/MAT/LAW66
Block Format Keyword This law models an isotropic tensioncompression elastoplastic material law using userdefined functions for the workhardening portion of the stressstrain (plastic strain versus stress). This law can be defined for compression and tension.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/MAT/LAW66/mat_ID/unit_ID  
mat_title  
${\rho}_{i}$  
E  $\upsilon $  C_{hard}  F_{cut}  F_{smooth}  I_{yld_rate}  
P_{c}  P_{t}  Ec  RPCT 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

fct_ID_{c}  fct_ID_{t}  Fscale_{c}  Fscale_{t}  
${\dot{\epsilon}}_{0}$  c  ${\sigma}_{y0}$  VP 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

fct_ID_{c}  fct_ID_{t}  Fscale_{c}  Fscale_{t}  
Frate_ID_{c}  Frate_ID_{t}  Fscale_rate_{c}  Fscale_rate_{t} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

NFUNCC  NFUNCT 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

fct_ID_{c}  ${\dot{\epsilon}}_{i}^{c}$  Fscale_{c} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

fct_ID_{t}  ${\dot{\epsilon}}_{i}^{t}$  Fscale_{t} 
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) 
$\left[\text{Pa}\right]$ 
$\upsilon $  Poisson's ratio. (Real) 

C_{hard}  Hardening coefficient.
(Real) 

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

F_{cut}  Cutoff frequency for strain rate
filtering, Appendix: Filtering. Default = 10^{30} (Real) 
$\text{[Hz]}$ 
I_{yld_rate}  Rate effect on the yield stress flag.
(Integer) 

P_{c}  Limit pressure in compression. Default = 0 (Real) 
$\left[\text{Pa}\right]$ 
P_{t}  Limit pressure in tensile. Default = 0 (Real) 
$\left[\text{Pa}\right]$ 
Ec  (Optional) Compression Young’s modulus.
2 (Real) 
$\left[\text{Pa}\right]$ 
RPCT  Scale factor used on
P_{c} and
P_{t}. 2 (Real) 

fct_ID_{c}  Compression yield
stress. (Integer) 

fct_ID_{t}  Tension yield
stress. (Integer) 

Fscale_{c}  Scale factor for ordinate (stress) in
fct_ID_{c}. Default = 1.0 (Real) 
$\left[\text{Pa}\right]$ 
Fscale_{t}  Scale factor for ordinate (stress) in
fct_ID_{t}. Default = 1.0 (Real) 
$\left[\text{Pa}\right]$ 
c  Strain rate
parameter. (Real) 

${\dot{\epsilon}}_{0}$  Reference strain rate. Default = 1.0 (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
${\sigma}_{y0}$  Initial yield stress. Default = 0 (Real) 
$\left[\text{Pa}\right]$ 
VP  Strain rate choice flag.
(Integer) 

Frate_ID_{c}  Compression strain rate effect function
identifier. (Integer) 

Frate_ID_{t}  Tension strain rate effect function
identifier. (Integer) 

Fscale_rate_{c}  Scale factor for ordinate (stress) in
Frate_ID_{c}. Default = 1.0 (Real) 
$\left[\text{Pa}\right]$ 
Fscale_rate_{t}  Scale factor for ordinate (stress) in
Frate_ID_{t}. Default = 1.0 (Real) 
$\left[\text{Pa}\right]$ 
NFUNCC  Number of compression
function. (Integer) 

NFUNCT  Number of tension
function. (Integer) 

