The Shape Memory Alloy feature is used to model stress-strain relationships that are nonlinear even at infinitesimal strains. This material model requires the Nonlinear Structural Materials Module. Shape Memory Alloy is available for 3D, 2D, and 2D axisymmetry.

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 https://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. 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, the Shape memory alloy reference temperature T0, the Poisson’s ratio ν, and the 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, select which Transformation parameters will describe the phase transitions: Temperature or Stress.

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.

When Lagoudas model is selected, a Phase Transformation Direction subnode is added to the Shape memory alloy node. Select a Transformation direction from the list: Automatic (default) or User defined.

For Souza-Auricchio 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 Reference temperature T*, the Slope of limit curve β, the Maximum transformation strain εtr,max, the Elastic domain radius σ0, the Hardening modulus Hk, and the Indicator function coefficient γ.

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

For the 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 Geometrically linear formulation 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.

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

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

Select the Reduced integration check box to reduce the integration points for the weak contribution of the feature. Select a method for Hourglass stabilization — Automatic, Manual, or None to use in combination with the reduced integration scheme. The default Automatic stabilization technique is based on the shape function and shape order of the displacement field.

Control the hourglass stabilization scheme by using the Manual option. Select Shear stabilization (default) or Volumetric stabilization.

When Shear stabilization is selected, enter a stabilization shear modulus, Gstb. The value should be in the order of magnitude of the equivalent shear modulus.

When Volumetric stabilization is selected, enter a stabilization bulk modulus, Kstb. The value should be in the order of magnitude of the equivalent bulk modulus.

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

Physics tab with Solid Mechanics selected:

Physics tab with Truss selected: