Influence of second-phase inclusions on the electro-deformation of ferroelectric ceramics

Abstract

Theoretical estimates are given for the overall dissipative response of ferroelectric ceramics with second-phase inclusions, under arbitrary electromechanical loading histories. The ferroelectric behavior of the constituent phases is described via a stored energy density and a dissipation potential in accordance with the theory of generalized standard materials. An implicit time-discretization scheme is used to generate a variational representation of the overall response in terms of a single incremental potential. Estimates are then generated by constructing sequentially laminated microgeometries of particulate type whose overall incremental potential can be computed exactly. Because they are realizable, by construction, these estimates are guaranteed to conform with any material constraints, to satisfy all pertinent bounds, and to exhibit the required convexity properties with no duality gap. By way of example, the theory is used to study the influence of metallic particles and of microcavities on the electro-deformability of a lead zirconate titanate. In particular, the role of remanent polarization fluctuations on the piezoelectric properties is assessed.