The effect of localized internal defects on the field distributions of electrostrictive composites

Abstract

The electromechanical field distributions in electrostrictive periodic composites with localized defects are determined. The composite is subjected to a combined electromechanical loading which is sufficiently far away from the localized internal defects. The present analysis forms a generalization of the linearly constitutive equations based approach for electro–magneto–elastic composites which has been recently presented. Presently, the nonlinear terms in the fully coupled constitutive relations of the phases as well as the effect of defects are combined and represented by eigen-electromechanical field terms which are a priori unknown, thus requiring an iterative procedure for establishing the solution. The analysis is based on the combined use of three approaches. In the first one, a micromechanical analysis establishes the concentration matrices needed for the determination of the far-field distributions in the composite’s phases induced by the remote loading. In the second approach, the representative cell method is employed as a result of which the problem for a periodic composite, discretized into numerous identical cells, is reduced to a problem of a single cell in the discrete Fourier transform domain. The third approach consists of the application of the higher-order theory where the single cell is divided into several subcells, and the governing equations and interfacial conditions in the transform domain, imposed in an average (integral) sense, are solved. The inverse of the Fourier transform provides the actual electroelastic field at any point of the damaged composite. The offered method is verified by comparisons with analytical solutions, and several applications are presented for localized defects in the form of cavities and inclusions in an electrostrictive material subjected to combined electromechanical loadings. Next, the field distributions in two types of unidirectional composites with a missing fiber, subjected to electromechanical loadings are presented. In the first type, the composite consists of electrostrictive ceramic fibers reinforcing a polymeric matrix, whereas in the second one the electrostriction effect is enhanced by PZT fibers reinforcing an electrostrictive polymeric matrix. Comparisons between the resulting responses are discussed.