coupled Mooney-Rivlin

Module: solid

Category: material

Type string: "coupled Mooney-Rivlin"

Parameters

Name	Description	Default	Units
density	density	1	[M/L^3]
c1	c1	-6.27744e+66	[P]
c2	c2	-6.27744e+66	[P]
k	k	-6.27744e+66	[P]

Description

The coupled Mooney-Rivlin material describes an unconstrained formulation of the Mooney-Rivlin material. The material type for this material is coupled Mooney-Rivlin.

The strain-energy function is given by the following expression.

\[ W=c_{1}\left(I_{1}-3\right)+c_{2}\left(I_{2}-3\right)-2\left(c_{1}+2c_{2}\right)\ln J+\frac{k}{2}\left(\ln J\right)^{2} \]

Here, \(I_{1}\) and \(I_{2}\) are the first and second invariants of the right Cauchy-Green deformation tensor \(\mathbf{C}\) and \(J\) is the determinant of the deformation gradient tensor.

This material model uses a standard displacement-based element formulation, so care must be taken when modeling materials with nearly-incompressible material behavior to avoid element locking. For (nearly-) incompressible materials, use the Mooney-Rivlin material described in Section Mooney-Rivlin.

Example:

<material id="1" type="coupled Mooney-Rivlin">
  <c1>10.0</c1>
  <c2>1.0</c2>
  <k>100.0</k>
</material>