/MAT/LAW36 (PLAS_TAB)
Block Format Keyword This law models an isotropic elastoplastic material using userdefined functions for the workhardening portion of the stressstrain curve (for example, stress vs. plastic strain) for different strain rates.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/MAT/LAW36/mat_ID/unit_ID or /MAT/PLAS_TAB/mat_ID/unit_ID  
mat_title  
${\rho}_{i}$  
E  $\nu $  ${\epsilon}_{p}^{max}$  ${\epsilon}_{t}$  ${\epsilon}_{m}$  
N_{funct}  F_{smooth}  C_{hard}  F_{cut}  ${\epsilon}_{f}$  VP  
fct_ID_{p}  Fscale  fct_ID_{E}  E_{inf}  C_{E} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

fct_ID_{1}  fct_ID_{2}  fct_ID_{3}  fct_ID_{4}  fct_ID_{5} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

Fscale_{1}  Fscale_{2}  Fscale_{3}  Fscale_{4}  Fscale_{5} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

${\dot{\epsilon}}_{1}$  ${\dot{\epsilon}}_{2}$  ${\dot{\epsilon}}_{3}$  ${\dot{\epsilon}}_{4}$  ${\dot{\epsilon}}_{5}$ 
Definitions
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) 
$\left[\frac{\text{kg}}{{\text{m}}^{3}}\right]$ 
E  Young's modulus. (Real) 
$\left[\text{Pa}\right]$ 
$\nu $  Poisson's ratio. (Real) 

${\epsilon}_{p}^{max}$  Failure plastic strain. Default = 10^{20} (Real) 

${\epsilon}_{t}$  Tensile failure strain at which stress
starts to reduce. Default = 10^{20} (Real) 

${\epsilon}_{m}$  Maximum tensile failure strain at which
the stress in element is set to zero. Default = 2.0 x 10^{20} (Real) 

N_{funct}  Number of functions
($1\le {N}_{funct}\le 100$
). (Integer) 

F_{smooth}  Smooth strain rate option flag.
(Integer) 

C_{hard}  Hardening coefficient.
(Real) 

F_{cut}  Cutoff frequency for strain rate
filtering. Only available for shell and solid elements, Appendix: Filtering. Default = 1.0 x 10^{20} (Real) 
$\text{[Hz]}$ 
VP  Strain rate choice flag.
(Integer) 

${\epsilon}_{f}$  Tensile strain for element
deletion. Default = 3.0 x 10^{20} (Real) 

fct_ID_{p}  Yield factor vs. pressure function.
7 Default = 0 (Integer) 

Fscale  Scale factor for yield factor in fct_ID_{p}. Default = 1.0 (Real) 
$\left[\text{Pa}\right]$ 
fct_ID_{E}  Function identifier for the scale factor
of Young's modulus, when Young's modulus is function of the plastic
strain. Default = 0: in this case the evolution of Young's modulus depends on E_{int} and C_{E}. (Integer) 

E_{int}  Saturated Young's modulus for infinitive
plastic strain. (Real) 

C_{E}  Parameter for Young's modulus
evolution. (Real) 

fct_ID_{1}  Yield stress function identifier 1
corresponding to strain rate
${\dot{\epsilon}}_{1}$
. (Integer) 

fct_ID_{2}  Yield stress function identifier 2
corresponding to strain rate
${\dot{\epsilon}}_{2}$
. (Integer) 

fct_ID_{3}  Yield stress function identifier 3
corresponding to strain rate
${\dot{\epsilon}}_{3}$
. (Integer) 

fct_ID_{4}  Yield stress function identifier 4
corresponding to strain rate
${\dot{\epsilon}}_{4}$
. (Integer) 

fct_ID_{5}  Yield stress function identifier 5
corresponding to strain rate
${\dot{\epsilon}}_{5}$
. (Integer) 

