Simple algebraic formulae are derived for estimates of the overall thermoelectroelastic moduli of multiphase fibrous composites with the self-consistent and Mori-Tanaka methods. The results are formulated with the help of an overall constraint tensor, which can be obtained analytically by solving a problem for a cylindrical cavity in a piezoelectric medium. It is shown that, although the two methods are different in nature, their estimates of the effective elastic, piezoelectric and dielectric constants, as well as the thermal stress tensor and pyroelectric coefficients of the composite, have a similar structure. In addition, when the phases have equal transverse rigidities in shear, the overall electroelastic moduli predicted by both methods reproduce the exact solutions for composites with arbitrary transverse geometry.
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