Piezoelectric Material

The 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 multiphysics coupling node and a corresponding node in the interface. This node is added by default to the interface when adding a multiphysics interface.

The 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 , , or nodes. It is however possible to override some data from a 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 nodes with the same (or partially overlapping) geometrical selections, but with different layer selections.

By adding the following subnodes to the node you can incorporate many other effects:

•

Initial Stress and Strain

•

Thermal Expansion (for Materials)

•

Mechanical Damping

•

Coupling Loss

•

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 option, you will override that material property for all selected layers.

Piezoelectric Material Properties

Select a — or . For each of the following, the default uses values . For enter other values in the matrix or field as needed.

•

For , select an (cE).

•

For a , select a (sE).

•

Select a (d).

•

Select a (erS or erT).

•

Enter values for the Dr.

•

Select a (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 is selected, the list will appear in the section. As a default, the value of Tref is obtained from a . You can also select 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

•

Mass Density and Volume Reference Temperature.

•

Using Common Model Input

•

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 — (default), , or to set the kinematics of the deformation and the definition of strain. When is selected, the study step controls the kinematics and the strain definition.

•

With the default , a total Lagrangian formulation for large strains is used when the 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 , or . When is selected, the physics will force the 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 — (default), , or to decide how the inelastic deformations are treated. This option is not available when the formulation is set to .

•

When is selected, a multiplicative or additive decomposition is used with a total Lagrangian formulation, depending on the check box status in the study step.

•

Select to force an additive decomposition of strains.

•

Select to force a multiplicative decomposition of deformation gradients. This option is only visible if is set to .

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

•

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.

•

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 button (

) and select in the dialog box.

Select the check box as needed to compute the energy dissipated by .

Quadrature Settings

Select the check box to reduce the integration points for the weak contribution of the feature. Select a method for — , , or to use in combination with the reduced integration scheme. The default stabilization technique is based on the shape function and shape order of the displacement field.

Control the hourglass stabilization scheme by using the option. Select (default) or .

When 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 is selected, enter a stabilization bulk modulus, Kstb. The value should be in the order of magnitude of the equivalent bulk modulus.

•

Modeling Piezoelectric Problems

•

Modeling Geometric Nonlinearity

Location in User Interface

Context Menus

Ribbon

Physics tab with selected: