_h1p1–multiplanar_material_interfaces_zig_zag_h1_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_zig_zag_h1p2 zig_zag_h1p2–multiplanar_material_interfaces_zig_zag_h1_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_zig_zag_h1p3 zig_zag_h1p3–multiplanar_material_interfaces_zig_zag_h1_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_zig_zag_h2p1 zig_zag_h2p1–multiplanar_material_interfaces_zig_zag_h2_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_zig_zag_h2p2 zig_zag_h2p2–multiplanar_material_interfaces_zig_zag_h2_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_zig_zag_h2p3 zig_zag_h2p3–multiplanar_material_interfaces_zig_zag_h2_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_zig_zag_h3p1 zig_zag_h3p1–multiplanar_material_interfaces_zig_zag_h3_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_zig_zag_h3p2 zig_zag_h3p2–multiplanar_material_interfaces_zig_zag_h3_model.jnl
Test_abaqus_verification_multiplanar_material_interfaces_zig_zag_h3p3 zig_zag_h3p3–multiplanar_material_interfaces_zig_zag_h3_model.jnl

9.3 Supported Abaqus keywords

The deck below is reproduced from the monolithic \(h_0p_2\) test with comments stripped and instance-specific names redacted.

*Heading
*Preprint, echo=NO, model=NO, history=NO, contact=NO
*Include, input=<iga-mesh-inp>
*System
*Material, name=<material>
*Elastic
 1e+11, 0.3
*User Output Variables
1,
*Boundary
<node-set>, PINNED
*Step, name=<step>, nlgeom=NO
*Static
1., 1., 1e-05, 1.
*Restart, write, frequency=0
*Output, field
*Node Output
U,
*Element Output, position=AVERAGED AT NODES, directions=YES
S,
*Output, history, variable=PRESELECT
*End Step

9.4 Provenance

The records below identify the execution environment and verification basis for every simulation and study CTest reported on this page.

Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (0 positive)
Test date 27-Jul-2026 20:31:14
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (0 positive)
Test date 27-Jul-2026 20:36:20
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:41:37
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:55:11
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:31:29
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:36:25
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:42:13
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:57:00
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:31:42
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:36:36
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:43:04
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:58:57
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (0 positive)
Test date 27-Jul-2026 20:31:35
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (0 positive)
Test date 27-Jul-2026 20:36:25
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:42:39
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:56:28
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:31:37
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:36:43
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:43:10
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:57:18
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:31:50
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:37:19
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:43:33
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:59:52
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (0 positive)
Test date 27-Jul-2026 20:32:18
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (0 positive)
Test date 27-Jul-2026 20:37:14
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:43:05
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:57:33
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:32:32
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:37:22
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:43:19
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:58:16
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:32:40
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:37:57
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:44:20
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 21:01:42
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (0 positive)
Test date 27-Jul-2026 20:30:19
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (0 positive)
Test date 27-Jul-2026 20:35:42
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:41:05
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:53:03
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:31:02
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:35:44
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:41:14
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:53:48
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:31:14
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:36:07
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:41:37
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:55:23
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (0 positive)
Test date 27-Jul-2026 20:33:00
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (0 positive)
Test date 27-Jul-2026 20:38:09
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:43:41
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:58:52
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:33:09
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:38:14
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:45:22
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 21:00:37
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:33:44
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:38:58
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:45:53
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 21:03:44
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (0 positive)
Test date 27-Jul-2026 20:33:50
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (0 positive)
Test date 27-Jul-2026 20:38:51
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:45:22
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 21:00:59
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:34:00
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:38:59
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:45:41
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 21:02:56
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:34:16
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:39:40
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:46:31
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 21:06:21
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (0 positive)
Test date 27-Jul-2026 20:32:46
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (0 positive)
Test date 27-Jul-2026 20:37:45
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:43:37
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:57:27
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:32:54
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:37:59
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:43:44
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:58:27
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:33:03
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:38:06
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 20:44:51
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 27-Jul-2026 21:02:24
Operating system Ubuntu Linux 24.04.2 LTS (Noble Numbat)
Coreform IGA version 2026.7-dev+gvernon2_1785204663
Source revision db258ffe9358
Abaqus version 2026_06_24-12.44.52 DEVr428 214170
Parameter Value
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 28-Jul-2026 03:09:22 UTC
Operating system —
Coreform IGA version Not applicable — postprocessing-only CTest
Source revision db258ffe9358
Abaqus version Not applicable — postprocessing-only CTest
Parameter Value
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 28-Jul-2026 03:09:22 UTC
Operating system —
Coreform IGA version Not applicable — postprocessing-only CTest
Source revision db258ffe9358
Abaqus version Not applicable — postprocessing-only CTest
Parameter Value
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 28-Jul-2026 03:09:22 UTC
Operating system —
Coreform IGA version Not applicable — postprocessing-only CTest
Source revision db258ffe9358
Abaqus version Not applicable — postprocessing-only CTest
Parameter Value
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 28-Jul-2026 03:09:22 UTC
Operating system —
Coreform IGA version Not applicable — postprocessing-only CTest
Source revision db258ffe9358
Abaqus version Not applicable — postprocessing-only CTest
Parameter Value
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 28-Jul-2026 03:09:22 UTC
Operating system —
Coreform IGA version Not applicable — postprocessing-only CTest
Source revision db258ffe9358
Abaqus version Not applicable — postprocessing-only CTest
Parameter Value
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 28-Jul-2026 03:09:22 UTC
Operating system —
Coreform IGA version Not applicable — postprocessing-only CTest
Source revision db258ffe9358
Abaqus version Not applicable — postprocessing-only CTest
Parameter Value
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 28-Jul-2026 03:09:22 UTC
Operating system —
Coreform IGA version Not applicable — postprocessing-only CTest
Source revision db258ffe9358
Abaqus version Not applicable — postprocessing-only CTest
Parameter Value
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 28-Jul-2026 03:09:22 UTC
Operating system —
Coreform IGA version Not applicable — postprocessing-only CTest
Source revision db258ffe9358
Abaqus version Not applicable — postprocessing-only CTest
Parameter Value
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 28-Jul-2026 03:09:22 UTC
Operating system —
Coreform IGA version Not applicable — postprocessing-only CTest
Source revision db258ffe9358
Abaqus version Not applicable — postprocessing-only CTest
Parameter Value
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 28-Jul-2026 03:09:22 UTC
Operating system —
Coreform IGA version Not applicable — postprocessing-only CTest
Source revision db258ffe9358
Abaqus version Not applicable — postprocessing-only CTest
Parameter Value
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 28-Jul-2026 03:09:22 UTC
Operating system —
Coreform IGA version Not applicable — postprocessing-only CTest
Source revision db258ffe9358
Abaqus version Not applicable — postprocessing-only CTest
Parameter Value
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 28-Jul-2026 03:09:22 UTC
Operating system —
Coreform IGA version Not applicable — postprocessing-only CTest
Source revision db258ffe9358
Abaqus version Not applicable — postprocessing-only CTest
Parameter Value
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 28-Jul-2026 03:09:22 UTC
Operating system —
Coreform IGA version Not applicable — postprocessing-only CTest
Source revision db258ffe9358
Abaqus version Not applicable — postprocessing-only CTest
Parameter Value
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 28-Jul-2026 03:09:22 UTC
Operating system —
Coreform IGA version Not applicable — postprocessing-only CTest
Source revision db258ffe9358
Abaqus version Not applicable — postprocessing-only CTest
Parameter Value
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 28-Jul-2026 03:09:22 UTC
Operating system —
Coreform IGA version Not applicable — postprocessing-only CTest
Source revision db258ffe9358
Abaqus version Not applicable — postprocessing-only CTest
Parameter Value
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 28-Jul-2026 03:09:22 UTC
Operating system —
Coreform IGA version Not applicable — postprocessing-only CTest
Source revision db258ffe9358
Abaqus version Not applicable — postprocessing-only CTest
Parameter Value
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 28-Jul-2026 03:09:22 UTC
Operating system —
Coreform IGA version Not applicable — postprocessing-only CTest
Source revision db258ffe9358
Abaqus version Not applicable — postprocessing-only CTest
Parameter Value
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 28-Jul-2026 03:09:22 UTC
Operating system —
Coreform IGA version Not applicable — postprocessing-only CTest
Source revision db258ffe9358
Abaqus version Not applicable — postprocessing-only CTest