Micromechanical modeling for the prediction of time-dependent effective properties and macroscopic coupled field response of polymer reinforced piezoelectric composites

Abstract

In the time domain, a new straightforward micromechanical modeling is developed to predict the time-dependent behavior and the macroscopic coupled response of polymer piezoelectric composite materials. The modeling is based on the dynamic electroelastic Green’s tensor allowing the derivation of convolution localization equations in Stieltjes space. The Mori-Tanaka micromechanical model is adopted to derivate the dynamic electroelastic localization tensor. The presented modeling leads to an expression of the time-dependent effective electroelastic properties directly in the time domain, without an iteration procedure, through convolution products in Stieltjes space. It allows the prediction of the time-dependent behavior and the coupled macroscopic response while taking into account the constituent properties, volume fractions, and shape of inclusions. In implementing the expression of the effective behavior, one has to go through the computation of direct and inverse tensorial convolution products. A trapezoidal numerical scheme is adopted for this sake. Many numerical results are presented, and for the sake of validation, a comparison is made with the ones obtained based on the Laplace transform approach as well as with experimental and numerical results.