Influence of metallic inclusions on the electromechanical response of ferroelectric ceramics

Abstract

Theoretical estimates are given for the overall dissipative response of ferroelectric ceramics with random dispersions of metallic inclusions under arbitrary loading histories. The fer- roelectric behavior of the matrix 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 se- quentially 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. Sample results for isotropic composites are reported and discussed.