Yeoh

Module: solid

Category: material

Type string: "Yeoh"

Parameters

Name	Description	Default	Range	Units
density	density	1	\(\ge 0\)	M/L^3
k	bulk modulus	0	\(\ge 0\)	P
pressure_model	pressure_model	0	\([0, 3]\)
c1	c1	0	\(\in \mathbb{R}\)	P
c2	c2	0	\(\in \mathbb{R}\)	P
c3	c3	0	\(\in \mathbb{R}\)	P
c4	c4	0	\(\in \mathbb{R}\)	P
c5	c5	0	\(\in \mathbb{R}\)	P
c6	c6	0	\(\in \mathbb{R}\)	P

Description

This material implements a Yeoh material, as presented online (https://en.wikipedia.org/wiki/Yeoh_hyperelastic_model). The material formulation is selected by setting the type attribute to Yeoh.

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

\[ \Psi=\sum_{i=1}^{6}c_{i}\left(\tilde{I}_{1}-3\right)^{i} \]

Example:

<material id="1" name="material1" type="Yeoh">
  <k>100</k>
  <c1>0.75</c0>
  <c1>-0.04</c1>
  <c2>0.08</c2>
</material>