9 materials#(struct:traverse-element #<procedure:...lib/render-cond.rkt:38:12>)

9 materials (release)

The materials object holds all materials objects, identified by user defined identifiers.

Name	Type	Description	Default
label	STRING	User provided identifier for this material definition.
mass_density [optional] (beta)	DOUBLE	Defines the mass density of the material.
elastic (release) \| neohookean (beta) \| mooney_rivlin (beta) \| isotropic_heat_conduction (alpha) \| neohookean_isotropic_plasticity (beta)	SUB OBJECT \| SUB OBJECT \| SUB OBJECT \| SUB OBJECT \| SUB OBJECT	Any of the given options can be defined

Example Usage:
materials: [ { label: "cast_iron", mass_density: 0.000001, elastic: { youngs_modulus: 24000000, poissons_ratio: 0.29, } } ]

9.1 elastic (release)

Defines the parameters for a small strain isotropic linear elastic material. Two of the five available material moduli must be specified.

Name	Type	Description	Default
youngs_modulus \| temperature_dependent_youngs_modulus (alpha) \| poissons_ratio \| lame_first \| shear_modulus \| bulk_modulus	DOUBLE \| STRING \| DOUBLE \| DOUBLE \| DOUBLE \| DOUBLE	2 of the given options must be defined
pressure_stabilization (beta) [optional]	SUB OBJECT	See linked documentation
thermal_expansion (alpha) [optional]	SUB OBJECT	See linked documentation

Example Usage:
elastic: { youngs_modulus: 24000000, poissons_ratio: 0.29, }

9.1.1 youngs_modulus | temperature_dependent_youngs_modulus | poissons_ratio | lame_first | shear_modulus | bulk_modulus

N of the given options can be defined

Name	Type	Description	Default
youngs_modulus	DOUBLE	Defines the Young's Modulus of the material as a constant value. Note: Young's modulus may alternatively be supplied as a temperature-dependent function using the keyword temperature_dependent_youngs_modulus.
temperature_dependent_youngs_modulus (alpha)	STRING	Identifier of a piecewise-linear function determining the material's Young's modulus as a function of temperature. This may only be paired with a Poisson's ratio for the second elastic parameter, and the material must also have thermal expansion properties specified. If no temperature is provided, it will be evaluated at the reference temperature from the thermal expansion properties. Note: Young's modulus may alternatively be supplied as a constant value using the keyword youngs_modulus.
poissons_ratio	DOUBLE	Defines Poisson's Ratio for the material.
lame_first	DOUBLE	Defines Lamé's first parameter for the material.
shear_modulus	DOUBLE	Defines the shear modulus for the material. Also known as Lamé's second parameter.
bulk_modulus	DOUBLE	Defines the bulk modulus for the material.

9.1.2 pressure_stabilization (beta)

Options for stabilization to prevent pressure oscillation and/or locking in the nearly-incompressible limit. Stabilization is included in the analysis if and only if this keyword is present. Recommended to be used for elasticity with Poisson’s ratios greater than about 0.49 and in any problems with large plastic deformations, but is only currently supported for statics and implicit dynamics.

Name	Type	Description	Default
stabilization_parameter (beta)	DOUBLE	Dimensionless scaling factor applied to pressure stabilization. The value 0.1 works well for most problems. Larger values will lead to smoother pressures, but may reduce accuracy if taken to an extreme.
thermal_pressure_approximation [optional] (alpha)	true\|false	Whether to approximate thermal expansion with a pressure instead of a pre-strain, under an assumption of small volume changes. Equivalent to pre-strain for linearized kinemaics, optional for finite-strain statics and implicit dynamics, and required for explicit dynamics.

9.1.3 thermal_expansion (alpha)

Thermal expansion parameter definitions

Name	Type	Description	Default
thermal_expansion_coefficient (alpha) \| thermal_expansion_coefficient_function (alpha)	DOUBLE \| STRING
reference_temperature (alpha)	DOUBLE	The reference temperature at which thermal strains are considered to be zero and about which the secant coefficient of thermal expansion is calibrated.
use_engineering_strain [optional] (alpha)	true\|false	If this is true, then the secant thermal expansion coefficient times the temperature change is interpreted as an engineering strain. Otherwise it is interpreted as logarithmic strain. The latter interpretation is more common when integrating secant coefficients from tabulated tangent coefficients. This option has no effect in small-deformation analysis.

9.1.3.1 thermal_expansion_coefficient | thermal_expansion_coefficient_function

Name	Type	Description	Default
thermal_expansion_coefficient (alpha)	DOUBLE	Secant coefficient of thermal expansion, determining thermal expansion strain due to a temperature change.
thermal_expansion_coefficient_function (alpha)	STRING	Identifier of a piecewise-linear function determining the secant coefficient of thermal expansion as a function of temperature.