${\dot{\epsilon}}_{i}^{c}$  i^{th}
compression strain rate i
=1,NFUNCC. (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
${\dot{\epsilon}}_{i}^{t}$  i^{th}
tension strain rate
i=1,NFUNCT. (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
Example (Aluminum)
#RADIOSS STARTER
/UNIT/1
unit for mat
g mm ms
#12345678910
# 2. MATERIALS:
#12345678910
/MAT/LAW66/1/1
Aluminum
# RHO_I
.0027
# E Nu C_hard F_cut F_smooth Iyld_rate
60400 .33 0 0 0 4
# P_c P_t
500 600
# NFUNCC NFUNCT
2 2
#funct_IDc Epsilon_c Fscalec
38 10 1
40 40 1.6
#funct_IDt Epsilon_t Fscalet
38 10 1
40 40 1.6
#12345678910
# 3. FUNCTIONS:
#12345678910
/FUNCT/38
function_38
# X Y
0 90
.08 170
#12345678910
/FUNCT/40
function_40
# X Y
0 90
.08 170
#12345678910
#ENDDATA
/END
#12345678910
Example (Optional Compression Young’s Modulus)
#RADIOSS STARTER
#12345678910
## Material Law
#12345678910
/MAT/LAW66/1
20MAT124_20degree
# RHO_I
1.25000000000000E09
# E Nu C_hard F_cut F_smooth Iyld_rate
210000.0 0.33 0.0 0.0 0 1
# P_c P_t EC RPCT
0.0 0.0 70000.
#funct_IDc funct_IDt Fscalec Fscalet
34 34 100.0 200.0
# Epsilon_0 c Sigma_Y0 VP
0.0 0.0 0.0 0
#12345678910
##HWCOLOR curves 24 9
/FUNCT/24
20deg_TENSION
# X Y
0.0 0.200535124
1.11148000000000E04 0.23893938
2.47763000000000E04 0.274602617
3.84248000000000E04 0.308164207
5.81974000000000E04 0.354639794
7.98180000000000E04 0.395218545
1.03131900000000E03 0.43242102
0.001382833 0.473801266
0.001747862 0.508073173
0.002139804 0.539268776
0.002704889 0.577068218
0.003299031 0.610692299
0.004078009 0.646563755
0.005715537 0.702190108
1.0 0.75
#12345678910
/FUNCT/34
20deg_COMPRESSION
# X Y
0.0 0.709520996
0.002556758 0.768542475
0.005112572 0.814793042
0.007700089 0.850991269
0.010231756 0.877769462
0.012846771 0.896395146
0.015380438 0.909432849
0.020500175 0.924867455
0.030979299 0.948100519
0.073545677 1.001804424
0.126630132 1.075808748
0.245056814 1.17707424
1.0 1.2
#enddata
Comments
 This is an
isotropic elasticplastic law. The yield stress is defined by using the compression and
tension yield stress versus effective plastic strain for the both (compression and tension).
When exceeded, the two pressures P_{t} and
P_{c}, determine if the tension yield stress
or compression yield stress is used respectively.
If the pressure is between these two values, the yield stress is given by:
If ${P}_{t}\le P\le {P}_{c}$
$$\begin{array}{l}{\sigma}_{y}=\alpha {\sigma}_{y}^{t}\text{\hspace{0.17em}}({\epsilon}_{p})+(1\alpha )\text{\hspace{0.17em}}{\sigma}_{y}^{c}\text{\hspace{0.17em}}({\epsilon}_{p})\hfill \\ \alpha =\frac{{P}_{c}P}{{P}_{e}+{P}_{t}}\hfill \end{array}$$If ${P}_{t}={P}_{c}=0$ , or the pressure is out of the two values range, the yield stress is given by:
${\sigma}_{y}={\sigma}_{y}^{t}\left({\epsilon}_{p}\right)$ if $P\le 0$
${\sigma}_{y}={\sigma}_{y}^{c}\left({\epsilon}_{p}\right)$ if $P>0$
 If Ec is defined, the
Young's modulus is defined as:
 Young’s modulus is E, if P > RPCT * P_{t}
 Young’s modulus is Ec, if P < RPCT * P_{c}
 Linear interpolation is done between E and Ec, if RPCT * P_{t} < P < RPCT * P_{c}
 Yield stress is computed as:
If VP= 1:
${\sigma}_{y}\left({\epsilon}_{p},{\dot{\epsilon}}_{p}\right)={\sigma}_{y}^{s}\left({\epsilon}_{p}\right)+{\sigma}_{y0}{\left(\frac{{\dot{\epsilon}}_{p}}{{\dot{\epsilon}}_{0}}\right)}^{\frac{1}{c}}$ if ${\sigma}_{y0}>0$
${\sigma}_{y}\left({\epsilon}_{p},{\dot{\epsilon}}_{p}\right)={\sigma}_{y}^{s}\left({\epsilon}_{p}\right)\left[1+{\left(\frac{{\dot{\epsilon}}_{p}}{{\dot{\epsilon}}_{0}}\right)}^{\frac{1}{c}}\right]$ if ${\sigma}_{y0}=0$
If VP= 0:
${\sigma}_{y}\left({\epsilon}_{p},{\dot{\epsilon}}_{p}\right)={\sigma}_{y}^{s}\left({\epsilon}_{p}\right)$ if ${\sigma}_{y0}>0$
${\sigma}_{y}\left({\epsilon}_{p},{\dot{\epsilon}}_{p}\right)={\sigma}_{y}^{s}\left({\epsilon}_{p}\right)$ if ${\sigma}_{y0}=0$
with ${\sigma}_{y}^{t}\left({\epsilon}_{p}\right)$ being static yield stress and ${\sigma}_{y0}$ being initial yield stress.
 /VISC/PRONY can be used with this material law to include viscous effects.