Extended Locally Exact Homogenization Theory for Effective Coefficients and Localized Responses of Piezoelectric Composites

Herein, the elasticity-based locally exact homogenization theory (LEHT) is extended to study the effective and localized responses of piezoelectric fiber composites. Based on the Trefftz concept, coupled internal solutions for electric fields and elastic displacements are developed for repeating unit cells (RUCs) that are characterized from the composite domain. The unknown coefficients of the internal fields can be determined by imposing interfacial continuity conditions between fiber and matrix and implementing the newly proposed multiphysics periodic boundary conditions. Finally, the generalized constitutive relations are established to predict the effective coefficients. The accuracy of the proposed technique is tested by validating the present simulations against the analytical Eshelby solution and asymptotic method, classical Mori-Tanaka (M-T) model, finite element (FE)- and finite volume (FV)-based methods, as well as the experimental measurement in the literature with excellent agreement. What is more, several microstructural effects, such as phase volume fraction, fiber arrangement, etc., are varied to test their effects on the piezoelectric composites at both homogenized and localized levels. Based on the presented computational efficiency, the multiphysics LEHT is encapsulated into a blackbox with input/output data constructions for easy implementation by professionals or nonprofessionals.