uncoupled isotropic Lee-Sacks

Module: solid

Category: material

Type string: "uncoupled isotropic Lee-Sacks"

Parameters

Name	Description	Default	Units
density	density	1	[M/L^3]
k	bulk modulus	0	[P]
pressure_model	pressure_model	0	[]
c0	c0	0	[P]
c1	c1	0	[P]
c2	c2	0	[]
tangent_scale	tangent_scale	1	[]

Description

This material implements a Fung-type material, as presented in Kamensy, CMAME 2018. The material formulation is selected by setting the type attribute to uncoupled isotropic Lee-Sacks.

The strain-energy density function for this material combines a neo-Hookean matrix with a Fung-type exponential term, and is defined as follows.

\[ \Psi=\frac{c_{0}}{2}\left(I_{1}-3\right)+\frac{c_{1}}{2}\left(e^{c_{2}\left(I_{1}-3\right)^{2}}-1\right) \]

As reported in Kamensky, the exponential term may cause convergence difficulties under certain loading conditions. It was reported that increasing the value of \(c_{0}\) during the stiffness evaluation may improve convergence. The default value for tangent_scale is 1, and thus tangent scaling is not applied. A tangent scale factor of 20 was used in Kamensky.

Example:

<material id="1" name="material1" type="uncoupled isotropic Lee-Sacks">
  <k>1000</k>
  <c0>10</c0>
  <c1>0.209</c1>
  <c2>9.046</c2>
</material>