# MATX33

Bulk Data Entry Defines additional material properties for visco-elastic plastic foam material for geometric nonlinear analysis.

## Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MATX33 MID KA TID FSCALE P0 PHI EPSV0
A B C E1 E2 ET ETAC ETAS

## Example

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MAT1 133 0.11   0.11 9.92E-07
MATX33 133 0

## Definitions

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

No default (Integer > 0)

KA Analysis type flag.
ELAST (Default)
Skeletal behavior before yield is elastic.
VISCO
Skeletal behavior before yield is visco-elastic.

(Character)

TID Identification number of TABLES1 entry that defines the yield stress versus volumetric strain curve.

If defined, ${\sigma }_{y}$ versus $\gamma$ is read from input of the curve.

No default (Integer > 0)

FSCALE Scale factor for stress in yield curve.

Default = 1.0 (Real)

P0 Initial air pressure. 4

Default = 0.0 (Real)

PHI Ratio of foam to polymer density.

Default = 0.0 (Real)

EPSV0 Initial volumetric strain.

Default = 0.0 (Real)

A Yield parameter.

Default = 0.0 (Real)

B Yield parameter.

Default = 1.0 (Real)

C Yield parameter.

Default = 1.0 (Real)

E1 Coefficient for Young's modulus update.

No default (Real)

E2 Coefficient for Young's modulus update.

No default (Real)

ET Tangent modulus.

No default (Real ≥ 0)

ETAC Viscosity coefficient in pure compression.

Default = 1.0 (Real ≥ 0)

ETAS Viscosity coefficient in pure shear.

Default = 1.0 (Real ≥ 0)

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. MATX33 is only applied in geometric nonlinear analysis subcases which are defined by ANALYSIS = EXPDYN. It is ignored for all other subcases.
3. This material can be used only with solid elements, typically used to model low density, closed cell polyurethane foams such as impact limiters.
4. The air pressure is computed as:

Pair = ${P}_{0}$ * $\gamma$ / (1+ $\gamma$ - $\varphi$ ),

with $\gamma$ = $\gamma$ 0 + V/V0 - 1

Where,
$\gamma$
Volumetric strain
$\varphi$
Porosity
${P}_{0}$
Initial air pressure
$\gamma$ 0
Initial volumetric strain

The volumetric strain $\gamma$ < 0 in compression.

5. TID is blank or zero, then

${\sigma }_{y}$ = A + B(1+ C $\gamma$ ),

with $\gamma$ = V/V0 - 1 = $\rho$ / ${\rho }_{0}$ - 1 = - $\mu$ /(1+ $\mu$ )

6. The Young's modulus used in the calculation is:(1)
$\text{E}=\text{max}\left(\text{E}, {\text{E}}_{1}\stackrel{˙}{\epsilon }+{\text{E}}_{2}\right)$

This material assumes NU = 0 no matter what is defined on the corresponding MAT1. Hence, G = 0.5 * E.

7. This card is represented as an extension to a MAT1 material in HyperMesh.