Correspondence relations among equivalent classes of heterogeneous piezoelectric solids under anti-plane mechanical and in-plane electrical fields

Abstract

Correspondence relations of the nature discovered by Milton [(1988) Classical Hall Effect in two-dimensional composites : A characteristic of the set of realizable effective conductivity sensors. Physical Review B 38, 11296–11303] between equivalent classes of solids in two-dimensional conductivity problems are shown to exist in certain problems of two-dimensional heterogeneous piezoelectric media. The piezoelectric solid is assumed to possess local and overall monoclinic symmetry of class 2, while the mode of deformation is anti-plane in shear, and coupled to an in-plane electric field. The established correspondence relations allow the derivation of new reciprocal connections, phase interchange relations, and microstructure independent expressions for the effective moduli of piezoelectric solids and polycrystals.