MATX82

Format

Example

Definitions

Comments

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 i^th 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)

   $$\text{K}=\frac{2(1+\text{v})}{3(1-2\text{v})}\text{G}$$

   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.