Defining the Hyperelastic Material Continuum

You model the rubber diaphragm with the Neo-Hookean model for hyperelastic materials. This model requires the bulk modulus and the $c_{10}$ coefficient as inputs.

The bulk modulus of a material, $k_{b}$ , is a measure of how resistant the material is to compression, and can be derived from the Young's Modulus and Poisson's ratio (see Eqn. (4513)). The $c_{10}$ coefficient is defined as the ratio of shear stress to shear strain, or equivalently a proportion of the shear modulus (see Eqn. (4534)).

In the simulation, you can calculate

k_{b}

and

c_{10}

using expression reports:

Right-click the Reports node and select New > User > Expression.
Rename the Expression 1 node to Rubber_BulkModulus_Computed.

Select the Reports > Rubber_BulkModulus_Computed node and set the following properties:


Property	Setting
Dimensions	Pressure
Units	GPa
Definition	${Rubber_YoungsModulus_InputReport}/(3(1-2${Rubber_PoissonsRatio_InputReport}))

Repeat steps 1 and 2 but rename the Expression 1 node to Rubber_c10_Computed.

Select the Reports > Rubber_c10_Computed node and set the following properties:


Property	Setting
Dimensions	Pressure
Units	GPa
Definition	${Rubber_YoungsModulus_InputReport}/(4*(1+${Rubber_PoissonsRatio_InputReport}))

注	Units definition only affects the output of the report in the Output window and not the interpretation of the input Definition. For example, Units of Pa defined as <10MPa> would have an output of 1.0e7 Pa. However, units of MPa defined as 10 would have an output of 10e-5 MPa.

Modeling the hyperelastic material behavior in Simcenter STAR-CCM+ requires that you use the Nonlinear Geometry model in conjunction with the respective material law. To define the hyperelastic solid material:

Create a physics continuum.
Rename the Continua > Physics 1 node to Structure.

For the Structure physics continuum, select the following models in order:


Group Box	Model
Space	Three Dimensional
Material	Solid
Time	Implicit Unsteady
Optional Models	Solid Stress Material Law Models (Selected automatically) Nearly Incompressible Material Nonlinear Geometry

To define the material law in the Structure Model Selection dialog:

Expand the Structure > Material Law Models > Material Laws node to the left of the Optional Models group box.
Right-click the Default Material Law node and rename it to HyperElastic.

For the HyperElastic node, select the following models:


Group Box	Model
Material Stiffness Models	Hyperelasticity
Material Strain Measures	Green-Lagrange (Large Strain) (selected automatically)
Hyperelastic Material Models	Neo-Hookean

Click Close.

Specify the solid material and define its properties:
1. Right-click the Structure > Models > Solid > Al node and select Replace with....
2. In the Replace Material dialog, select Rubber (Arion Thermabond 99180T010), and click OK.
Edit the Rubber > Material Properties node.
Select the Bulk Modulus > Constant node and set Value to ${Rubber_BulkModulus_ComputedReport}.
Select the Neo-Hookean Material Parameters > Neo-Hookean Parameters > c10 > Constant node and set Value to ${Rubber_c10_ComputedReport}.

Assign the Structure physics continuum to the solid region:

Select the Regions > Structure node, and set Physics Continuum to Structure.
Save the simulation.