Fscale_{1}  Scale factor for ordinate (stress) in
fct_ID_{1}. Default = 1.0 (Real) 
$\left[\text{Pa}\right]$ 
Fscale_{2}  Scale factor for ordinate (stress) in
fct_ID_{2}. Default = 1.0 (Real) 
$\left[\text{Pa}\right]$ 
Fscale_{3}  Scale factor for ordinate (stress) in
fct_ID_{3}. Default = 1.0 (Real) 
$\left[\text{Pa}\right]$ 
Fscale_{4}  Scale factor for ordinate (stress) in
fct_ID_{4}. Default = 1.0 (Real) 
$\left[\text{Pa}\right]$ 
Fscale_{5}  Scale factor for ordinate (stress) in
fct_ID_{5}. Default = 1.0 (Real) 
$\left[\text{Pa}\right]$ 
${\dot{\epsilon}}_{1}$  If VP
=0 total strain rate for fct_ID_{1}. If VP =1 plastic strain rate for fct_ID_{1}. (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
${\dot{\epsilon}}_{2}$  If VP
=0 total strain rate for fct_ID_{2}. If VP =1 plastic strain rate for fct_ID_{2}. (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
${\dot{\epsilon}}_{3}$  If VP
=0 total strain rate for fct_ID_{3}. If VP =1 plastic strain rate for fct_ID_{3}. (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
${\dot{\epsilon}}_{4}$  If VP
=0 total strain rate for fct_ID_{4}. If VP =1 plastic strain rate for fct_ID_{4}. (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
${\dot{\epsilon}}_{5}$  If VP
=0 total strain rate for fct_ID_{5}. If VP =1 plastic strain rate for fct_ID_{5}. (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
Example (Aluminum)
#RADIOSS STARTER
#12345678910
/UNIT/1
unit for mat
g mm ms
#12345678910
# 2. MATERIALS:
#12345678910
/MAT/PLAS_TAB/1/1
Aluminium_example
# RHO_I
.0027 0
# E Nu Eps_p_max Eps_t Eps_m
60400 .33 0 0 0
# N_funct F_smooth C_hard F_cut Eps_f VP
14 0 0 0 0 0
# fct_IDp Fscale Fct_IDE EInf CE
0 0 0 0 0
# func_ID1 func_ID2 func_ID3 func_ID4 func_ID5
1 2 3 4 5
6 7 8 9 10
11 12 13 14
# Fscale_1 Fscale_2 Fscale_3 Fscale_4 Fscale_5
1 1.2 1.4 1.6 1.9
10 10.2 10.4 10.6 10.9
20 20.2 20.4 20.6
# Eps_dot_1 Eps_dot_2 Eps_dot_3 Eps_dot_4 Eps_dot_5
0 20 30 40 50
110 120 130 140 150
210 220 230 240
#12345678910
# 3. FUNCTIONS:
#12345678910
/FUNCT/1
function_36
# X Y
0 90
2.5E4 100
.001 104
.009 121
.017 136
.021 143
.036 156
.045 162
.055 165
.072 170
.075 170
#12345678910
/FUNCT/2
function_36
# X Y
0 90
2.5E4 100
.001 104
.009 121
.017 136
.021 143
.036 156
.045 162
.055 165
.072 170
.075 170
#12345678910
/FUNCT/3
function_36
# X Y
0 90
2.5E4 100
.001 104
.009 121
.017 136
.021 143
.036 156
.045 162
.055 165
.072 170
.075 170
#12345678910
/FUNCT/4
function_36
# X Y
0 90
2.5E4 100
.001 104
.009 121
.017 136
.021 143
.036 156
.045 162
.055 165
.072 170
.075 170
#12345678910
/FUNCT/5
function_36
# X Y
0 90
2.5E4 100
.001 104
.009 121
.017 136
.021 143
.036 156
.045 162
.055 165
.072 170
.075 170
#12345678910
/FUNCT/6
function_36
# X Y
0 90
2.5E4 100
.001 104
.009 121
.017 136
.021 143
.036 156
.045 162
.055 165
.072 170
.075 170
#12345678910
/FUNCT/7
function_36
# X Y
0 90
2.5E4 100
.001 104
.009 121
.017 136
.021 143
.036 156
.045 162
.055 165
.072 170
.075 170
#12345678910
/FUNCT/8
function_36
# X Y
0 90
2.5E4 100
.001 104
.009 121
.017 136
.021 143
.036 156
.045 162
.055 165
.072 170
.075 170
#12345678910
/FUNCT/9
function_36
# X Y
0 90
2.5E4 100
.001 104
.009 121
.017 136
.021 143
.036 156
.045 162
.055 165
.072 170
.075 170
#12345678910
/FUNCT/10
function_36
# X Y
0 90
2.5E4 100
.001 104
.009 121
.017 136
.021 143
.036 156
.045 162
.055 165
.072 170
.075 170
#12345678910
/FUNCT/11
function_36
# X Y
0 90
2.5E4 100
.001 104
.009 121
.017 136
.021 143
.036 156
.045 162
.055 165
.072 170
.075 170
#12345678910
/FUNCT/12
function_36
# X Y
0 90
2.5E4 100
.001 104
.009 121
.017 136
.021 143
.036 156
.045 162
.055 165
.072 170
.075 170
#12345678910
/FUNCT/13
function_36
# X Y
0 90
2.5E4 100
.001 104
.009 121
.017 136
.021 143
.036 156
.045 162
.055 165
.072 170
.075 170
#12345678910
