# Shape Memory Superelastic Material (LAW71)

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

- 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:

The stress deviator and pressure are updated using the fraction of martensite and transformation strain:

$G$ 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:

- $e$
- 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:

The conversion of austenite to martensite takes place when the following conditions are verified:

^{1}F. Auricchio, R.L. Taylor. Shape memory alloys: modeling and numerical simulations of the finite- strain superelastic behavior. Comput. Methods Appl. Mech. Engrg. 143 (1997) 175-194.