9.2 neohookean (beta)

Defines the parameters for a two parameter isotropic hyperelastic neo-Hookean material. The potential energy per unit reference volume is given by the functional $\frac{1}{2}\kappa\left(\frac{1}{2}(J^2 - 1) - \ln J\right) + \frac{1}{2}\mu\left(\bar{I_1}-3\right)$ , where $\kappa$ is the bulk modulus, $\mu$ is the shear modulus, $\bar{I_1} = J^{-2/3}I_1$ , $\bar{I_2} = J^{-4/3}I_2$ , and $J = \sqrt{I_3}$ . $I_1$ , $I_2$ , and $I_3$ are the three invariants of the right (or left) Cauchy–Green tensor. This model converges to the linear elastic model in the small deformation limit, so the bulk and shear modulus can be defined from other pairs of linear elastic parameters for convenience, using standard linear-elastic conversion formulas. This model should be used in place of linear elasticity whenever there are large rotational motions, even if the strains remain small.

Name	Type	Description	Default
youngs_modulus (beta) \| poissons_ratio (beta) \| lame_first (beta) \| shear_modulus (beta) \| bulk_modulus (beta)	DOUBLE \| DOUBLE \| DOUBLE \| DOUBLE \| DOUBLE	2 of the given options must be defined
pressure_stabilization (beta) [optional]	SUB OBJECT	See linked documentation
thermal_expansion (alpha) [optional]	SUB OBJECT	See linked documentation
viscous_overstresses (alpha) [optional]	LIST

9.2.1 youngs_modulus | poissons_ratio | lame_first | shear_modulus | bulk_modulus

N of the given options can be defined

Name	Type	Description	Default
youngs_modulus (beta)	DOUBLE	The equivalent Young's Modulus of the material in the small-strain limit.
poissons_ratio (beta)	DOUBLE	The equivalent Poisson's Ratio for the material in the small-strain limit.
lame_first (beta)	DOUBLE	The equivalent Lamé's first parameter for the material in the small-strain limit.
shear_modulus (beta)	DOUBLE	The shear modulus for the material. Also known as Lamé's second parameter in the small-strain limit.
bulk_modulus (beta)	DOUBLE	The bulk modulus for the material. Incompressibility can be approximated by choosing a large value for this parameter (relative to the shear modulus). However, this may lead to locking phenomena when using low-order splines or coarse meshes with no pressure stabilization.

9.2.2 pressure_stabilization (beta)

Options for stabilization to prevent pressure oscillation and/or locking in the nearly-incompressible limit. Stabilization is included in the analysis if and only if this keyword is present. Recommended to be used for elasticity with Poisson’s ratios greater than about 0.49 and in any problems with large plastic deformations, but is only currently supported for statics and implicit dynamics.

Name	Type	Description	Default
stabilization_parameter (beta)	DOUBLE	Dimensionless scaling factor applied to pressure stabilization. The value 0.1 works well for most problems. Larger values will lead to smoother pressures, but may reduce accuracy if taken to an extreme.
thermal_pressure_approximation [optional] (alpha)	true\|false	Whether to approximate thermal expansion with a pressure instead of a pre-strain, under an assumption of small volume changes. Equivalent to pre-strain for linearized kinemaics, optional for finite-strain statics and implicit dynamics, and required for explicit dynamics.

9.2.3 thermal_expansion (alpha)

Thermal expansion parameter definitions

Name	Type	Description	Default
thermal_expansion_coefficient (alpha) \| thermal_expansion_coefficient_function (alpha)	DOUBLE \| STRING
reference_temperature (alpha)	DOUBLE	The reference temperature at which thermal strains are considered to be zero and about which the secant coefficient of thermal expansion is calibrated.
use_engineering_strain [optional] (alpha)	true\|false	If this is true, then the secant thermal expansion coefficient times the temperature change is interpreted as an engineering strain. Otherwise it is interpreted as logarithmic strain. The latter interpretation is more common when integrating secant coefficients from tabulated tangent coefficients. This option has no effect in small-deformation analysis.

9.2.3.1 thermal_expansion_coefficient | thermal_expansion_coefficient_function

Name	Type	Description	Default
thermal_expansion_coefficient (alpha)	DOUBLE	Secant coefficient of thermal expansion, determining thermal expansion strain due to a temperature change.
thermal_expansion_coefficient_function (alpha)	STRING	Identifier of a piecewise-linear function determining the secant coefficient of thermal expansion as a function of temperature.

9.2.4 viscous_overstresses (alpha)

Name		Type		Description		Default
neohookean_viscosity (alpha)		SUB OBJECT

9.2.4.1 neohookean_viscosity (alpha)

Viscous term in a Prony series, whose stress response is based on a neo-Hookean potential.

