# MATX82

Bulk Data Entry Defines additional material properties for Ogden material for geometric nonlinear analysis. This material is used to model rubber, polymers, and elastomers.

## Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MATX82 MID
LAW MU1 ALFA1 D1 MU2 ALFA2 D2
MU3 ALFA3 D3 MU4 ALFA4 D4
etc

## Example

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MAT1 102 10.0   0.495 6.0E-10
MATX82 102
LAW 0.10 2.0   -0.010 -2.0

## Definitions

Field Contents SI Unit Example
MID Material ID of the associated MAT1. 1

No default (Integer > 0)

LAW Indicates that material parameters MUi, ALFAi, and Di follow.
MUi Parameter ${\mu }_{i}$ .

(Real)

ALFAi Parameter ${\alpha }_{i}$ .

(Real)

Di Parameter Di.

(Real)

1. The material identification number must be that of an existing MAT1 Bulk Data Entry. Only one MATXi material extension can be associated with a particular MAT1.
2. MATX82 is only applied in geometric nonlinear analysis subcases which are defined by ANALYSIS=EXPDYN. It is ignored for all other subcases.
3. NU is defined on the corresponding MAT1. For material without Poisson effect, a small NU (for example, =1.E-10) should be defined.
4. The strain energy density $W$ is computed using:(1)
$\text{W}=\sum _{\text{i}=1}^{\text{N}}\frac{2{\mu }_{\text{i}}}{{\alpha }_{\text{i}}^{2}}\left({\overline{\lambda }}_{1}^{{\alpha }_{\text{i}}}+{\overline{\lambda }}_{2}^{{\alpha }_{\text{i}}}+{\overline{\lambda }}_{3}^{{\alpha }_{\text{i}}}-3\right)+\sum _{\text{i}=1}^{\text{N}}\frac{1}{{\text{D}}_{1}}{\left(\text{J}-1\right)}^{2\text{i}}$

with ${\lambda }_{i}$ being the ith principal stretch, J = $\lambda$ 1 * $\lambda$ 2 * $\lambda$ 3 being the relative volume and $\overline{\lambda }={\text{J}}^{-\frac{1}{3}}\lambda$ .

5. The Bulk Modulus K is:
If NU = 0,(2)
$\text{K}=\frac{2}{{\text{D}}_{1}}$
If NU ≠ 0, then the value ${D}_{1}$ is modified to respect.(3)
$\text{K}=\frac{2\left(1+\text{v}\right)}{3\left(1-2\text{v}\right)}\text{G}$

If NU = 0 and ${D}_{1}$ = 0, then $\mu$ = 0.475.

6. The ground shear modulus is:(4)
$\text{G}=\sum _{1}^{\text{N}}{\mu }_{\text{i}}$
7. This card is represented as a material in HyperMesh.