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, Time Explicit multiphysics coupling node and a corresponding Charge Conservation, Piezoelectric node in the Electrostatics interface. This node is added by default to the Elastic Waves, Time Explicit interface when adding a Piezoelectric Waves, Time Explicit multiphysics interface.
This material model requires the Structural Mechanics Module, MEMS Module, or Acoustics Module.
When the Piezoelectric Material node is added to the Elastic Waves, Time Explicit interface in the absence of an active Piezoelectric Effect, Time Explicit multiphysics coupling node, the material behaves similarly to an Elastic Waves, Time Explicit Model 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.
Coordinate System Selection
Select the Coordinate system that defines the polarization orientation of the piezoelectric crystal. The default is the Global coordinate system. The polarization is defined in the local x-axis direction in 2D, while it uses the local z-axis in 2D axisymmetry and 3D.
For entering the material properties matrices (see below), use the following order (Voigt notation), which is the common convention for piezoelectric materials: xx, yy, zz, yz, xz, zy.
Piezoelectric Material Properties
Select a Constitutive relation as Stress-charge form (the default) 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).
Lax-Friedrich Flux Parameter
See Lax–Friedrichs Flux Parameter.
Filter Parameters
See Filter Parameters.
Estimate of Maximum Wave Speed
See Estimate of Maximum Wave Speed.