# MAT5

Material Property ElementMAT5 lets you define a hyper-elastic material model for NLFE elements based on the Yeoh material model.

## Format

<MAT5
id       = "integer"
C10      = "real"
C20      = "real"
C30      = "real"
nu       = "real"
rho      = "real"
YS       = "real"
/> 

## Attributes

id
Unique material property identification number.
C10
Material constant ( ${C}_{10}$ ).
C20
Material constant ( ${C}_{20}$ ).
C30
Material constant ( ${C}_{30}$ ).
nu
Poisson's ratio for the element. Default is 0.49.
rho
Element density.
An elastic limit for strain. Default is 0.0.
YS >= 0.0

## Example

The example demonstrates the definition of a MAT5 element.

<MAT5 id="1" C10="1e+4"  C20="5e+3" C30="2e+3" nu="0.499" rho="7.810e-6" YS="0.125"/>

1. This material element defines a hyper-elastic material that follows the Yeoh material model law for the strain energy density function:
$U={C}_{10}\left({\overline{I}}_{1}-3\right)+{C}_{20}{\left({\overline{I}}_{1}-3\right)}^{2}+{C}_{30}{\left({\overline{I}}_{1}-3\right)}^{3}+\frac{k}{2}{\left(J-1\right)}^{2}$

where

${C}_{10},{C}_{20},{C}_{30}$ are the material properties.

$k=\frac{2\mu \left(1+v\right)}{3\left(1-2v\right)}$ is the bulk modulus

$v$ is the Poisson's ratio

${\overline{I}}_{1}={J}^{\frac{-2}{3}}{I}_{1}$

${I}_{1}=tr\left(C\right)={r}_{x}^{T}{r}_{x}+{r}_{y}^{T}{r}_{y}+{r}_{z}^{T}{r}_{z}$

$J=\mathrm{det}\left(J\right)={r}_{x}^{T}\left({r}_{y}×{r}_{z}\right)$

Each element must have a unique material identification number.

2. The constants C10, C20 and C30 denote material parameters of shear modulus that are usually determined experimentally.
3. YS lets you specify a maximum limit on the elastic strain that the component is allowed. If, during the simulation, the component strain (at any element in the component) exceeds this value, MotionSolve issues a warning message.