A rigorous theoretical framework is presented for the analysis of thermoelectroelastic heterogeneous media. These materials include, among others, piezoelectric composite media which exhibit pyroelectricity. Formal definitions of a representative volume element, phase constitutive behavior, and numerous averaging theorems are presented. Expression for the average fields in the constituent phases in terms of thermal and electroelastic concentration factors are presented as are exact expressions for the effective moduli in terms of the concentration factors. An approach is presented to estimate the phase concentration factors which is based on the rigorous solution for the auxiliary problem of a single piezoelectric inhomogeneity embedded in an infinite matrix (which is also outlined). The theoretical principles are presented in the framework of a convenient 9 x 9 and 9 x 1 matrix formulation which greatly simplifies their numerical implementation. The framework presented here allows for the clean delineation between exact and assumed relations and allows a clear interpretation of all assumptions. Applications are made to polycrystalline piezoelectric ceramics, cracked piezoelectric solids, and two-phase piezoelectric composites.
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