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 Piezoelectric Effect 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 Piezoelectric Effect 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.
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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Default Model Inputs and Model Input in the COMSOL Multiphysics Reference Manual.
Geometric Nonlinearity
This section is only available when the check box Use multiplicative formulation is not selected.
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.
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Modeling Piezoelectric Problems
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Modeling Geometric Nonlinearity
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