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 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 an 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 an expression for the reference temperature locally.

The Global coordinate system is selected by default. The Coordinate system list contains all applicable coordinate systems in the component. The coordinate system is used for interpreting directions of orthotropic and anisotropic material data and 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 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, specify the parameters that describe the phase transitions in terms of Temperature or Stress levels.

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 specify how the Equivalent stress is computed. Select von Mises for a symmetric elastic domain radius in tension or compression. Select Prager–Lode to specify the Stress ratio between the elastic domain radius in compression and tension.

The default values for the Slope of limit curve β and the Maximum transformation strain εtr,max are taken From material. For User defined enter other values or expressions.

Specify the parameters that describe the phase transitions in terms of Temperature or Stress levels.

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.

Select a Formulation — From study step, Total Lagrangian, or Geometrically linear to set the kinematics of the deformation and the definition of strain. When From study step is selected, the study step controls the kinematics and the strain definition.

When From study step is selected, a total Lagrangian formulation for large strains is used when the Include geometric nonlinearity checkbox is selected in the study step. If the checkbox is not selected, the formulation is geometrically linear, with a small strain formulation.

To have full control of the formulation, select either Total Lagrangian, or Geometrically linear. When Total Lagrangian is selected, the physics will force the Include geometric nonlinearity checkbox in all study steps.

Select a Strain decomposition — Automatic, Additive, Logarithmic, or Multiplicative to decide how the inelastic deformations are treated. This option is not available when the formulation is set to Geometrically linear.

The Strain decomposition input is only visible for material models that support both additive and multiplicative decomposition of the deformation gradient.

Only the additive decomposition of strains is available for Lagoudas model.

Select how to compute the energy dissipated by Creep, Plasticity, Viscoplasticity, or other dissipative processes.

Select how to Store dissipation — From physics interface, Individual contributions, Total, Domain ODEs (legacy), or Off.

Use From physics interface to treat the dissipative processes as specified in the settings of the physics interface, see for instance Energy Dissipation in the Solid Mechanics interface.

Use Individual contributions to treat each dissipative process independently. Selecting this option gives a more flexible implementation for problems where dissipation occurs at different time scales, and you want to distinguish each phenomenon separately.

Use Total to accumulate all the dissipative processes into one common variable.

Use Domain ODEs to accumulate the dissipative processes into ODE variables instead of internal state variables.

Select the Reduced integration checkbox to reduce the number of integration points used for the weak contribution in the material. Reduced integration give faster computations at the element level and help mitigate locking issues. However, reduced integration may also introduce numerical instabilities, which then require an additional stabilization term.

By default, the Reduced integration checkbox is cleared, except in interfaces designed for explicit dynamic analysis, where it is always selected.

Select a method for Hourglass stabilization — Automatic, Energy sampling, Hessian, Flanagan–Belytschko, Manual, or None to be used in combination with the reduced integration scheme.

The Automatic option selects the stabilization method and its properties based on the physics interface, space dimension, shape function type and order of the displacement field, and the study type.

For the Energy sampling, Hessian, and Flanagan–Belytschko methods, the hourglass stiffness can be scaled by specifying a stiffness multiplier fstb. This multiplier can be an expression of any parameter or variable in the model. This multiplier can be expressed as any parameter or variable in the model. However, to maintain computational efficiency, avoid expensive definitions such as nonlocal coupling operators.

For the hourglass stabilization methods, the stiffness is automatically adjusted during the solution process using an internal multiplier. This accounts for the effect of inelastic deformations, such as damage and plasticity. This correction can be disabled by setting Inelastic deformations to Ignore. Ignoring inelastic deformations may be necessary for scenarios like cyclic loading, where the hourglass stiffness could become too small during unloading. Alternatively, adjust the value for the Minimum stiffness multiplier., which acts as a lower bound for the hourglass stiffness, which is applied in addition to any expression entered for fstb.

For the Energy sampling method, the default stabilization uses an isotropic linear elastic potential. Set the Energy Sampling Potential to Hyperelastic for large deformations. When selected, a neo-Hookean potential is used for nonlinear strains, while linear strains use the linear elastic potential.

The Hessian method evaluates a weak contribution using the reduced integration order. For hexahedral mesh elements, this approach may not suppress all hourglass modes. In most cases, non-stabilized modes are suppressed by constraints adjacent to the domain, but if they are not, select Use full integration to increase the integration order of the stabilization equations to suppress all modes. The higher integration order will increase the computational cost of the stabilization method.

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

Select the Local method to solve the plasticity problem — Automatic or Backward Euler. When Backward Euler is selected, it is possible to specify the maximum number of iterations and the relative tolerance used to solve the local plasticity equations. Enter the following settings:

For the Lagoudas model, under Volume fraction constraint enter the Penalty factor γ to constrain the martensite volume fraction by the inequality ξM − 1 < 0.

For the Souza–Auricchio model, under Transformation strain constraint enter the Penalty factor γ to constrain the equivalent transformation strain by the inequality εtre − εtre,max < 0.

Check the Use transition zone checkbox to specify a transition zone size for the inequality.

Physics tab with Solid Mechanics selected:

Physics tab with Truss selected: