Micromechanical Modeling of a Composite Containing Piezoelectric and Shape Memory Alloy Inclusions

Macroscopic constitutive relations based on the mean-field theory and the Mori–Tanaka method are derived for a 3-phase composite consisting of a polymer matrix and shape memory alloy (SMA) and piezoceramic (PZT) inclusions. Effective moduli are computed for likewise oriented spherical and cylindrical inclusions. Results are also computed for cylindrical PZT and ellipsoidal SMA inclusions. Even though the PZT and the matrix materials are assumed to be linear, the overall response of the composite is nonlinear because of the phase transformations in the SMA inclusions. The 3-phase composite exhibits pyroelectric effects even when none of its constituents is pyroelectric. It is found that the spherical inclusions are more effective than the cylindrical inclusions in the sense that lower values of the average axial stress induce phase transformations in the SMA inclusions, and the maximum principal tensile strain induced in the PZT inclusions is only about 7% of the average axial strain. However, spherical PZT inclusions require a very high value of the electric field to induce any noticeable axial strain in the hybrid composite.