/MAT/LAW60 (PLAS_T3)
Block Format Keyword This law models an isotropic elastoplastic material using userdefined functions for the workhardening portion of the stressstrain curve (that is, plastic strain versus stress) for different strain rates.
It is similar to LAW36, except yield stress is a nonlinear interpolation from the functions.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/MAT/LAW60/mat_ID/unit_ID or /MAT/PLAS_T3/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}  
fct_ID_{p}  Fscale  fct_ID_{E}  E_{inf}  C_{E}  
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) 

fct_ID_{6}  fct_ID_{7}  fct_ID_{8}  fct_ID_{9}  fct_ID_{10} 
(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) 

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

${\dot{\epsilon}}_{1}$  ${\dot{\epsilon}}_{2}$  ${\dot{\epsilon}}_{3}$  ${\dot{\epsilon}}_{4}$  ${\dot{\epsilon}}_{5}$ 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

${\dot{\epsilon}}_{6}$  ${\dot{\epsilon}}_{7}$  ${\dot{\epsilon}}_{8}$  ${\dot{\epsilon}}_{9}$  ${\dot{\epsilon}}_{10}$ 
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) 
$\left[\text{Pa}\right]$ 
$\nu $  Poisson's
ratio. (Real) 

${\epsilon}_{p}^{max}$  Failure plastic
strain. Default = 1.0 × 10^{30} (Real) 

${\epsilon}_{t}$  Tensile failure strain at
which stress starts to reduce. Default = 1.0 x 10^{30} (Real) 

${\epsilon}_{m}$  Maximum tensile failure
strain at which the element is deleted. Default = 2.0 x 10^{30} (Real) 

N_{funct}  Number of functions. It
should be 4 <
N_{funct} <
10. Default ≤ 10 (Integer) 

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

C_{hard}  Hardening coefficient.
(Real) 

F_{cut}  Cutoff frequency for
strain rate filtering. 7 Default = 1.0 × 10^{30} (Real) 
$\text{[Hz]}$ 
fct_ID_{p}  Pressure versus yield
factor function. 9 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. 6 Default = 0: in this case the evolution of Young's modulus depends on E_{inf}_{.} and C_{E}. (Integer) 

E_{inf}  Saturated Young's modulus
for infinitive plastic strain. (Real) 
$\left[\text{Pa}\right]$ 
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) 

fct_ID_{6}  Yield stress function
identifier 6 corresponding to strain rate
${\dot{\epsilon}}_{6}$
. (Integer) 

fct_ID_{7}  Yield stress function
identifier 7 corresponding to strain rate
${\dot{\epsilon}}_{7}$
. (Integer) 

fct_ID_{8}  Yield stress function
identifier 8 corresponding to strain rate
${\dot{\epsilon}}_{8}$
. (Integer) 

fct_ID_{9}  Yield stress function
identifier 9 corresponding to strain rate
${\dot{\epsilon}}_{9}$
. (Integer) 

fct_ID_{10}  Yield stress function
identifier 10 corresponding to strain rate
${\dot{\epsilon}}_{10}$
. (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) 
$\left[\text{Pa}\right]$ 
Fscale_{6}  Scale factor for ordinate
(stress) in fct_ID_{6}. Default = 1.0 (Real) 
$\left[\text{Pa}\right]$ 
Fscale_{7}  Scale factor for ordinate
(stress) in fct_ID_{7}. Default = 1.0 (Real) 
$\left[\text{Pa}\right]$ 
Fscale_{8}  Scale factor for ordinate
(stress) in fct_ID_{8}. Default = 1.0 (Real) 
$\left[\text{Pa}\right]$ 
Fscale_{9}  Scale factor for ordinate
(stress) in fct_ID_{9}. Default = 1.0 (Real) 
$\left[\text{Pa}\right]$ 
Fscale_{10}  Scale factor for ordinate
(stress) in fct_ID_{10}. Default = 1.0 (Real) 
$\left[\text{Pa}\right]$ 
${\dot{\epsilon}}_{1}$  Strain rate
1. (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
${\dot{\epsilon}}_{2}$  Strain rate
2. (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
${\dot{\epsilon}}_{3}$  Strain rate
3. (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
${\dot{\epsilon}}_{4}$  Strain rate
4. (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
${\dot{\epsilon}}_{5}$  Strain rate
5. (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
${\dot{\epsilon}}_{6}$  Strain rate
6. (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
${\dot{\epsilon}}_{7}$  Strain rate
7. (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
${\dot{\epsilon}}_{8}$  Strain rate
8. (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
${\dot{\epsilon}}_{9}$  Strain rate
9. (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
${\dot{\epsilon}}_{10}$  Strain rate
10. (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/LAW60/1/1
Aluminium_example
# RHO_I
.0027
# E Nu Eps_p_max Eps_t Eps_m
60400 .33 0 0 0
# N_funct F_smooth C_hard F_cut
4 0 0 0
# fct_IDp Fscale Fct_IDE EInf CE
0 0 0 0 0
# Funtions
1 2 3 4
# Scale factors Fscale_5
1 1.2 1.4 1.6
# Strain rates Eps_dot_5
0 20 30 40
#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
#ENDDATA
#12345678910
Comments
 The first point of yield stress functions (plastic strain versus 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 ${\epsilon}_{p}$ .
 If ${\epsilon}_{p}$ (plastic strain) reaches ${\epsilon}_{p}^{max}$ , in one integration point, the element is deleted.
 If (largest principal strain)
${\epsilon}_{1}>{\epsilon}_{t}$
, stress is reduced using:
(1) $$\sigma =\sigma \left(\frac{{\epsilon}_{m}{\epsilon}_{1}}{{\epsilon}_{m}{\epsilon}_{t}}\right)$$  If ${\epsilon}_{1}>{\epsilon}_{m}$ , the element is deleted.
 The kinematic hardening model is not available in global formulation (hardening is fully isotropic).
 For kinematic hardening and strain rate dependency, yield stress depends on the strain rate.
 Strain rate filtering input (F_{cut}) is only available for shell and solid elements.
 Strain rate filtering is used to smooth strain rates.
 fct_ID_{p} is used to distinguish the behavior in tension and compression for certain materials (that is, pressure dependent yield). This is available for solid elements only. The effective yield stress is then obtained by multiplying the nominal yield stress by the yield factor corresponding to the actual pressure.
 If ${\dot{\epsilon}}_{n}\le \dot{\epsilon}\le {\dot{\epsilon}}_{n+1}$ , yield stress is a cubic interpolation between functions f_{n1}, f_{n}, f_{n+1} and f_{n+2}.
 If $\dot{\epsilon}\le {\dot{\epsilon}}_{1}$ , yield stress is interpolated between functions ${\mathrm{f}}_{1}$ , ${\mathrm{f}}_{2}$ and ${\mathrm{f}}_{3}$ .
 If ${\dot{\epsilon}}_{\mathit{Nfunc}1}\le \dot{\epsilon}\le {\dot{\epsilon}}_{\mathit{Nfunc}}$ , yield is extrapolated between functions f_{Nfunc3}, f_{Nfunc2}, f_{Nfunc1} and f_{Nfunc}.
 If $\dot{\epsilon}>{\dot{\epsilon}}_{\mathit{Nfunc}}$ , yield is extrapolated between functions f_{Nfunc2}, f_{Nfunc1} and f_{Nfunc}.
 Functions describing strain dependence must be defined for different strain rates values.
 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
$\mathrm{f}\left({\overline{\epsilon}}_{p}\right)$
:

$E\left(t\right)=E\cdot f\left({\overline{\epsilon}}_{p}\right)$
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:
(2) $$E\left(t\right)=E\left(E{E}_{\mathit{inf}}\right)\left[1exp\left({C}_{E}{\overline{\epsilon}}_{p}\right)\right]$$

$E\left(t\right)=E\cdot f\left({\overline{\epsilon}}_{p}\right)$
Where,
E and E_{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
$\mathrm{f}\left({\overline{\epsilon}}_{p}\right)$
: