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)
MATX82	`MID`
	`LAW`	`MU1`	`ALFA1`	`D1`	`MU2`	`ALFA2`	`D2`
		`MU3`	`ALFA3`	`D3`	`MU4`	`ALFA4`	`D4`
		etc

Example

(1)	(2)	(3)	(4)	(5)	(6)	(7)
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 $μ_{i}$ . (Real)
`ALFAi`	Parameter $α_{i}$ . (Real)
`Di`	Parameter `Di`. (Real)

Comments

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.
MATX82 is only applied in geometric nonlinear analysis subcases which are defined by ANALYSIS=EXPDYN. It is ignored for all other subcases.
NU is defined on the corresponding MAT1. For material without Poisson effect, a small NU (for example, =1.E-10) should be defined.
The strain energy density $W$ is computed using:(1)
$W = \sum_{i = 1}^{N} \frac{2 μ_{i}}{α_{i}^{2}} ({\bar{λ}}_{1}^{α_{i}} + {\bar{λ}}_{2}^{α_{i}} + {\bar{λ}}_{3}^{α_{i}} - 3) + \sum_{i = 1}^{N} \frac{1}{D_{1}} {(J - 1)}^{2 i}$

with $λ_{i}$ being the i^th principal stretch, J = $λ$ ₁ * $λ$ ₂ * $λ$ ₃ being the relative volume and $\bar{λ} = J^{- \frac{1}{3}} λ$ .
The Bulk Modulus K is:
If NU = 0,(2)
$K = \frac{2}{D_{1}}$

If NU ≠ 0, then the value $D_{1}$ is modified to respect.(3)
$K = \frac{2 (1 + v)}{3 (1 - 2 v)} G$

If NU = 0 and $D_{1}$ = 0, then $μ$ = 0.475.
The ground shear modulus is:(4)
$G = \sum_{1}^{N} μ_{i}$
This card is represented as a material in HyperMesh.