An analytical solution for periodic multi-phase fibrous piezoelectric composites under antiplane deformation

The electro-elastic field of multi-phase fibrous piezoelectric composites with periodic microstructure under antiplane deformation was studied. By introducing non-uniform generalized eigen strain in each inhomogeneous phase, the original problem was replaced by a homogenous medium problem with the periodically distributed generalized eigen strains, the equivalent condition between the two problems was established. By use of the continuity conditions of generalized stress and the compatibility conditions of generalized displacement on the interfaces of each neighboring region in equivalent problem, together with doubly quasi-periodic Riemann boundary value problem theory and equivalent condition, the analytical solutions of the electro-elastic fields in each phase of composites were derived, and the effective piezoelectric coefficient of the composites was evaluated by using average field theorem. The differences of the effective piezoelectric coefficient of composites with hollow piezoelectric fibers, carbon core piezoelectric structural fibers and solid piezoelectric fibers were demonstrated under the same piezoelectric material volume fraction, and the effects of the stiffness of non-piezoelectric core in the piezoelectric structural fibers and coatings between piezoelectric structural fibers and matrix on the effective piezoelectric coefficient were discussed. The conclusions can provide valuable references for designing piezoelectric composites with high sensibility.