coupled Veronda-Westmann

Module: solid

Category: material

Type string: "coupled Veronda-Westmann"

Parameters

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

Description

The material type for the coupled Veronda-Westmann material is coupled Veronda-Westmann.

The coupled Veronda-Westmann material is an unconstrained formulation of the Veronda-Westmann material and is defined by the following strain-energy function.

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

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 Veronda-Westmann material described in Section Veronda-Westmann.

Example:

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