/FUNCT/14
function_36
# X Y
0 90
2.5E4 100
.001 104
.009 121
.017 136
.021 143
.036 156
.045 162
.055 165
.072 170
.075 170
#12345678910
#ENDDATA
/END
#12345678910
Comments
 The first point of yield stress functions (plastic strain vs stress) should have a plastic strain value of zero. If the last point of the first (static) function equals 0 in stress, default value of ${\epsilon}_{p}^{max}$ is set to the corresponding value of ${\epsilon}_{p}$ .
 Element deletion:
 Once ${\epsilon}_{p}$ (plastic strain) reaches ${\epsilon}_{p}^{max}$ , in one integration point, the element is deleted.
 If
${\epsilon}_{1}$
reaches
${\epsilon}_{t}$
, the stress is reduced using the following relation:
(1) $$\sigma =\sigma \left(\frac{{\epsilon}_{m}{\epsilon}_{1}}{{\epsilon}_{m}{\epsilon}_{t}}\right)$$  If ${\epsilon}_{1}$ (largest principal strain) reaches ${\epsilon}_{m}$ ( ${\epsilon}_{1}>{\epsilon}_{m}$ ), the stress in element is reduced to 0 (but the element is not deleted).
 Once ${\epsilon}_{1}$ (largest principal strain) reaches ${\epsilon}_{f}$ (maximum tensile failure strain), the element is deleted.
 The kinematic hardening model is not available in global formulation (N=0 in shell property keyword) that is, hardening is fully isotropic.
 In case of kinematic hardening and strain rate dependency, the yield stress depends on the strain rate.
 Strain rate filtering is used to smooth strain rates.
 The first function in fct_ID_{1} is used for strain rate values from 0 to its corresponding strain rate, strain rate 1. However, the last function used in the model does not extend to the maximum strain rate; for higher strain rates, a linear extrapolation will be applied. This could lead to instability and/or unusual deformation. This instability can be overcome by repeating the stress strain curve, corresponding to the last strain rate, again with a much higher strain rate.
 fct_ID_{p} is used to distinguish the behavior in tension and compression for certain materials (pressure dependent yield). This is available for both shell and solid elements. The effective yield stress is then obtained by multiplying the nominal yield stress by the yield factor corresponding to the actual pressure.
 If $\dot{\epsilon}\le {\dot{\epsilon}}_{n}$ , the yield stress is interpolated between ${\mathrm{f}}_{n}$ and ${\mathrm{f}}_{n1}$ .
 If $\dot{\epsilon}\le {\dot{\epsilon}}_{1}$ , function ${\mathrm{f}}_{1}$ is used.
 Above
${\dot{\epsilon}}_{\mathrm{max}}$
, yield stress is extrapolated.
Where,
 $\dot{\epsilon}$
 Total strain rate for VP =0
 $\dot{\epsilon}$
 Plastic strain rate for VP =1
 Separate functions must be defined for different strain rates.
 Strain rate values must be given in strictly ascending order.
 The evolution of Young's modulus:
 If fct_ID_{E} > 0, the curve defines a scale factor for Young's modulus
evolution with equivalent plastic strain, which means the Young's modulus is scaled by
the function
$\text{f}\left({\overline{\epsilon}}_{p}\right)$
:
(2) $$\mathrm{E}\left(t\right)=f\left({\overline{\epsilon}}_{p}\right)E$$The initial value of the scale factor should be equal to 1 and it decreases.
 If fct_ID_{E} = 0, the Young's modulus is calculated as:
(3) $$\mathrm{E}\left(t\right)=E(E{E}_{\mathrm{inf}})\left(1\mathrm{exp}({C}_{E}{\overline{\epsilon}}_{p})\right)$$Where, $E$ and ${E}_{\mathrm{inf}}$ are respectively the initial and asymptotic value of Young's modulus, and ${\overline{\epsilon}}_{p}$ is the accumulated equivalent plastic strain.Note: If fct_ID_{E} = 0 and ${C}_{E}$ = 0, Young's modulus $E$ is kept constant.
 If fct_ID_{E} > 0, the curve defines a scale factor for Young's modulus
evolution with equivalent plastic strain, which means the Young's modulus is scaled by
the function
$\text{f}\left({\overline{\epsilon}}_{p}\right)$
: