Elastic dielectric composites: Theory and application to particle-filled ideal dielectrics

A microscopic field theory is developed with the aim of describing, explaining, and predicting the macroscopic response of elastic dielectric composites with two-phase particulate (periodic or random) microstructures under arbitrarily large deformations and electric fields. The central idea rests on the construction - via an iterated homogenization technique in finite electroelastostatics - of a specific but yet fairly general class of particulate microstructures which allow to compute exactly the homogenized response of the resulting composite materials. The theory is applicable to any choice of elastic dielectric behaviors (with possibly even or odd electroelastic coupling) for the underlying matrix and particles, and any choice of the one- and two-point correlation functions describing the microstructure. In spite of accounting for fine microscopic information, the required calculations amount to solving tractable first-order nonlinear (Hamilton-Jacobi-type) partial differential equations. As a first application of the theory, explicit results are worked out for the basic case of ideal elastic dielectrics filled with initially spherical particles that are distributed either isotropically or in chain-like formations and that are ideal elastic dielectrics themselves. The effects that the permittivity, stiffness, volume fraction, and spatial distribution of the particles have on the overall electrostrictive deformation (induced by the application of a uniaxial electric field) of the composite are discussed in detail.