# Materials

Use the tool to view, add, and edit the material properties that are used for NLFE bodies.

## Create and Edit Materials

### Hyper Elastic Materials Overview

For hyper elastic materials, different constitutive material models are supported, such as: Neo-Hookean (both compressible and incompressible), Mooney-Rivlin, and Yeoh models that are used to model a hyper elastic NLFE Body.

Hyper elastic materials can undergo large deformations with a non-linear stress strain relationship.

The constitutive models for hyper elastic materials are characterized using the strain energy density function.

Type | Equation | Description |
---|---|---|

Neo-Hookean Compressible | $$U=\frac{\mu}{2}({I}_{1}-3)-\mu \mathrm{ln}J+\frac{\lambda}{2}{(\mathrm{ln}J)}^{2}$$ | U - Strain Energy density function μ - Shear modulus $${I}_{1}-{r}_{x}^{T}{r}_{x}+{r}_{y}^{T}{r}_{y}+{r}_{z}^{T}r{}_{z}$$ - rx, ry, and rz are the gradients of NLFE grids $$\lambda =\frac{2\mu v}{1-2v}$$, is called the 2nd Lame's constant, v is the Poisson's ratio $$J=\mathrm{det}(J)={r}_{x}^{T}({r}_{y}\times {r}_{z})$$ |

Neo-Hookean Incompressible | $$U=\frac{\mu}{2}({\overline{I}}_{1}-3)+\frac{k}{2}{(J-1)}^{2}$$ | $${\overline{I}}_{1}={J}^{\frac{-2}{3}}{I}_{1}$$ $$k=\frac{2\mu (1+v)}{3(1-2v)}$$, bulk modulus |

Mooney-Rivlin | $$U={\mu}_{10}(\overline{I}{}_{1}-3)+{\mu}_{01}({\overline{I}}_{2}-3)+\frac{k}{2}{(J-1)}^{2}$$ | μ_{01} and μ_{10} are material constants$${\overline{I}}_{2}={J}^{\frac{-4}{3}}{I}_{2}$$ $${\overline{I}}_{2}=\frac{1}{2}\left({\left(tr\left(C\right)\right)}^{2}-\left(tr\left({C}^{2}\right)\right)\right)$$, where C is the Cauchy-Green deformation tensor $$C={J}^{T}J$$ $$J=\left[{r}_{x}{r}_{y}{r}_{z}\right]$$ $${r}_{x}{r}_{y}{r}_{z}$$ are the gradient vectors |

Yeoh | $$U={C}_{10}({\overline{I}}_{1}-3)+{C}_{20}{({\overline{I}}_{1}-3)}^{2}+{C}_{30}{({\overline{I}}_{1}-3)}^{3}+\frac{k}{2}{(J-1)}^{2}$$ | C_{10}, C_{20}, and C_{30} are
material constants |

The material constants for these models have to be derived through testing, such as: uniaxial, bending, and shear tests.