The Shape Memory Alloy feature is used to model stress-strain relationships which are nonlinear even at infinitesimal strains. It is available in the Solid Mechanics interface. This material model requires the Nonlinear Structural Materials Module.

By adding the following subnodes to the Shape Memory Alloy node you can incorporate other effects:

Note: Some options are only available with certain COMSOL products (see http://www.comsol.com/products/specifications/)

From the Temperature T list, select an existing temperature variable from a heat transfer interface (for example, Temperature (ht)), if any temperature variables exist, or select User defined to enter a value or expression for the temperature.

If any material in the model has a temperature dependent mass density, and From material is selected for the density, the Volume reference temperature list will appear in the Model Input section. As a default, the value of Tref is obtained from a Common model input. You can also select User defined to enter a value or expression for the reference temperature locally.

The Global coordinate system is selected by default. The Coordinate system list contains any additional coordinate systems that the model includes (except boundary coordinate systems). The coordinate system is used when stresses or strains are presented in a local system. The coordinate system must have orthonormal coordinate axes, and be defined in the material frame. Many of the possible subnodes inherit the coordinate system settings.

Select a Shape memory alloy model from the list: Lagoudas or Souza-Auricchio.

For Lagoudas enter the Shape memory alloy reference temperature T0. The defaults for the Poisson’s ratio ν and Density ρ, are taken From material. For User defined enter other values or expressions.

For Austenite, select a material from the list. The Young’s modulus EA and the Heat capacity at constant pressure Cp,A are taken from the selected material. For Martensite, select a material from the list. The Young’s modulus EM and the Heat capacity at constant pressure Cp,M are taken from the selected material. For User defined enter other values or expressions.

Under Phase transformation parameters, enter the Martensite start temperature Ms, the Martensite finish temperature Mf, the Slope of martensite limit curve CM, the Austenite start temperature As, the Austenite finish temperature Af, and the Slope of austenite limit curve CA.

Under the Maximum transformation strain list select Constant to directly enter the Maximum transformation strain εtr,max, or Exponential law to specify a stress-dependent maximum transformation strain. Under Exponential law, enter the Initial maximum transformation strain εtr,min, the Ultimate transformation strain εtr,sat, the Critical stress σcrit, and the Saturation exponent k. Enter the Calibration stress level σ*.

Under Phase transformation kinetics, select the Transformation function from the list: Quadratic, Cosine, Smooth or User defined.

For Smooth, enter the smoothing parameters η1, η2, η3, and η4.

For User defined enter the Yield stress σys, the Forward transformation law, and the Reverse transformation law.

For Souza-Auriccio the defaults for the Poisson’s ratio ν and Density ρ, are taken From material. For User defined enter other values or expressions.

For Austenite, select a material from the list. The Young’s modulus EA is taken from the selected material. For Martensite, select a material from the list. The Young’s modulus EM is taken from the selected material. For User defined enter other values or expressions.

Under Phase transformation parameters, enter the Martensite finish temperature Mf, the Slope of limit curve β, the Maximum transformation strain εtr,max, the Initial yield stress σys0, the Hardening modulus Hk, and the Indicator function coefficient γ.

For Laogudas model, enter the Initial martensite volume fraction, the Initial transformation strain tensor and the Initial transformation strain tensor at reverse point.

For Souza-Auricchio model, enter the Initial transformation strain tensor.

If a study step is geometrically nonlinear, the default behavior is to use a large strain formulation in all domains. There are, however, some cases when the use of a small strain formulation for a certain domain is needed. In those cases, select the Force linear strains check box. When selected, a small strain formulation is always used, independently of the setting in the study step. The check box is not selected by default to conserve the properties of the model.

When a geometrically nonlinear formulation is used, the elastic deformations used for computing the stresses can be obtained in two different ways if inelastic deformations are present: additive decomposition and multiplicative decomposition. The default is to use multiplicative decomposition. Select Additive strain decomposition to change to an assumption of additivity.

To display this section, click the Show More Options button () and select Advanced Physics Options in the Show More Options dialog box.

Select the Calculate dissipated energy check box as needed to compute the energy dissipated.

Physics tab with Solid Mechanics selected:

The Phase Transformation Direction node is automatically added to Shape Memory Alloy node. Since in many applications the transformation direction is known a priori (for instance, mechanical loading or unloading, or temperature increment/decrement) a user input enables to set the transformation direction manually to 1 or -1, thus speeding up the computational time.

Select a Transformation Direction — Automatic or User Defined.

Physics tab with Shape Memory Alloy node selected in the model tree: