/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 loading-unloading 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)	(3)	(5)	(7)	(9)
/MAT/LAW71/`mat_ID`/`unit_ID`
`mat_title`
$ρ_{i}$
`E`	$υ$	`E_mart`
$σ_{sas}$	$σ_{fas}$	$σ_{ssa}$	$σ_{fsa}$	$α$
`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)
$ρ_{i}$	Initial density (Real)	$[\frac{kg}{m^{3}}]$
`E`	Young's modulus (Real)	$[Pa]$
$υ$	Poisson's ratio (Real)
`E_mart`	Martensite Young's modulus (only available for solid element). ≠ 0 `E` is austenite young's modulus. Default = `E` (Real)	$[Pa]$
$σ_{sas}$	Material parameter defining the start of phase transformation from austenite to martensite (AS). 1 (Real)	$[Pa]$
$σ_{fas}$	Material parameter defining the end of phase transformation from austenite to martensite (AS). 1 (Real)	$[Pa]$
$σ_{ssa}$	Material parameter defining the start of phase transformation from martensite to austenite (SA). 1 (Real)	$[Pa]$
$σ_{fsa}$	Material parameter defining the end of phase transformation from martensite to austenite (SA). 1 (Real)	$[Pa]$
α	Material parameter measuring the difference in response between tension and compression. Default = 0 (Real)
`EpsL`	Maximum residual strain. 2 (Real)
`CAS`	Stress-Temperature rate during loading. Default = 0 (Real)	$[\frac{Pa}{K}]$
`CSA`	Stress-Temperature rate during unloading. Default = 0 (Real)	$[\frac{Pa}{K}]$
`TSAS`	Initial temperature for transformation (AS). Default = 0 (Real)	$[K]$
`TFAS`	Final temperature for transformation (AS). Default = 0 (Real)	$[K]$
`TSSA`	Initial temperature for transformation (SA). Default = 0 (Real)	$[K]$
`TFSA`	Final temperature for transformation (SA). Default = 0 (Real)	$[K]$
`C`_p	Specific heat capacity. Default = 10³⁰ (Real)	$[\frac{J}{kg \cdot K}]$
`T`_ini	Initial temperature. Default = 360 K (Real)	$[K]$

Example

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
                  Mg                  mm                   s
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  2. MATERIALS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW71/1/1
metal
#              RHO_I
             6.50E-9
#                  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
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

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 ${(σ_{sas})}_{T}$ and compression ${(σ_{sas})}_{C}$ from the relation:(1)
$α \sqrt{\frac{2}{3}} \frac{{(σ_{sas})}_{C} - {(σ_{sas})}_{T}}{{(σ_{sas})}_{C} + {(σ_{sas})}_{T}}$

Figure 1.
List of Animation output (/ANIM/BRICK/USRI):
- USR 1= Martensite phase fraction
- USR 2= Loading function
- USR 3= Unloading function