# MAT1

Material Property ElementMAT1 lets you define a linearly elastic, isotropic material model for NLFE elements that follows Hooke's law.

## Format

```
<MAT1
id = "integer"
e = "real"
nu = "real"
rho = "real"
YS = "real"
AP = "integer"
/>
```

## Attributes

`id`- Unique material property identification number.
`e`- Young's modulus for the element.
`nu`- Poisson's ratio for the element. Default is 0.0.
`rho`- Element density.
`YS`- An elastic limit for strain. Default is 0.0.
`AP`- Selector for the elastic model used. Default is 1.

## Example

The example demonstrates the definition of a MAT1 element.

`<MAT1 id="1" e="2.07e+5" nu="0.3" rho="7.810e-6" YS="0.002" AP="2"/>`

## Comments

- This material element defines a linearly elastic, isotropic material that obeys the Hooke's law. Each element must have a unique material identification number.
- In this approach, the stress-strain relationship is
$\sigma ={E}_{m}{\epsilon}_{m}$
. The strain components are defined as
(1) $${\epsilon}_{m}=\left[{\epsilon}_{x}\text{}{\epsilon}_{y}\text{}{\epsilon}_{z}\text{}{\epsilon}_{xy}\text{}{\epsilon}_{xz}\text{}{\epsilon}_{yz}\text{}\right]$$(2) $${\epsilon}_{m}=\left[\begin{array}{l}\frac{1}{2}\left({r}_{x}^{T}{r}_{x}-1\right)\\ \frac{1}{2}\left({r}_{y}^{T}{r}_{y}-1\right)\\ \frac{1}{2}\left({r}_{z}^{T}{r}_{z}-1\right)\\ {r}_{x}^{T}{r}_{y}\\ {r}_{x}^{T}{r}_{z}\\ \text{}{r}_{z}^{T}{r}_{y}\end{array}\right]$$ `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.-
`AP`is a selector that allows you to choose the elastic model that is used to calculate the internal resistance of the NLFE component. The following approaches are available for the BEAM (BEAM12 and BEAMC) elements:**Approach (AP)****Description**`AP`="1"- Continuum mechanics approach.
`AP`="2"- Elastic line approach
`AP`="3"- Euler Bernoulli beam theory
`AP`="4"- Timoshenko beam theory