The Hyperelastic Material subnode adds the equations for hyperelasticity at large strains. Hyperelastic materials can be suitable for modeling rubber and other polymers, biological tissue, and also for applications in acoustoelasticity. The Hyperelastic Material is available in the Solid Mechanics, Layered Shell, and Membrane interfaces. This material model requires the Nonlinear Structural Materials Module.

When a hyperelastic material is included in your model, all studies are geometrically nonlinear. The Include geometric nonlinearity check box in the study settings is selected and cannot be cleared.

By adding the following subnodes to the Hyperelastic Material node you can incorporate many other effects:

Select a hyperelastic Material model from the list and then go to the applicable section for more information.

Hyperelastic materials can use a mixed formulation by adding the negative mean pressure as an extra dependent variable, or a weak constrain to enforce the incompressibility condition. Depending on the hyperelastic material model, select from the Compressibility list:

All hyperelastic material models have density as an input. The default Density ρ uses values From material. For User defined enter another value or expression.

If any material in the model has a temperature dependent mass density, and From material is selected, the Volume reference temperature list will appear in the Model Input section. As a default, the value of Tref is obtained from a Common model input. You can also select User defined to enter a value or expression for the reference temperature locally.

The default values for both Lamé parameter λ and Lamé parameter μ use values From material. If the Nearly incompressible material option is selected from the Compressibility list, enter the Bulk modulus κ instead of the Lamé parameter λ to define the volumetric strain energy density. If the Incompressible material option is selected from the Compressibility list, enter the Lamé parameter μ only.

The default values for both Lamé parameter λ and Lamé parameter μ use values From material.

For Mooney-Rivlin, two-parameters the Model parameters C10 and C01 both use values From material. If the Nearly incompressible material option is selected from the Compressibility list, enter the Bulk modulus κ.

For Mooney-Rivlin, five-parameters the Model parameters C10, C01, C20, C02, and C11 all use values From material. If the Nearly incompressible material option is selected from the Compressibility list, enter the Bulk modulus κ.

For Mooney-Rivlin, nine-parameters the Model parameters C10, C01, C20, C02, C11, C30, C03, C21, and C12 all use values From material. If the Nearly incompressible material option is selected from the Compressibility list, enter the Bulk modulus κ.

For Yeoh the Model parameters c1, c2, and c3 all use values From material. If the Nearly incompressible material option is selected from the Compressibility list, enter the Bulk modulus κ.

In the table for the Ogden parameters, enter values or expressions in each column: Shear modulus (Pa), and Alpha parameter.

If the Nearly incompressible material option is selected from the Compressibility list, enter the Bulk modulus κ.

For Storakers, in the table for the Storakers parameters, enter values or expressions in each column: Shear modulus (Pa), Alpha parameter, and Beta parameter.

For Varga the Model parameters c1, c2, and c3 all use values From material. If the Nearly incompressible material option is selected from the Compressibility list, enter the Bulk modulus κ.

For Arruda-Boyce the default values for the Macroscopic shear modulus μ0 and the Number of segments N use values From material. If the Nearly incompressible material option is selected from the Compressibility list, enter the Bulk modulus κ.

For Gent the default values for the Macroscopic shear modulus μ and the model parameter jm use values From material. If the Nearly incompressible material option is selected from the Compressibility list, enter the Bulk modulus κ.

For Blatz-Ko the Shear modulus μ and the Model parameters β and φ all use values From material.

For Gao the Model parameters a and n use values From material.

For Murnaghan the Murnaghan third-order elastic moduli constants l, m, and n and the Lamé parameters λ and μ use values From material.

For Delfino the Model parameters a and b use values From material. If the Nearly incompressible material option is selected from the Compressibility list, enter the Bulk modulus κ.

For Fung the Coefficient matrix A and Fung parameter c use values From material.

The Coefficient matrix A provides the anisotropic material properties that vary in the directions given by the Coordinate system list. The Material data ordering can be specified in either Standard or Voigt notation. When User defined is selected, a 6-by-6 symmetric matrix is displayed.

If the Nearly incompressible material option is selected from the Compressibility list, enter the Bulk modulus κ.

For Extended tube the Model parameters Gc, Ge, α, and β use values From material. If the Nearly incompressible material option is selected from the Compressibility list, enter the Bulk modulus κ.

If Compressible material is selected from the Compressibility list, enter an expression for the Elastic strain energy density Ws.

You can also use a mixed formulation by adding the negative mean pressure as an extra dependent variable. In this case, select from the Compressibility list either Nearly incompressible material or Incompressible material.

If Nearly incompressible material is selected, enter the Isochoric strain energy density Wsiso and the Volumetric strain energy density Wvol.

If Incompressible material is selected, enter the Isochoric strain energy density Wsiso only. An extra weak constrain is added to enforce the incompressibility condition Jel = 1.

To display this section, click the Show More Options button () and select Advanced Physics Options in the Show More Options dialog box.

Select the Calculate dissipated energy check box to compute the energy dissipated by Plasticity.

Physics tab with Solid Mechanics selected:

Physics tab with Shell, Layered Shell or Membrane selected: