# /MAT/PLAS_ZERIL

Block Format Keyword This law defines an isotropic elasto-plastic material using the Zerilli-Armstrong plasticity model.

## Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/PLAS_ZERIL/mat_ID/unit_ID
mat_title
${\rho }_{i}$
E v VP
C0 C5 n ${\epsilon }_{p}^{max}$ ${\sigma }_{\mathrm{max}\text{​}0}$
C1 ${\stackrel{˙}{\epsilon }}_{0}$ ICC Fsmooth Fcut
C3 C4 $\rho {C}_{p}$ Tr

## Definition

Field Contents SI Unit Example
mat_ID Material identifier.

(Integer, maximum 10 digits)

unit_ID Unit Identifier.

(Integer, maximum 10 digits)

mat_title Material title.

(Character, maximum 100 characters)

${\rho }_{i}$ Initial density.

(Real)

$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$
E Young's modulus.

(Real)

$\left[\text{Pa}\right]$
v Poisson's ratio.

(Real)

VP Formulation for rate effects.
= 0
Set to 2
= 1
Plastic strain rate.
= 2 (Default)
Total strain rate.
= 3
Deviatoric strain rate.

(Integer)

C0 Plasticity yield stress.

(Real)

$\left[\text{Pa}\right]$
C5 Plasticity hardening parameter.

(Real)

$\left[\text{Pa}\right]$
n Plasticity hardening exponent. 5

Default = 1.0 (Real)

${\epsilon }_{p}^{max}$ Failure plastic strain.

Default = 1030 (Real)

${\sigma }_{\mathrm{max}\text{​}0}$ Plasticity maximum stress.

Default = 1030 (Real)

$\left[\text{Pa}\right]$
C1 Strain rate formulation coefficient.

(Real)

$\left[\text{Pa}\right]$
${\stackrel{˙}{\epsilon }}_{0}$ Reference strain rate (must be 1 s-1 converted into user's units).

(Real)

$\left[\frac{\text{1}}{\text{s}}\right]$
ICC Strain rate computation flag. 7
= 0 (Default)
Set to 1
= 1
Strain rate effect on ${\sigma }_{max}$ .
= 2
No strain rate effect on ${\sigma }_{max}$ .

(Integer)

Fsmooth Smooth strain rate option flag.
= 0 (Default)
No strain rate smoothing.
= 1
Strain rate smoothing active.

(Integer)

Fcut Cutoff frequency for strain rate filtering. 8

Default = 1030 (Real)

$\text{[Hz]}$
C3 Temperature effect coefficient.

(Real)

$\left[\frac{1}{\text{K}}\right]$
C4 Temperature effect coefficient.
= 0
No strain rate effect.

(Real)

$\left[\frac{1}{\text{K}}\right]$
$\rho {C}_{p}$ Specific heat per unit of volume.
= 0
Temperature is constant: T = Tr

(Real)

$\left[\frac{\text{J}}{{\text{m}}^{3}\cdot \text{K}}\right]$
Tr Reference temperature.

Default = 298 K (Real)

$\left[\text{K}\right]$

1. The Zerilli-Armstrong law is applicable only to shells and solids.
2. The equation that describes stress during plastic deformation is:
$\sigma ={C}_{0}+\left({C}_{1}\mathrm{exp}\left(\left(-{C}_{3}T+{C}_{4}T\mathrm{ln}\left(\frac{\stackrel{˙}{\epsilon }}{{\stackrel{˙}{\epsilon }}_{0}}\right)\right)\right)\right)+{C}_{5}{\epsilon }_{p}{}^{n}$
Where,
${\epsilon }_{p}$
Plastic strain
$\stackrel{˙}{\epsilon }$
Strain rate
$T$
Temperature
3. Yield stress should be strictly positive.
4. When ${\overline{\epsilon }}_{p}$ reaches ${\epsilon }_{p}^{max}$ in one integration point, then based on the element type:
• Shell elements:

The corresponding shell element is deleted.

• Solid elements:

The deviatoric stress of the corresponding integral point is permanently set to 0; however, the solid element is not deleted.

5. n must be less than 1.
6. If ${\stackrel{˙}{\epsilon }}_{0}$ is 0, there is no strain rate effect.
7. ICC is a flag of the strain rate effect on material maximum stress ${\sigma }_{\mathrm{max}}$ :
8. Strain rate filtering input (Fcut) is only available for shell and solid elements.
9. The strain rate filtering is used to smooth strain rates.
10. Temperature is computed assuming adiabatic conditions:
$Τ={Τ}_{r}+\frac{{E}_{int}}{\rho {C}_{\rho }\left(Volume\right)}$

Where, Eint is the internal energy computed by Radioss.

11. When the temperature is not initialized using /HEAT/MAT or /INITEMP, the reference temperature (Tr) is also the initial temperature.