FOR 5208 - Modelling and simulation of the coupled acoustic, electrical, and thermal dynamics of piezoceramics

The determination of material parameters of piezoceramics for actuator applications by means of an inverse method requires an efficient method for the simulation of the different physical processes in the piezoceramic sample. In addition to the electrostatic equations and acoustic wave propagation, this project focuses on the causal description of damping effects using a Zener model, self-heating of the piezoceramic material, heat transport and the nonlinear dependence of the material parameters on the field quantities. These physical processes will be represented in a phenomenological continuum model, which is described mathematically as a coupled nonlinear partial differential equation system. While in the subproject ANA an analytical approach is planned, in this subproject an efficient numerical evaluation with the help of the transient nodal Discontinous-Galerkin method is aimed at. For this purpose, the various physical processes will be considered successively, with the mathematical analyses from the subprojects ANA and OPT being incorporated in each step. Based on this, for each case the differential equations will be transformed into the DG formalism and implemented in a highly parallelized software tool. The implementations will be tested for convergence and verified with analytical solution properties from the subproject ANA. Together with the subproject OPT, algorithmic differentiation will be integrated into the simulation tool, so that sensitivity analyses are possible and gradient-based optimization methods can be used. A comparison with the experimental results from the subproject MESS takes place continuously. As a result, it will be possible to determine material parameters by means of an inverse method in the nonlinear operating regime, which is typical for power sound applications.

DFG Programme Research Units

Subproject of FOR 5208: Model-based determination of nonlinear properties of piezoceramics for high-power ultrasound applications (NEPTUN)