coupled trans-iso Mooney-Rivlin¶

Module: solid

Category: material

Type string: "coupled trans-iso Mooney-Rivlin"

Parameters¶

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

Description¶

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

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

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

The first three terms define the coupled Mooney-Rivlin matrix response. The third term is the fiber response which is a function of the fiber stretch \(\lambda\) and is defined as in ¹. 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 Mooney-Rivlin">
  <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>

Weiss, J.A., Maker, B.N., and Govindjee, S., "Finite element implementation of incompressible, transversely isotropic hyperelasticity", Computer Methods in Applications of Mechanics and Engineering 135 (1996), pp. 107-128. ↩