Material Law Models Reference

Model Controls (Child Nodes)

Material Laws

Allows you to create the material laws that define the stress-strain relationship in solid materials. When you right-click the Material Laws node and select New, Simcenter STAR-CCM+ creates a material law with the default name [Material Law 1].

[Material Law 1] > Models

Allows you to select the physics models that define the material law. The available models are:

Material Stiffness Models	Material Strain Measures	Material Models
Linear Elasticity Defines a linear elastic stress-strain relationship for the material (Eqn. (4503)). This model cannot be used if you have selected both the Nearly Incompressible Material and Nonlinear Geometry models in the solid physics continuum. In this case, select the Hyperelasticity model.	Linear Strain (Small Strain) Defines the material strain using Eqn. (4444). Green-Lagrange (Small Strain) Defines the material strain using Eqn. (4445). Only available when the Nonlinear Geometry model is activated.	Isotropic Linear Elastic Defines the material as isotropic (see Eqn. (4511)). The mechanical properties of isotropic materials are the same in all directions. See Material Properties. Orthotropic Linear Elastic Defines the material as orthotropic (see Eqn. (4505)). The mechanical properties of orthotropic materials are specified independently along three mutually-orthogonal directions. Anisotropic Linear Elastic Defines the material as anisotropic (see Eqn. (4504)). The mechanical properties of anisotropic materials depend on direction.
Hyperelasticity Defines a nonlinear hyperelastic stress-strain relationship in terms of the strain energy potential (Eqn. (4529)).	Green-Lagrange (Large Strain) Defines the material strain using Eqn. (4446).	Neo-Hookean Uses a Neo-Hookean strain energy potential (see Eqn. (4533)). This model is the simplest hyperelastic model and is suitable for strains <20%. Use this model when the available material test data are not sufficient for a Mooney-Rivlin or Ogden approach. Mooney-Rivlin Uses either a 2-term, 5-term, or 9-term Mooney-Rivlin potential (see Eqn. (4535)). This model requires accurate material test data. Ogden Uses an Ogden strain energy potential (see Eqn. (4539)) up to the 6th order. This model is suitable for very large strains and requires accurate material test data.

Optional Models	Material Models
Plasticity Accounts for the plastic deformation that occurs for stresses above the yield stress. Available when you activate the Linear Elasticity model.	J2 Plasticity Models plastic yield using the von Mises potential model. For more information, see Elastoplastic Materials.
Thermal Expansion Accounts for the thermal strain due to temperature loads (see Eqn. (4452).	Isotropic Thermal Expansion Use this option for materials in which the coefficient of thermal expansion is the same in all directions. See Material Properties. For hyperelastic materials, this is the only available option. Orthotropic Thermal Expansion Use this option for materials in which the coefficient of thermal expansion is different along three mutually-orthogonal directions. Anisotropic Thermal Expansion Use this option when the coefficient of thermal expansion depends on direction generally.

Material Properties

Common Properties

The following material properties are available for all solid materials, regardless of the material law models in use:

Material Law

The Type property allows you to select a material law from the material laws under the [physics continuum] > Models > Material Law Models > Material Laws node. See Model Controls.

Anisotropic material laws also require you to specify the material law orientation for each region associated with the anisotropic law. For more information, see Material Law Orientation.

Density

Defines the mass per unit volume in the undeformed state (${\rho }_0$ in Eqn. (4456)).

Mechanical Properties

When you set the Material Law property, Simcenter STAR-CCM+ adds mechanical properties based on the stiffness models that define the material law.

表 1. Linear Elasticity

Material Law Models	Material Properties
Isotropic Linear Elastic	Poisson's Ratio Defines Poisson's ratio ( $\nu$ in Eqn. (4513)). Young's Modulus Defines the Young's modulus ( $E$ in Eqn. (4513)).
Orthotropic Linear Elastic	Poisson Ratios The nodes nu12, nu23, and nu13 define the Poisson coefficients of the orthotropic material ( ${\nu }_{12}$ , ${\nu }_{23}$ , ${\nu }_{13}$ in Eqn. (4506) and Eqn. (4507)). Young's Moduli The nodes E1, E2, and E3 define the Young modulus coefficients of the orthotropic material ( $E_1$ , $E_2$ , $E_3$ in Eqn. (4506) and Eqn. (4507)). Shear Moduli The nodes G1, G2, and G3 define the shear modulus coefficients of the orthotropic material ( $G_{12}$ , $G_{23}$ , and $G_{13}$ in Eqn. (4505)).
Anisotropic Linear Elastic	Anisotropic Stiffness Coefficients These define the independent components $c_{ij}$ of the material tangent $D$ (see Eqn. (4504)).

