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, Layered multiphysics coupling node and a corresponding Piezoelectric Layer node in the Electric Currents in Layered Shells interface. This node is added by default to the Layered Shell interface when adding a Piezoelectricity, Layered Shell multiphysics interface.
The Piezoelectric Material node is only available with some COMSOL products (see https://www.comsol.com/products/specifications/).
When working with layered shells, you almost invariably take the material data from what has been defined using Layered Material Link, Layered Material Stack, or Single Layer Material nodes. It is however possible to override some data from a Piezoelectric Material node.
In order to have a correct model, all layers must have been assigned material data for all boundaries selected in the settings for the interface. The override rules for the material models in the Layered Shell interface cannot enforce this, in the same way as for other physics interfaces. You can have several Piezoelectric Material nodes with the same (or partially overlapping) geometrical selections, but with different layer selections.
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
When the Piezoelectric Material node is added to the Layered Shell interface in the absence of an active Piezoelectricity, Layered multiphysics coupling node, the material behaves similarly to a Linear Elastic Material node. The elastic properties will 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.
Shell Properties
Select the layer or layers for which this material model is to be used.
Table 6-4: Layer Selections; Piezoelectric Material.
Selection
Use All Layers
Selection of Individual Layers
Boundary
Same as interface selection when the node is added.
When Use all layers is not selected.
Only a subset of the layers selected in the parent can be selected.
Data given in the other sections of this node applies to all layers. Thus, if you enter material data explicitly, rather relying on the default From material option, you will override that material property for all selected layers.
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 (d).
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Select a Relative permittivity (erS or erT).
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Enter values for the Remanent electric displacement Dr.
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Select a Density (p).
For entering these matrices, use the following order (Voigt notation), which is the common convention for piezoelectric materials: xx, yy, zz, yz, xz, zy.
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 for dynamic analysis, and also when computing mass forces for gravitational or rotating frame loads.
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.
Out-of-plane Material Orientation
The layered material always operates with a boundary coordinate system on the base surface (laminate system). For such systems, the third base vector direction is always normal to the surface. Use a special control available in this section if you need to change the out-of-plane orientation of the material. This is essential if your piezoelectric device requires the pole direction to be tangential to the shell, but the pole direction in the material data coincides with the third coordinate axis — such material orientation is assumed for all the piezoelectric material data available in COMSOL Material Library.
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
To display this section, click the Show More Options button () and select Advanced Physics Options in the Show More Options dialog box.
Select the Calculate dissipated energy check box as needed to compute the energy dissipated by Mechanical damping.
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, and the shear correction factor kstb. The value for Gstb 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.
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Modeling Piezoelectric Problems
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Modeling Geometric Nonlinearity
Location in User Interface
Context Menus
Layered Shell>Material Models>Piezoelectric Material
Ribbon
Physics tab with Layered Shell selected:
Boundaries>Material Models>Piezoelectric Material