/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  
${\sigma}_{\mathit{sas}}$  ${\sigma}_{\mathit{fas}}$  ${\sigma}_{\mathit{ssa}}$  ${\sigma}_{\mathit{fsa}}$  $\alpha $  
EpsL  CAS  CSA  TSAS  TFAS  
TSSA  TFSA  C_{p}  T_{ini} 
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) 
$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$ 
E  Young's
modulus (Real) 
$\left[\text{Pa}\right]$ 
$\upsilon $  Poisson's
ratio (Real) 

E_mart  Martensite Young's
modulus (only available for solid element).
Default = E (Real) 
$\left[\text{Pa}\right]$ 
${\sigma}_{\mathit{sas}}$  Material parameter
defining the start of phase transformation from austenite to
martensite (AS). 1 (Real) 
$\left[\text{Pa}\right]$ 
${\sigma}_{\mathit{fas}}$  Material parameter
defining the end of phase transformation from austenite to
martensite (AS). 1 (Real) 
$\left[\text{Pa}\right]$ 
${\sigma}_{\mathit{ssa}}$  Material parameter
defining the start of phase transformation from martensite
to austenite (SA). 1 (Real) 
$\left[\text{Pa}\right]$ 
${\sigma}_{\mathit{fsa}}$  Material parameter
defining the end of phase transformation from martensite to
austenite (SA). 1 (Real) 
$\left[\text{Pa}\right]$ 
α  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) 
$\left[\frac{\mathrm{Pa}}{\mathrm{K}}\right]$ 
TSAS  Initial temperature
for transformation (AS). Default = 0 (Real) 
$\left[\text{K}\right]$ 
TFAS  Final temperature
for transformation (AS). Default = 0 (Real) 
$\left[\text{K}\right]$ 
TSSA  Initial temperature
for transformation (SA). Default = 0 (Real) 
$\left[\text{K}\right]$ 
TFSA  Final temperature
for transformation (SA). Default = 0 (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
#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_sas sig_fas sig_ssa sig_fsa alpha
450 600 300 200 0.20
# EpsL CAS CSA TSAS TFAS
0.045 1 1 383 343
# TSSA TFSA CP TINI
363 403 837 360
#ENDDATA
/END
#12345678910
Comments
 The different stresses defining the start and the end of phase transformations, as well as the residual strain, correspond to the case of a uniaxial tensile test.
 The parameter α is computed from the initial value of the A → S phase transformation in
tension
${\left({\sigma}_{\mathit{sas}}\right)}_{T}$
and compression
${\left({\sigma}_{\mathit{sas}}\right)}_{C}$
from the relation:
(1) $$\alpha \sqrt{\frac{2}{3}}\frac{{\left({\sigma}_{\mathit{sas}}\right)}_{C}{\left({\sigma}_{\mathit{sas}}\right)}_{T}}{{\left({\sigma}_{\mathit{sas}}\right)}_{C}+{\left({\sigma}_{\mathit{sas}}\right)}_{T}}$$List of Animation output (/ANIM/BRICK/USRI): USR 1= Martensite phase fraction
 USR 2= Loading function
 USR 3= Unloading function