An Electro-Elastic Coupling Model for Piezoelectric Composites Based on the Voronoi Cell Finite Element Method

Abstract

The Voronoi cell finite element method (VCFEM) has successfully characterized the linear elastic behavior of the composites. This study is dedicated to develop an electro-elastic coupling VCFEM model mimicking the fully-coupled electro-elastic behavior of piezoelectric composites. For fiber-reinforced piezoelectric composites considering interfacial cracks, the interface traction reciprocity, the interface charge density reciprocity on bonded interfaces and the interface traction-free, the interface charge density-free on debonded interfaces are comprised in the new assumed stress and electric displacement hybrid variational functional. The new variational functional is derived on the base of the element multifield energy functionals. Independent stress/electric displacement fields are respectively assumed within the two-phase material domain. Several numerical examples considering perfectly-bonded interface and partially cracked interface were used to demonstrate the accuracy of the proposed method by comparing the piezoelectric Voronoi element model results with those obtained by ABAQUS. Then this model is used to study the effect of several microscopic details, such as the property ratio of fiber to matrix, volume fraction, interfacial crack length and polarization direction on macroscopic equivalent physical and mechanical properties, as well as local stress/electric displacement fields. It is clear that the proposed model is suitable for analyzing piezoelectric composites containing many microstructures with bonded interface or debonded interface.