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:
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
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.
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When Temperature is selected from the Specify list, 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.
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When Stress is selected from the Specify list, enter the Martensite start stress σMs, the Martensite finish stress σMf, the Slope of martensite limit curve CM, the Austenite start stress σAs, the Austenite finish stress σAf, the Slope of austenite limit curve CA, and the Measurement temperature Tσ.
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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.
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When Standard is selected from the Specify list, enter the Elastic domain radius σ0, the Hardening modulus Hk, and the Reference temperature T*.
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When Stress is selected from the Specify list, enter the Martensite start stress σMs, the Martensite finish stress σMf, the Austenite finish stress σAf, and the Measurement temperature Tσ.
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When Temperature is selected from the Specify list, enter the Martensite start temperature Ms, the Martensite finish temperature Mf, and the Austenite finish temperature Af.
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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 (default),
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.
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With the default From study step, a total Lagrangian formulation for large strains is used when the Include geometric nonlinearity check box is selected in the study step. If the check box is not selected, the formulation is geometrically linear, with a small strain formulation.
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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 check box in all study steps.
Select a Strain decomposition —
Automatic (default),
Additive, or
Multiplicative to decide how the inelastic deformations are treated. This option is not available when the formulation is set to
Geometrically linear.
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When Automatic is selected, a multiplicative or additive decomposition is used with a total Lagrangian formulation, depending on the Include geometric nonlinearity check box status in the study step.
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Select Additive to force an additive decomposition of strains.
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Select Multiplicative to force a multiplicative decomposition of deformation gradients. This option is only visible if Formulation is set to Total Lagrangian.
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The Strain decomposition input is only visible for material models that support both additive and multiplicative decomposition of deformation gradients.
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.
Select the Local method to solve the plasticity type 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:
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Maximum number of local iterations. To determine the maximum number of iteration in the Newton loop when solving the local plasticity equations. The default value is 25 iterations.
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Relative tolerance. To check the convergence of the local plasticity equations based on the step size in the Newton loop. The final tolerance is computed based on the current solution of the local variable and the entered value. The default value is 1e-6.
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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 check box to specify a transition zone size for the inequality.
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:
