# MATX38

Bulk Data Entry Defines additional material properties for viscoelastic foam tabulated material (tabulated form) for geometric nonlinear analysis.

## Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MATX36 MID E0 NUT NUC RNU IFLAG ITOTA
BETA H RD KR KD THETA
KAIR NP FSCALEP
P0 RP PMAX PHI
TIDUN   FSCAUN EPSUN A B
CUTOFF IINSTA
EFINAL EPSFIN LAMBDA VISC TOL
TIDL1 TIDU1 FSCA1 EPSR1
etc etc etc
TIDLi TIDUi FSCAi EPSRi

## Example

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MAT1 102 60.4   0.33 2.70E-06
MATX38 102
1.0-30 1.0 0.5     0.67
1.0

4   1.0 0.0

## Definitions

Field Contents SI Unit Example
MID Material identifier of the associated MAT1 Bulk Data Entry. 1

No default (Integer > 0)

E0 Minimum tension modulus, used for interface and time step computation.

No default (Real > 0)

NUT Maximum Poisson's ratio in tension.

Default = 10-30 (Real > 0)

NUC Maximum Poisson's ratio in compression.

No default (Real > 0)

RNU Exponent for Poisson's ratio computation.

No default (Real > 0)

IFLAG Analysis formulation type flag.
= 0 (Default)
Corresponds to the viscoelastic foam tabulated material - visco-elasticity is computed in each principal stress direction.
= 1
Behavior is linear in both tension and compression, following Hook's relations. 7

(Integer)

ITOTA Incremental formulation flag.
Total: 0 or 1
= 0
Behavior in tension is linear
= 1
Bbehavior in tension is read from stress curves
Incremental: 2 or 3
= 2
Behavior in tension is linear
= 3
Behavior in tension is read from stress curves

Default = 0 (Integer)

BETA Relaxation rate for unloading.

Default = 10-30 (Real)

H Hysteresis coefficient for unloading.

Default = 1.0 (Real)

RD Damping factor on strain rate.

Default = 0.5 (Real)

KR Recovery model flag on unloading for hysteresis.
= 0 (Default)
No stress recovery on unloading
= 1
Stress recovery on unloading

(Integer)

KD Decay model flag, hysteresis type.
= 0 (Default)
Decay is active during loading and unloading
= 1
Decay is active only during loading
= 2
Decay is active only during unloading

(Integer)

THETA Integration coefficient for instantaneous module update.

Default = 0.67 (Real)

KAIR Air content computation flag.
= 0 (Default)
No confined air content
= 1
Confined air content computation active 9
= 2
Read hydrostatic curve (number defined by NP). The difference between pure compression and hydrostatic will be taken into account.

(Integer)

NP Pressure curve number (pressure versus relative volume).

No default (Integer)

FSCALEP Pressure curve scale factor.

No default (Real)

P0 Atmospheric pressure.

No default (Real)

RP Relaxation rate of pressure.

Default = 10-30 (Real > 0)

PMAX Maximum air pressure.

Default = 1030 (Real > 0)

PHI Porosity (density of foam/density of polymer).

No default (Real)

TIDUN Identification number of a TABLES1 that defines the unloading yield stress versus plastic strain curve "i" corresponding to EPSRUN.

No default (Integer > 0)

FSCAUN Unloading function scale factor.

Default = 1.0 (Real)

EPSUN Unloading strain rate (must be greater than EPSR1).

(Real)

A Exponent for stress interpolation.

Default = 1.0 (Real)

B Exponent for stress interpolation.

Default = 1.0 (Real)

CUTOFF Tension cutoff stress.

Default = 1030 (Real > 0)

IINSTA Material instability control flag.
= 0 (Default)
No material instability control
= 1
Material instability control

(Integer)

EFINAL Maximum tension modulus.

Default = E0 (Real)

EPSFIN Absolute value of strain at final modulus.

Default = 1.0 (Real)

LAMBDA Modulus interpolation coefficient.

Default = 1.0 (Real)

VISC Maximum viscosity. 15

Default = 1030 (Real)

TOL Tolerance on principal direction update.

Default = 1.0 (Real)

TIDLi Identification number of a TABLES1 Bulk Data Entry that defines the loading yield stress versus plastic strain curve "i" corresponding to EPSRi. Separate functions must be defined for different strain rates.

No default (Integer > 0)

TIDUi Identification number of a TABLES1 Bulk Data Entry that defines the unloading yield stress versus plastic strain curve "i" corresponding to EPSRi. Separate functions must be defined for different strain rates.
Unloading functions TIDUi are used only if the unloading curve TIDUN is not defined.
= 0
The TIDL1 curve is used for the corresponding unloading process.

No default (Integer > 0)

FSCAi Scale factor for TIDLi and TIDUi.

Default = 1.0 (Real)

EPSRi Strain rate(s) for TIDLi and TIDUi.
Note: EPSRi is (are) referred to as ${\stackrel{˙}{\epsilon }}_{i}$ in the comments.

