Piezoelectric Material
The Piezoelectric Material node defines the piezoelectric material properties either in stress-charge form using the elasticity matrix and the coupling matrix, or in strain-charge form using the compliance matrix and the coupling matrix. It is normally used together with a Piezoelectricity multiphysics coupling node and a corresponding Charge Conservation, Piezoelectric node in the Electrostatics interface. This node is added by default to the Solid Mechanics interface when adding a Piezoelectricity interface. Piezoelectric Material available for 3D, 2D, and 2D axisymmetry.
This material model requires the Structural Mechanics Module, or MEMS Module, or Acoustics Module.
By adding the following subnodes to the Piezoelectric Material node you can incorporate many other effects:
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Initial Stress and Strain
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Thermal Expansion (for Materials)
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Mechanical Damping
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Coupling Loss
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Dielectric Loss
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Conduction Loss (Time-Harmonic)
When the Piezoelectric Material node is added to the Solid Mechanics interface in the absence of an active Piezoelectricity multiphysics coupling node, the material behaves similarly to a Linear Elastic Material node. The elastic properties correspond to the elasticity or compliance matrix entered (see below). The piezoelectric effect is then not included in the equation system.
See also Piezoelectricity in the Structural Mechanics Theory chapter.
The Piezoelectric Material node is only available with some COMSOL products (see https://www.comsol.com/products/specifications/).
Piezoelectric Material Properties
Select a Constitutive relation — Stress-charge form or Strain-charge form. For each of the following, the default uses values From material. For User defined enter other values in the matrix or field as needed.
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For Stress-charge form, select an Elasticity matrix, Voigt notation (cE).
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For a Strain-charge form, select a Compliance matrix, Voigt notation (sE).
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Select a Coupling matrix, Voigt notation (eES or dET).
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Select a Relative permittivity (εrS or εrT).
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Enter values for the Remanent electric displacement (Dr).
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Select a Density (ρ).
For entering these matrices, use the following order (Voigt notation), which is the common convention for piezoelectric materials: xx, yy, zz, yz, xz, zy.
Check the Use multiplicative formulation check box to use a formulation based on the multiplicative decomposition of elastic and inelastic (piezoelectric) strains.
When the Use multiplicative formulation check box is selected, all studies in the model become geometrically nonlinear. The Include geometric nonlinearity check box on the study step Settings window is selected and cannot be cleared.
See also Multiplicative Formulation for Piezoelectricity in the Structural Mechanics Theory chapter.
Mixed Formulation
For a material with a very low compressibility, using only displacements as degrees of freedom may lead to a numerically ill-posed problem. You can then use a mixed formulation, which adds an extra dependent variable for either the pressure or for the volumetric strain. For details, see the Mixed Formulation section in the Structural Mechanics Theory chapter.
From the Use mixed formulation list, select None, Pressure formulation, or Strain formulation.
Density
If any material in the model has a temperature dependent mass density, and From material is selected, 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 density is needed for dynamic analysis and when computing mass forces for gravitational or rotating frame loads, and when computing mass properties (Computing Mass Properties).
See also
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Mass Density and Volume Reference Temperature.
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Using Common Model Input.
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Modeling Piezoelectric Problems in the Structural Mechanics Modeling chapter.
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Default Model Inputs and Model Input in the COMSOL Multiphysics Reference Manual.
Geometric Nonlinearity
The settings in this section control the overall kinematics, the definition of the strain decomposition, and the behavior of inelastic contributions, for the material.
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.
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.
When inelastic deformations are present, such as for plasticity, the elastic deformation can be obtained in two different ways: using additive decomposition of strains or using multiplicative decomposition of deformation gradients.
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.
The Strain decomposition input is only visible for material models that support both additive and multiplicative decomposition of deformation gradients.
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There are some cases when a small strain formulation could be useful for a certain domain, even though the study step is geometrically nonlinear. One such case is contact analysis, where the study step is always geometrically nonlinear, but where a geometrically linear formulation is sufficient for the material.
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When a multiplicative decomposition is used, the order of the subnodes matters. The inelastic deformations are assumed to occur in the same order as the subnodes appear in the model tree.
See Lagrangian Formulation, Deformation Measures, and Inelastic Strain Contributions in the Structural Mechanics Theory chapter.
See Modeling Geometric Nonlinearity in the Structural Mechanics Modeling chapter.
See Study Settings in the COMSOL Multiphysics Reference Manual.
Energy Dissipation
You can select to compute and store various energy dissipation variables in a time-dependent analysis. Doing so will add extra degrees of freedom to the model.
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.
Quadrature Settings
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.
See also Reduced Integration and Hourglass Stabilization in the Structural Mechanics Theory chapter.
Location in User Interface
Context Menus
Solid Mechanics>Material Models>Piezoelectric Material
Ribbon
Physics tab with Solid Mechanics selected:
Domains>Material Models>Piezoelectric Material