Model for piezoelectric/ferroelectric composites polarized with interdigitated electrodes

Abstract

A piezoelectric composite homogenization model (PCHM) is presented in this article. A systematic method for predicting the composite macroscopic history-dependent electromechanical response is developed and particularized for piezoelectric fiber composites polarized with interdigitated electrodes. As other composite models, the proposed PCHM requires appropriate constitutive equations describing each pure constituent namely, fiber and matrix. In this work, dielectric matrix is modeled as electromechanically linear while an existing non-linear phenomenological model is used for the fibers. Additionally, a cutting-plane algorithm is developed and implemented to integrate the fibers constitutive equation. The proposed PCHM is implemented in a previously developed ABAQUS/UEL piezoelectric shell.

To evaluate the proposed model, a representative elementary volume (REV) is analyzed with a finite element (FE) model using an ABAQUS/UEL piezoelectric brick and the same material models for each constituent of the composite. Practical examples are addressed with both, FE/REV and the proposed PCHM. Electromechanical responses predicted with both approaches are in good agreement. Numerical results illustrate the ability of the proposed PCHM to capture important aspects of piezoelectric devices such as quasi-linear range, as well as both, pressure and electric-field driven depolarization. Finally, a brief convergence analysis is performed indicating an encouraging computational performance of the proposed PCHM.