# MAT2

Material Property ElementMAT2 lets you define a hyper-elastic material model for NLFE elements that follows the incompressible Neo-Hookean material law.

## Format

<MAT2
id       = "integer"
mu       = "real"
nu       = "real"
rho      = "real"
YS       = "real"
/> 

## Attributes

id
Unique material property identification number.
mu
Shear modulus for the element.
nu
Poisson's ratio for the element. Default is 0.49.
rho
Element density.
YS
An elastic limit for strain. Default is 0.0.
YS >= 0.0

## Example

The example demonstrates the definition of a MAT2 element.

<MAT2 id="1" mu="1.906036" nu="0.499" rho="2.150e-6" YS="0.125"/>

1. This material element defines a hyper-elastic material that obeys the incompressible Neo-Hookean law for the strain energy density function:

$U=\frac{\mu }{2}\left({\overline{I}}_{1}-3\right)+\frac{k}{2}{\left(J-1\right)}^{2}$

where

$\mu$ is the shear modulus; $\mu =NKT$ , where N is the number of polymer chains per unit volume, K is the Boltzmann constant, and T is temperature

$k=\frac{2\mu \left(1+v\right)}{3\left(1-2v\right)}$ 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. This material model can only be used with a fully parameterized element (BEAM12, QUAD12, TRIA12 and solid elements).
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.