Simulation Based Determination of Piezoelectric Material Parameters

Abstract

AbstractThe exact numerical simulation of piezoelectric transducers needs the knowledge of all material tensors that occur in the piezoelectric constitutive relations. The determination of these tensors is achieved by a simulation based algorithm which adjusts the 3D ‐ FEM simulated data with electrical measurements of a piezoelectric transducer. Its advantage compared to the standards (see [1], [2]) lies in the fact that a determination of the complete set of material parameters from one arbitrarily shaped specimen with a high precision is possible. The reconstruction of the material tensors is formulated as a parameter identification problem for a system of PDEs. Since unique solvability of this inverse problem may hardly be verified, the system of equations we have to solve for recovering the material tensor entries can be rank deficient and therefore requires application of appropriate regularization strategies. For this purpose, we use inexact Newton methods. The material parameters are assumed to be complex‐valued which allows to account for mechanical, dielectric and piezoelectric losses. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)