/MAT/LAW71
Block Format Keyword This law describes the behavior of superelastic materials. It allows modeling the behavior of the shape memory alloys (such as Nitinol).
The particularity of these materials is that all of the strain is recovered upon unloading even when large deformations are reached. Besides, the material shows a hysteretic response in a complete loadingunloading cycle. The full recovery is due to phase change in the microstructure. The model is based on the work of Auricchio et al. 1997. This law is compatible with solid and shell elements.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/MAT/LAW71/mat_ID/unit_ID  
mat_title  
${\rho}_{i}$  
E  $\upsilon $  E_mart  
${\sigma}_{S}^{AS}$  ${\sigma}_{F}^{AS}$  ${\sigma}_{S}^{SA}$  ${\sigma}_{F}^{SA}$  $\alpha $  
EpsL  CAS  CSA  TS_AS  TF_AS  
TS_SA  TF_SA  C_{p}  T_{ini} 
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) 

E_mart  Martensite Young's
modulus Default = 0.0 (Real) 
$\left[\text{Pa}\right]$ 
${\sigma}_{S}^{AS}$  Material parameter
defining the start of phase transformation from austenite to
martensite (AS). 1 (Real) 
$\left[\text{Pa}\right]$ 
${\sigma}_{F}^{AS}$  Material parameter
defining the end of phase transformation from austenite to
martensite (AS). 1 (Real) 
$\left[\text{Pa}\right]$ 
${\sigma}_{S}^{SA}$  Material parameter
defining the start of phase transformation from martensite
to austenite (SA). 1 (Real) 
$\left[\text{Pa}\right]$ 
${\sigma}_{F}^{SA}$  Material parameter
defining the end of phase transformation from martensite to
austenite (SA). 1 (Real) 
$\left[\text{Pa}\right]$ 
$\alpha $  Material parameter
measuring the difference in response between tension and
compression. Default = 0 (Real) 

EpsL  Maximum residual
strain. 2 (Real) 

CAS  StressTemperature
rate during loading. Default = 0 (Real) 
$\left[\frac{\mathrm{Pa}}{\mathrm{K}}\right]$ 
CSA  StressTemperature
rate during unloading. Default = 0 (Real) 
$\left[\frac{\mathrm{Pa}}{\mathrm{K}}\right]$ 
TS_AS  Reference
temperature for start of transformation (AS). Default = 298K (Real) 
$\left[\text{K}\right]$ 
TF_AS  Reference
temperature for rend of transformation (AS). Default = 298K (Real) 
$\left[\text{K}\right]$ 
TS_SA  Reference
temperature for start of transformation (SA). Default = 298K (Real) 
$\left[\text{K}\right]$ 
TF_SA  Reference
temperature for end of transformation (SA). Default = 298K (Real) 
$\left[\text{K}\right]$ 
C_{p}  Specific heat
capacity. Default = 10^{30} (Real) 
$\left[\frac{\text{J}}{\text{kg}\cdot \text{K}}\right]$ 
T_{ini}  Initial
temperature. Default = 360 K (Real) 
$\left[\text{K}\right]$ 
Example (Metal)
#RADIOSS STARTER
#12345678910
/UNIT/1
unit for mat
Mg mm s
#12345678910
# 2. MATERIALS:
#12345678910
/MAT/LAW71/1/1
metal
# RHO_I
6.50E9
# E Nu E_mart
62500 .3 51000
# sig_AS_s sig_AS_f sig_SA_s sig_SA_f alpha
450 600 300 200 0.20
# EpsL CAS CSA TS_AS TF_AS
0.045 1 1 383 343
# TS_SA TF_SA CP TINI
363 403 837 360
#ENDDATA
/END
#12345678910
Comments
 If E_mart=0, then Young's modulus is considered constant, equal to E, and not dependent on the phase fraction of the material.
 The different stresses ${\sigma}_{S}^{SA}$ , ${\sigma}_{F}^{AS}$ , ${\sigma}_{S}^{SA}$ and ${\sigma}_{F}^{SA}$ , defining the start and the end of phase transfomation, as well as the residual strain EpsL, correspond to the case of a uniaxial tensile test:
 The parameter
$\alpha $
is computed from the initial value of the
austenite to martensite phase transformation in tension
${\left({\sigma}_{S}^{AS}\right)}_{T}$
and compression
${\left({\sigma}_{S}^{AS}\right)}_{C}$
from the relation.
(1) $$\alpha =\sqrt{\frac{2}{3}}\frac{{\left({\sigma}_{S}^{AS}\right)}_{C}{\left({\sigma}_{S}^{AS}\right)}_{T}}{{\left({\sigma}_{S}^{AS}\right)}_{C}+{\left({\sigma}_{S}^{AS}\right)}_{T}}$$  The DruckerPragertype
loading function
$F$
is introduced using the stress deviator
$s$
, the pressure
$p$
and the temperature.
(2) $$F=\Vert s\Vert +3\alpha p$$Two functions are defined for the start and the final point of transformation from austenite to martensite (A → S) or from martensite to austenite (S → A).(A→S) (S →A) Start point of transformation ${F}_{S}^{AS}=F{R}_{S}^{AS}$ ${R}_{S}^{AS}={\sigma}_{S}^{AS}\left(\sqrt{\frac{2}{3}}+\alpha \right){C}^{AS}\left(T{T}_{S}^{AS}\right)$
${F}_{S}^{SA}=F{R}_{S}^{SA}$ ${R}_{S}^{SA}={\sigma}_{S}^{SA}\left(\sqrt{\frac{2}{3}}+\alpha \right){C}^{SA}\left(T{T}_{S}^{SA}\right)$
Final point of transformation ${F}_{F}^{AS}=F{R}_{F}^{AS}$ ${R}_{F}^{AS}={\sigma}_{F}^{AS}\left(\sqrt{\frac{2}{3}}+\alpha \right){C}^{AS}\left(T{T}_{F}^{AS}\right)$
${F}_{F}^{SA}=F{R}_{F}^{SA}$ ${R}_{F}^{SA}={\sigma}_{F}^{SA}\left(\sqrt{\frac{2}{3}}+\alpha \right){C}^{SA}\left(T{T}_{F}^{SA}\right)$
Condition ${F}_{S}^{AS}>0$ ${F}_{F}^{AS}<0$
$\dot{F}>0$
${F}_{S}^{SA}<0$ ${F}_{F}^{SA}>0$
$\dot{F}<0$
Evolution equation of martensite During loading: ${\dot{X}}_{m}=(1{X}_{m})\frac{\dot{F}}{F{R}_{F}^{AS}}$
During unloading: ${\dot{X}}_{m}={X}_{m}\frac{\dot{F}}{F{R}_{F}^{SA}}$
${\sigma}_{S}^{AS},{\sigma}_{F}^{AS},{T}_{S}^{AS},{T}_{F}^{AS},\alpha ,{C}^{AS},{\sigma}_{S}^{SA},{\sigma}_{F}^{SA},{T}_{S}^{SA},{T}_{F}^{SA},{C}^{SA}$ are the material parameters. The conversion of austenite to martensite takes place when above conditions (in table) are verified.
 List of Animation output
(/ANIM/BRICK/USRI):
 USR 1= Martensite phase fraction
 USR 2= Loading function
 USR 3= Unloading function