Finite element modeling of piezoelectric elements with complex electrode configuration

Abstract

It is well known that the material properties of piezoelectric materials stronglydepend on the state of polarization of the individual element. While an unpolarizedmaterial exhibits mechanically isotropic material properties in the absence of globalpiezoelectric capabilities, the piezoelectric material properties become transversallyisotropic with respect to the polarization direction after polarization. Therefore, forevaluating piezoelectric elements the material properties, including the couplingbetween the mechanical and the electromechanical behavior, should be addressedcorrectly. This is of special importance for the micromechanical description ofpiezoelectric elements with interdigitated electrodes (IDEs). The best knownrepresentatives of this group are active fiber composites (AFCs), macro fibercomposites (MFCs) and the radial field diaphragm (RFD), respectively. While thematerial properties are available for a piezoelectric wafer with a homogeneouspolarization perpendicular to its plane as postulated in the so-called uniform fieldmodel (UFM), the same information is missing for piezoelectric elements withmore complex electrode configurations like the above-mentioned ones with IDEs.This is due to the inhomogeneous field distribution which does not automaticallyallow for the correct assignment of the material, i.e. orientation and property. Avariation of the material orientation as well as the material properties can beaccomplished by including the polarization process of the piezoelectric transducer in thefinite element (FE) simulation prior to the actual load case to be investigated. Acorresponding procedure is presented which automatically assigns the piezoelectricmaterial properties, e.g. elasticity matrix, permittivity, and charge vector, forfinite element models (FEMs) describing piezoelectric transducers according tothe electric field distribution (field orientation and strength) in the structure. Acorresponding code has been realized for a commercial finite element programallowing for an automatic assignment of different material properties for two- andthree-dimensional FEMs with arbitrary electrode configurations. Examples of piezoelectrictransducers with complex electrode configurations are presented and the influence ofthe material description on the behavior of the modeled element is discussed.Furthermore, as an attempt at verification of the FEM simulation, a comparison ofsimulated stress concentrations with experimental investigations is presented.