Piezocomposite with reciprocal polarization of oriented ellipsoidal inclusions and the matrix

Abstract

We consider statistically homogeneous two-phase random piezoactive structures with deterministic properties of inclusions and the matrix and with random mutual location of inclusions. We present the solution of a coupled stochastic boundary value problem of electroelasticity for the representative domain of a matrix piezocomposite with a random structure in the generalized singular approximation of the method of periodic components; the singular approximation is based on taking into account only the singular component of the second derivative of the Green function for the comparison media. We obtain an analytic solution for the tensor of effective properties of the piezocomposite in terms of the solution for the tensors of effective properties of a composite with an ideal periodic structure or with the “statistical mixture” structure and with the periodicity coefficient calculated for a given random structure with its specific characteristics taken into account. The effective properties of composites with auxiliary structures (periodic and “statistical mixture”) are also determined in the generalized singular approximation by varying the properties of the comparisonmedium. We perform numerical computations and analyze the effective properties of a quasiperiodic piezocomposite with reciprocal polarization of oriented ellipsoidal inclusions and the matrix, the layered structures with reciprocal polarization of the layers [1] of a polymer piezoelectric PVF, and find their unique properties such as a significant increase in the Young modulus along the normal to the layers and in dielectric permittivities, the appearance of negative values of the Poisson ratio under extension along the normal, and an increase in the absolute values of the basic piezomoduli.