coupled trans-iso Veronda-Westmann

Module: solid

Category: material

Type string: "coupled trans-iso Veronda-Westmann"

Parameters

Name	Description	Default	Units
density	density	1	[M/L^3]
c1	c1	0	[P]
c2	c2	0	[]
c3	c3	0	[P]
c4	c4	0	[]
c5	c5	0	[P]
lambda	lambda	1	[]
k	k	0	[P]
fiber			[]

Description

This material describes a transversely isotropic Veronda-Westmann material using a fully-coupled formulation. It is defined through the coupled trans-iso Veronda-Westmann material type.

The strain-energy function for this constitutive model is defined by,

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

The first two terms define the coupled Veronda-Westmann matrix response. The third term is the fiber response which is a function of the fiber stretch \(\lambda\) and is defined as in [#Weiss96]. For \(U\), the following form is chosen in FEBio.

\[ U\left(J\right)=\frac{1}{2}k\left(\ln J\right)^{2} \]

where \(J=\det\mathbf{F}\) is the Jacobian of the deformation.

Example:

<material id="1" type="coupled trans-iso Veronda-Westmann">
  <c1>1</c1>
  <c2>0.1</c2>
  <c3>1</c3>
  <c4>1</c4>
  <c5>1.34</c5>
  <lam_max>1.3</lam_max>
  <k>100</k>
</material>