Name	Type	Description	Default
shear_modulus (alpha)	DOUBLE	The shear modulus for this term of the Prony series.
timescale (alpha)	DOUBLE	The relaxation timescale for this term of the Prony series.

9.3 mooney_rivlin (beta)

Defines the parameters for a three parameter isotropic hyperelastic Mooney–Rivlin material. If we denote, $\mu_1$ = , $\mu_2$ = , and $\kappa$ = , the strain-energy function of the Mooney–Rivlin model is $\mu_1(\bar{I_1}-3)/2+\mu_2(\bar{I_2}-3)/2+\kappa(J-1)^2$ . $\bar{I_1} = J^{-2/3}I_1$ , $\bar{I_2} = J^{-4/3}I_2$ and $J = \sqrt{I_3}$ . $I_1$ , $I_2$ and $I_3$ are the three invariants of the right (or left) Cauchy–Green tensor. This model converges to the linear elastic model in the small deformation limit for which the shear modulus is $\mu_1+\mu_2$ and the bulk modulus is $\kappa$ .

Name	Type	Description	Default
shear_modulus_1 (beta)	DOUBLE	Defines the shear modulus for the material.
shear_modulus_2 (beta)	DOUBLE	Defines the shear modulus for the material.
bulk_modulus (beta)	DOUBLE	Defines the bulk modulus for the material.
pressure_stabilization (beta) [optional]	SUB OBJECT	See linked documentation
thermal_expansion (alpha) [optional]	SUB OBJECT	See linked documentation

9.3.1 pressure_stabilization (beta)

Options for stabilization to prevent pressure oscillation and/or locking in the nearly-incompressible limit. Stabilization is included in the analysis if and only if this keyword is present. Recommended to be used for elasticity with Poisson’s ratios greater than about 0.49 and in any problems with large plastic deformations, but is only currently supported for statics and implicit dynamics.

Name	Type	Description	Default
stabilization_parameter (beta)	DOUBLE	Dimensionless scaling factor applied to pressure stabilization. The value 0.1 works well for most problems. Larger values will lead to smoother pressures, but may reduce accuracy if taken to an extreme.
thermal_pressure_approximation [optional] (alpha)	true\|false	Whether to approximate thermal expansion with a pressure instead of a pre-strain, under an assumption of small volume changes. Equivalent to pre-strain for linearized kinemaics, optional for finite-strain statics and implicit dynamics, and required for explicit dynamics.

9.3.2 thermal_expansion (alpha)

Thermal expansion parameter definitions

Name	Type	Description	Default
thermal_expansion_coefficient (alpha) \| thermal_expansion_coefficient_function (alpha)	DOUBLE \| STRING
reference_temperature (alpha)	DOUBLE	The reference temperature at which thermal strains are considered to be zero and about which the secant coefficient of thermal expansion is calibrated.
use_engineering_strain [optional] (alpha)	true\|false	If this is true, then the secant thermal expansion coefficient times the temperature change is interpreted as an engineering strain. Otherwise it is interpreted as logarithmic strain. The latter interpretation is more common when integrating secant coefficients from tabulated tangent coefficients. This option has no effect in small-deformation analysis.

9.3.2.1 thermal_expansion_coefficient | thermal_expansion_coefficient_function

Name	Type	Description	Default
thermal_expansion_coefficient (alpha)	DOUBLE	Secant coefficient of thermal expansion, determining thermal expansion strain due to a temperature change.
thermal_expansion_coefficient_function (alpha)	STRING	Identifier of a piecewise-linear function determining the secant coefficient of thermal expansion as a function of temperature.

9.4 isotropic_heat_conduction (alpha)

Isotropic heat conduction.

Name		Type		Description		Default
thermal_conductivity (alpha)		DOUBLE		Defines the thermal conductivity of the material.

9.5 neohookean_isotropic_plasticity (beta)

Defines the parameters for an isotropic, nonlinear, rate-independent model based on J2 flow theory.

Name	Type	Description	Default
neohookean (beta)	SUB OBJECT	See linked documentation
isotropic_plasticity (beta)	SUB OBJECT	See linked documentation
pressure_stabilization (beta) [optional]	SUB OBJECT	See linked documentation
material_failure (alpha) [optional]	SUB OBJECT	See linked documentation
thermal_expansion (alpha) [optional]	SUB OBJECT	See linked documentation

9.5.1 neohookean (beta)

Two of the five available material moduli must be specified.

Name		Type		Description		Default
youngs_modulus (beta) \| poissons_ratio (beta) \| lame_first (beta) \| shear_modulus (beta) \| bulk_modulus (beta)		DOUBLE \| DOUBLE \| DOUBLE \| DOUBLE \| DOUBLE		2 of the given options must be defined

9.5.1.1 youngs_modulus | poissons_ratio | lame_first | shear_modulus | bulk_modulus

N of the given options can be defined

Name	Type	Description	Default
youngs_modulus (beta)	DOUBLE	Defines the Young's Modulus of the material.
poissons_ratio (beta)	DOUBLE	Defines Poisson's Ratio for the material.
lame_first (beta)	DOUBLE	Defines Lamé's first parameter for the material.
shear_modulus (beta)	DOUBLE	Defines the shear modulus for the material. Also known as Lamé's second parameter.
bulk_modulus (beta)	DOUBLE	Defines the bulk modulus for the material.

9.5.2 isotropic_plasticity (beta)

Parameters for isotropic-plasticity.

Name	Type	Description	Default
yield_stress (beta)	DOUBLE	Defines the yield stress of the material prior to any plastic strain and hardening. See documentation of hardening_function for additional details on hardening.
hardening_function (beta)	STRING	Specifies the user defined identifier of the function to use as the hardening function for the material. This hardening function is added to the parameter yield_stress to obtain the yield stress as a function of equivalent plastic strain. The function should be zero at zero plastic strain for the given yield_stress to correspond to the material's initial yield point. For perfect plasticity, the hardening function should be identically equal to zero. The hardening function must be a scalar-valued piecewise-linear function with non-negative slope, and it must be concave-down, i.e., the slope must decrease or stay the same as plastic strain increases.

9.5.3 pressure_stabilization (beta)

Options for stabilization to prevent pressure oscillation and/or locking in the nearly-incompressible limit. Stabilization is included in the analysis if and only if this keyword is present. Recommended to be used for elasticity with Poisson’s ratios greater than about 0.49 and in any problems with large plastic deformations, but is only currently supported for statics and implicit dynamics.

Name	Type	Description	Default
stabilization_parameter (beta)	DOUBLE	Dimensionless scaling factor applied to pressure stabilization. The value 0.1 works well for most problems. Larger values will lead to smoother pressures, but may reduce accuracy if taken to an extreme.
thermal_pressure_approximation [optional] (alpha)	true\|false	Whether to approximate thermal expansion with a pressure instead of a pre-strain, under an assumption of small volume changes. Equivalent to pre-strain for linearized kinemaics, optional for finite-strain statics and implicit dynamics, and required for explicit dynamics.

9.5.4 material_failure (alpha)

Add material failure.

Name		Type		Description		Default
uniform_triaxiality_cutoff (alpha)		SUB OBJECT		See linked documentation

9.5.4.1 uniform_triaxiality_cutoff (alpha)

Name	Type	Description	Default
failure_strain (alpha)	DOUBLE	The plastic strain at which the material failure occurs.
cutoff_triaxiality (alpha)	DOUBLE	The failure indicator is updated only when the triaxiality ratio is greater than this value.
minimum_stress_degradation (alpha)	DOUBLE	The minimum stress degradation value. If the degradation falls Below this value then the stress is set to 0.0.

9.5.5 thermal_expansion (alpha)

Thermal expansion parameter definitions

Name	Type	Description	Default
thermal_expansion_coefficient (alpha) \| thermal_expansion_coefficient_function (alpha)	DOUBLE \| STRING
reference_temperature (alpha)	DOUBLE	The reference temperature at which thermal strains are considered to be zero and about which the secant coefficient of thermal expansion is calibrated.
use_engineering_strain [optional] (alpha)	true\|false	If this is true, then the secant thermal expansion coefficient times the temperature change is interpreted as an engineering strain. Otherwise it is interpreted as logarithmic strain. The latter interpretation is more common when integrating secant coefficients from tabulated tangent coefficients. This option has no effect in small-deformation analysis.

9.5.5.1 thermal_expansion_coefficient | thermal_expansion_coefficient_function

Name	Type	Description	Default
thermal_expansion_coefficient (alpha)	DOUBLE	Secant coefficient of thermal expansion, determining thermal expansion strain due to a temperature change.
thermal_expansion_coefficient_function (alpha)	STRING	Identifier of a piecewise-linear function determining the secant coefficient of thermal expansion as a function of temperature.

contents ← prev up next →

1	An Overview of Coreform IGA
2	General Terminology
3	iga
4	procedures (release)
5	flex_ models (release)
6	solid_ mechanics_ definitions (release)
7	heat_ transfer_ definitions (alpha)
8	structural_ modal_ analysis_ definitions (alpha)
9	materials (release)
10	time_ steppers (release)
11	nonlinear_ equation_ solvers (beta)
12	linear_ equation_ solvers (release)
13	functions (release)
14	intervals (release)

9.1	elastic (release)
9.2	neohookean (beta)
9.3	mooney_ rivlin (beta)
9.4	isotropic_ heat_ conduction (alpha)
9.5	neohookean_ isotropic_ plasticity (beta)