Enthalpy-based homogenization procedure for composite piezoelectric modules with integrated electrodes
A new enthalpy-based procedure for the homogenization of the material parameters of composite piezoelectric modules is presented. It is based on a finite element (FE) modelling of the latter representative volume element (RVE). In contrast to previously published homogenization approaches that are based on averaged quantities, the presented method uses a direct evaluation of the electromechanical enthalpy. Hence, for the linear orthotropic piezoelectric composite full set of elastic, piezoelectric, and dielectric material parameters 17 load cases are used, where each load case leads directly to one material parameter. This gives the possibility to elaborate a very strict and easy to program processing. In conjunction with the 17 load cases, the enthalpy-based evaluation is necessary to consider piezoelectric modules with integrated electrodes correctly. In this case, the electric load has to be given at the electrodes rather than at the FE model boundaries. It is shown that this approach has the advantage to ensure consistent results for this case. The approach is demonstrated on an example derived from a previously published work on the so-called d15 shear piezoelectric macro-fibre composite module and is compared to the results achieved there.