Exact relations between the thermoelectroelastic moduli of heterogeneous materials

Abstract

Exact relations are obtained between the effective thermoelectroelastic moduli of two-phase heterogeneous media and their corresponding isothermal effective electroelastic moduli. The relations are obtained by generalizing the results of V. M. Levin, and B. W. Rosen and Z. Hashin to the inherently anisotropic coupling between the electric and elastic fields in thermoelectroelastic composites. The explicit expressions that are obtained can be used to obtain the effective thermal expansion and pyroelectric coefficients of the composite when the effective electroelastic (elastic, piezoelectric and dielectric) moduli are known, either by theory or experiment. The results also provide a means to assess the internal consistency of any micromechanics model that is proposed to estimate the thermoelectroelastic and electroelastic moduli of the composite. It is verified that when piezoelectric coupling is absent, the expressions reduce to those of B. W. Rosen and Z. Hashin for thermoelastic composite media. Finally, the resulting exact relations are exploited to prove the interesting phenomena that two-phase heterogeneous media can exhibit a net pyroelectric response even though neither of the individual phases exhibits pyroelectricity.