A Multi-scale Formulation for Predicting Non-linear Thermo-electro-mechanical Response in Heterogeneous Bodies

This study presents a multi-scale formulation for analyzing coupled heat conduction and thermo-electro-mechanical deformation in heterogeneous bodies, namely active composites. The studied active composite comprises ferroelectric inclusions dispersed in polymer matrix. The multi-scale framework is derived based on an integrated simplified micromechanical and finite element model. A non-linear thermo-electro-elastic constitutive model of materials undergoing large electric driving fields and small strains is used for the polarized ferroelectric inclusions. An integration algorithm with predictor and corrector schemes is developed to obtain approximate solutions of field variables: temperature, displacement, strain, stress, electric field, and electric displacement. The multi-scale model is capable of determining field variables at multiple length scales which is important when non-linear behaviors in the constituents of heterogeneous bodies are considered. We examine the effect of mismatches in the properties of the constituents in an active composite on the overall field coupling responses in the composite. We also compare the field coupling responses in an active composite to those of a homogeneous body, i.e., lead zirconate titanate (PZT). We finally present a simulation of controlling deformation in a smart cantilever beam using the multiscale framework.