Creating an anisotropic hyperelastic material model

From the menu bar in the Edit Material dialog box, select MechanicalElasticityHyperelastic.

(For information on displaying the Edit Material dialog box, see Creating or editing a material.)

Choose Anisotropic as the material type.

Click the arrow to the right of the Strain energy potential field, and select the strain energy potential of your choice.

Fung-Anisotropic

For the fully anisotropic strain-based Fung model, you must specify 21 independent components $b_{ijkl}$. For more information, see Generalized Fung form.

Fung-Orthotropic

For the orthotropic strain-based Fung model, you must specify 9 independent components $b_{ijkl}$. For more information, see Generalized Fung form.

Holzapfel

This form of invariant-based strain energy potential is used for modeling arterial layers with distributed collagen fiber orientations. For more information, see Holzapfel-Gasser-Ogden form.

User

You can use a user subroutine to define the form of a strain-based or invariant-based strain energy potential directly. For more information, see User-defined form: strain-based, and User-defined form: invariant-based.

To define material parameters that depend on field variables, click the arrows to the right of the Number of field variables field to increase or decrease the number of field variables.

Field variable columns appear in the data table.

For the Fung-Anisotropic, Fung-Orthotropic, and Holzapfel forms of strain energy potential, toggle on Use temperature-dependent coefficients to define material parameters that depend on temperature.

A column labeled Temp appears in the data table.

If you are defining the hyperelastic behavior of a viscoelastic material, click the arrow to the right of the Moduli field to specify either Long-term or Instantaneous elastic response. See Viscoelasticity, for more information.

For the Holzapfel strain energy potential, click the arrows to the right of the Number of local directions field to increase or decrease the number of preferred local directions (or fiber directions) in the material. The default (and minimum) is 1. See Creating an anisotropic hyperelastic material model below and Holzapfel-Gasser-Ogden form, for more information.

For a user-defined strain energy potential, you must specify the following options:

• Choose Strain or Invariant as the formulation defined by your user subroutine.

• Choose Incompressible or Compressible as the type of material defined by your user subroutine. See Compressibility, for more information.

• Specify the Number of property values needed as data in your user subroutine.

Enter the material parameters in the data table corresponding to the chosen strain energy potential.

Fung-Anisotropic

Enter $b_{1111}$, $b_{1122}$, $b_{2222}$, $b_{1133}$, $b_{2233}$, $b_{3333}$, $b_{1112}$, $b_{2212}$, $b_{3312}$, $b_{1212}$, $b_{1113}$, $b_{2213}$, $b_{3313}$, $b_{1213}$, $b_{1313}$, $b_{1123}$, $b_{2223}$, $b_{3323}$, $b_{1223}$, $b_{1323}$, $b_{2323}$, $c$ (units of FL⁻²), and $D$ (units of F⁻¹L²).

Fung-Orthotropic

Enter $b_{1111}$, $b_{1122}$, $b_{2222}$, $b_{1133}$, $b_{2233}$, $b_{3333}$, $b_{1212}$, $b_{1313}$, $b_{2323}$, $c$ (units of FL⁻²), and $D$ (units of F⁻¹L²).

Holzapfel

Enter $C_{10}$ (units of FL⁻²), $D$ (units of F⁻¹L²), $k_1$ (units of FL⁻²), $k_2$, and the fiber dispersion parameter $\kappa$ ($0\le \kappa \le 1/3$).

You may need to expand the dialog box to see all the columns in the data table. For detailed information on how to enter data, see Entering tabular data.

Click OK to create the material and to close the Edit Material dialog box. Alternatively, you can select another material behavior to define from the menus in the Edit Material dialog box (see Browsing and modifying material behaviors, for more information).