表 2. Plasticity

Material Law Models

Material Properties

J2 Plasticity

Plastic Yield Stress The Method property allows you to specify the hardening model that describes the plastic portion of the stress-strain curve. The available options are: Linear Isotropic Hardening—the yield stress is a linear function of the plastic strain (see Eqn. (4523)). Set the coefficients sigmaY and H0 (${\sigma }_{Y_0}$ and $H_0$ in Eqn. (4523)) under the Plastic Yield Stress > Linear Isotropic Hardening node. Saturation Hardening—the yield stress is a nonlinear function of the plastic strain (see Eqn. (4524)). Set the coefficients sigmaY_0, sigmaY_inf, m, H_bar, and delta (${\sigma }_{Y_0}$, ${\sigma }_{\infty }$, $m$, $\overline{H}$, and $\delta$ in Eqn. (4524)) under the Plastic Yield Stress > Saturation Hardening node. User-Defined—the stress-strain curve is defined by the yield stress and its derivative with respect to the plastic strain (see Eqn. (4525)). Set sigma_Y and d(sigma_Y) under the Plastic Yield Stress > User-Defined node.

表 3. Hyperelasticity

Material Law Models	Material Properties
Mooney-Rivlin	Bulk Modulus Defines the initial bulk modulus $k_b$ in Eqn. (4535). Mooney-Rivlin Material Parameters Define the coefficients $c_{ij}$ of the Mooney-Rivlin potential (see Eqn. (4535)). The number of coefficients depends on the number of terms of the polynomial that approximates the potential. See Eqn. (4536) (2-term model), Eqn. (4537) (5-term model), and Eqn. (4538) (9-term model).
Ogden	Ogden Material Parameters [i] Allows you to specify the parameters that define each term of the Ogden potential (Eqn. (4539)). That is: the i-th shear modulus mu[i] ( ${\mu }_i$ in Eqn. (4540)) the dimensionless coefficient alpha[i] ( ${\alpha }_i$ in Eqn. (4540)) the i-th bulk modulus K[i] ( $k_i$ in Eqn. (4539))
Neo-Hookean	Bulk Modulus Defines the initial bulk modulus $k_b$ in Eqn. (4533). The Bulk Modulus must be positive (> 0). Neo-Hookean Material Parameters Specifies the coefficient $c_{10}$ in the Neo-Hookean potential (see Eqn. (4534)). The Neo-Hookean Material Parameters must be positive (> 0). Poisson's Ratio Defines the initial Poisson's ratio, $\nu$ (see Eqn. (4513) andEqn. (4534)). The Poisson's Ratio must be between -1 and 0.5. Young's Modulus Defines the initial Young's modulus, $E$ (see Eqn. (4513) andEqn. (4534)). The Young's Modulus must be positive (> 0).

Thermal Properties

When the material law contains thermal expansion models, Simcenter STAR-CCM+ adds thermal properties that define the behavior of the solid material in response to temperature changes.

Material Law Models	Material Properties
All thermal expansion models	Zero Thermal Strain Reference Temperature Defines the reference temperature at which the thermal strain is zero ($T_{ref}$ in Eqn. (4452)).
Isotropic Thermal Expansion	Thermal Expansion Coefficient Defines $\alpha$ in Eqn. (4452).
Orthotropic Thermal Expansion	Orthotropic Thermal Expansion Coefficients Defines the components ${\alpha }_{11}$, ${\alpha }_{22}$, ${\alpha }_{33}$ in Eqn. (4510).
Anisotropic Thermal Expansion	Anisotropic Thermal Expansion Coefficients Defines the components ${\alpha }_{ij}$ in Eqn. (4504).

Material Law Orientation

When selecting non-isotropic material law models, you define most material properties as second-order tensors (see Tensor Quantities). You define the tensor components in a local coordinate system, which is specified at the region level using the Regions > [region] > Physics Values > Material Law Orientation node. For more information, see Orientation Manager and Local Orientations.

Field Functions

Common Field Functions:

Material Basis Vector 1, Material Basis Vector 2, Material Basis Vector 3

Vector field functions that represent the basis vectors of the coordinate system with respect to which the material properties are defined. See Material Law Orientation.

[Material Property]

Each material property is stored in a field function with the same name.

For orthotropic and anisotropic material properties, which are defined by several coefficients, Simcenter STAR-CCM+ creates a field function for each coefficient. In field function selection dialogs, Simcenter STAR-CCM+ organizes the coefficient field functions into groups. For example, the anisotropic thermal expansion coefficient field functions are grouped under Anisotropic Thermal Expansion.

Plasticity Field Functions:

The following field functions are available when the Plasticity model is active:

Equivalent Plastic Strain

Represents a scalar measure for the plastic strain that is accumulated as the plastic deformation increases (see Eqn. (4518)).

Effective Plastic Strain

Represents a scalar measure for the plastic strain (see Eqn. (4519)).

Plastic Strain Energy Density

Represents the energy that is dissipated due to plastic deformation (see Eqn. (4517)).

Plastic Strain Tensor

${\epsilon }_{pl}$ in Eqn. (4515).

Thermal Expansion Field Functions:

The following field functions are available when one of the Thermal Expansion models is active:

Thermal Strain Tensor

Represents the thermal strain tensor in Eqn. (4452).

注	When you map temperature data from a different mesh representation of the solid, for example, a FV solid region in a Simcenter STAR-CCM+ CHT analysis, the mapping operation generates a field function with the default name, MappedVertexTemperature. See Applying Thermal Loads.