Thermally Induced Fields in Electroelastic Composite Materials: Average Fields and Effective Behavior

The average thermally induced electroelastic fields and the effective thermal expansion and pyroelectric coefficients of two-phase composite materials are obtained by applying the Mori-Tanaka mean-field theory to the coupled response of electroelastic composites through a field superposition scheme. Results are obtained for composites reinforced by ellipsoidal piezoelectric and pyroelectric inhomogeneities and thus are applicable to a wide range of microstructural geometry including lamina, spherical particle, and continuous fiber reinforcement. The results are shown to obey the recently derived Levin-type equations relating the effective thermal expansion and pyroelectric coefficients of a two-phase composite to those of the constituents and the electroelastic moduli of the constituents and the composite. The analysis is developed in a matrix formulation convenient for numerical computation in which the electroelastic (elastic, piezoelectric, and dielectric) moduli are represented by a 9×9 matrix and the thermal expansion and pyroelectric coefficients by a 9×1 column vector. A limited parametric study is performed to illustrate the interesting behavior exhibited by some typical composite microstructures. Finally, analytical predictions are examined in light of existing experimental observations.