uncoupled Holmes-Mow¶

Module: solid

Category: material

Type string: "uncoupled Holmes-Mow"

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	\([0, 3]\)
`mu`	shear modulus	-6.27744e+66	\(\gt 0\)
`beta`	power exponent	-6.27744e+66	\(\ge 0\)

The material type for the uncoupled Holmes-Mow material is uncoupled Holmes-Mow.

This material model uncouples deviatoric and volumetric behaviors,

\[ \Psi_{r}=\tilde{\Psi}_{r}\left(\tilde{\mathbf{C}}\right)+U\left(J\right) \]

The deviatoric strain-energy function is given by

\[ \tilde{\Psi}_{r}=\frac{1}{2}\frac{\mu}{\beta}\left(e^{\tilde{Q}}-1\right) \]

where \(\mu\) is the shear modulus and

\[ \tilde{Q}=\beta\left(\tilde{I}_{1}-3\right) \]

where \(\beta\) is the exponential stiffening coefficient.

Example:

<material id="1" name="Material1" type="uncoupled Holmes-Mow">
  <density>1</density>
  <mu>0.5</mu>
  <beta>2</beta>
  <k>5000</k>
</material>