This material can be used to define elements to act as a void, or empty
space.
The constitutive model that is used in LAW71 to describe the shape memory alloy
superelastic behavior is based on the work of Auricchio.^{1}
Phase Transformation Conditions
Two phase transformations are considered:
 Transformation from austenite to martensite denoted AS (A→S)
 Transformation from martensite to austenite denoted SA (S→A)
A transformation strain is introduced dependent on the evolution of the fraction of
martensite:
(1)
$${\dot{\epsilon}}^{tr}={\epsilon}_{L}{\dot{X}}_{m}n$$
The stress deviator and pressure are updated using the fraction of martensite and
transformation strain:
(2)
$$s=2G(e{\epsilon}_{L}{X}_{m}n)$$
(3)
$$p=K(tr(\epsilon )3\alpha {\epsilon}_{L}{X}_{m})$$
$G$
and
$K$
are the shear and the bulk modulus, respectively. It
is possible to define these parameters dependent on the martensite fraction. In this
case,
$A$
and
$M$
subscripts refer to austenite and martensite,
respectively. The two moduli are calculated as:
(4)
$$G={G}_{A}+{X}_{m}({G}_{M}{G}_{A})$$
(5)
$K={K}_{A}+{X}_{m}({K}_{M}{K}_{A})$
Where,

$e$
 Deviator of the strain

$tr$
 Denotes the trace of the tensor

$Xm$
 Martensite fraction

${\epsilon}_{L}$
and
$a$
 Constant material parameters

$n$
 Unit vector is defined as
$n=\frac{e}{\Vert e\Vert}$
Transformation from Austenite to
Martensite
Two functions are defined for the start and the final point of
transformation. These functions are expressed as:
(6)
$${F}_{S}^{SA}={F}^{SA}{R}_{S}^{SA}$$
(7)
$${F}_{F}^{SA}={F}^{SA}{R}_{F}^{SA}$$
Where,
(8)
$${R}_{S}^{SA}={\sigma}_{S}^{SA}\left(\sqrt{\frac{2}{3}}+\alpha \right){C}^{SA}{T}_{S}^{SA}$$
(9)
$${R}_{F}^{SA}={\sigma}_{F}^{SA}\left(\sqrt{\frac{2}{3}}+\alpha \right){C}^{SA}{T}_{F}^{SA}$$
The loading function
${F}^{SA}$
is computed using the stress deviator
$s$
, the pressure
$p$
, and the temperature:
(10)
$${F}^{SA}=\Vert s\Vert +3\alpha p{C}^{SA}T$$
Where,
$a$
,
${\sigma}_{S}^{SA}$
,
${\sigma}_{F}^{SA}$
,
${T}_{S}^{SA}$
,
${T}_{F}^{SA}$
, and
${C}^{SA}$
are the material parameters.
The conversion of
austenite to martensite takes place when the following conditions are
verified:
(11)
$${F}_{S}^{SA}<0$$
(12)
$${F}_{F}^{SAS}>0$$
(13)
$${\dot{F}}_{}^{SAS}<0$$