MAT5

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"/>

Comments

1. This material element defines a hyper-elastic material that follows the Yeoh material model law for the strain energy density function:
   $U=C_{10}({\overline{I}}_1-3)+C_{20}{({\overline{I}}_1-3)}^2+C_{30}{({\overline{I}}_1-3)}^3+\frac{k}{2}{(J-1)}^2$

   where

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

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

   $v$ is the Poisson's ratio

   ${\overline{I}}_1=J^{\frac{-2}{3}}{I}_1$

   $I_1=tr(C)=r_x^T{r}_x+r_y^T{r}_y+r_z^T{r}_z$

   $J=\det (J)=r_x^T(r_y\times r_z)$

   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.