Analysis of Electromechanical Stress Singularity in Piezoelectrics by Computed Eigensolutions and Hybrid-trefftz Finite Element Models

Abstract

This paper concerns the determination of singular electromechanical stress field in piezoelectrics. A one-dimensional finite element procedure is generalized to compute the eigensolutions of the singular electromechanical field. The generalized procedure is capable of taking differently poled piezoelectrics, cracks and ultra-thin electrodes into account. To determine the strength of the singular electromechanical stress field, the hybrid-Trefftz finite element method is adopted. The independently assumed electromechanical stress modes are extracted from the eigensolutions previously computed from the one-dimensional procedure. Since the eigensolutions satisfy all the balance conditions, the hybrid-Trefftz models can be constructed by boundary integration. This feature enables the models to be interfaced compatibly with conventional finite element models. To illustrate the efficacy of the present approach, the eigensolutions and/or parameters directly related to the electromechanical stress intensity in crack, interfacial crack and bimorph with embedded electrode are considered. The predictions are in good agreement with the reference solutions reported in the literature or computed by using over 10,000 conventional finite elements.