(Real)

## 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. MATX38 is only applied in geometric nonlinear analysis subcases which are defined by ANALYSIS=EXPDYN. It is ignored for all other subcases.
3. Nominal stresses are computed by interpolation from input functions: (1)
$\sigma =f\left(\epsilon ,\stackrel{˙}{\epsilon }\right)$
for given $\text{ε}$ , read two values of functions with immediate availability for the two immediately lower and higher strain rates.
The interpolation function is defined as:(2)
$\sigma ={\sigma }_{2}+\left({\sigma }_{1}-{\sigma }_{2}\right) {\left(1-{\left(\frac{\stackrel{˙}{\epsilon }-{\stackrel{˙}{\epsilon }}_{1}}{{\stackrel{˙}{\epsilon }}_{2}-{\stackrel{˙}{\epsilon }}_{1}}\right)}^{A}\right)}^{B}$

Where, $\text{ε}$ , $\epsilon$ and $\sigma$ input are positive in compression, and ${\stackrel{˙}{\epsilon }}_{1}$ refers to the ESPRi stain rate data.

The parameters A and B define the shape of the interpolation function within each interval. If A = B = 1, the interpolation is linear.

The curves are always nominal stresses versus engineering strains.

4. If E0 is not defined, E on MAT1 card is used instead; if NUC is not empty, NU on the MAT1 card is used instead.
5. The strain is negative in compression. The tensile stress can either be negative or positive. The absolute stress value is used in the material law.
6. A "coupled" set of principal nominal stresses is computed with anisotropic Poisson's ratios:(3)
${\nu }_{\mathit{ij}}={\nu }_{c}+\left({\nu }_{t}-{\nu }_{c}\right) \left(1-\text{exp}\left(-{R}_{\nu }|{\epsilon }_{\mathit{ij}}|\right)\right)$
In tension ( ${\epsilon }_{\mathit{ij}}\ge 0$ ), and ${\upsilon }_{\mathit{ij}}={\upsilon }_{c}$ in compression.
Where,(4)
${\epsilon }_{\mathit{ij}}=\frac{\left({\epsilon }_{i}+{\epsilon }_{j}\right)}{2}$

Where, ${\epsilon }_{\mathit{ij}}\ge 0$ .

7. IFLAG = 1: For compression, Young's modulus E0 and Poisson's ratio NUC are used. Whereas, in tension the instantaneous Young's modulus ratio ET is used. The other data is ignored (especially, no viscous effect can be expected).
8. Hysteresis is only applied in compression, using the relation:(5)
$\sigma =\sigma \cdot H\cdot \text{min}\left(1,\left(1-{e}^{-\beta \epsilon \left(t\right)}\right)\right)$
9. When KAIR = 1:
If NP ≠ 0:(6)
${P}_{\mathit{air}}=\mathit{Fscal}{e}_{p}\cdot f\left(\frac{V}{{V}_{0}}\right)$

Where $f$ refers to the function number NP.

If NP = 0:(7)
${P}_{\mathit{air}}={P}_{0}\frac{\left(1-\frac{V}{{V}_{0}}\right)}{\left(\frac{V}{{V}_{0}}-\mathrm{\Phi }\right)}$
Relaxation is applied as: (8)
${P}_{\mathit{air}}=\mathit{Min}\left({P}_{\mathit{air}},{P}_{\text{max}}\right)\text{exp}\left(-{R}_{p}t\right)$

Where, ${R}_{p}$ is the relaxation rate of pressure and $t$ is the time.

10. If the unloading curve is not defined (TIDUN=blank) when unloading, then TIDUi are used. If both TIDUN and TIDUi are not defined, then $\sigma$ is computed from loading curve one (TIDL1).
11. If the unloading curve (TIDUN/TIDUi) is defined, $\sigma$ is interpolated between curve 1 (TIDUL1) and curve TIDUN. In this case, curve 1 (TIDUL1) must correspond to a quasi-static state.
12. If TIDUN > 0 and the unloading strain rate is equal to the quasi-static curve 1 (TIDUL1), the TIDUN curve is used for unloading.
13. E0 < E < EFINAL

EFINAL is the absolute value of the strain corresponding to the maximum compression modulus.

14. The instantaneous modulus is only used for tension.
15. If $VISC$ is input, interpolated stress will be limited by this value to have a larger timestep: (9)
$\sigma \le {\sigma }_{1}+\mathit{Visc}\cdot \left(\stackrel{˙}{\epsilon }-{\stackrel{˙}{\epsilon }}_{1}\right)$
16. The behavior is strain rate independent when the stress function interpolation is conducted for a queried strain rate ( $\text{ε}$ ) that is lower than the strain rate specified via EPSR1 ( ${\stackrel{˙}{\epsilon }}_{1}$ ), and strain rate independence occurs, if $-{\stackrel{˙}{\epsilon }}_{1}<\stackrel{˙}{\epsilon }\le {\stackrel{˙}{\epsilon }}_{1}$ .
17. This card is represented as a material in HyperMesh.