The effect of localized damage on the behavior of composites with periodic microstructure

Abstract

The effect of localized stationary and progressive damage on the behavior of elastic composites with periodic microstructure is investigated. To this end, an analysis that combines continuum damage mechanics considerations together with three different approaches is presented and applied. In the first one the representative cell method is employed according to which the periodic composite domain is reduced, in conjunction with the discrete Fourier transform to a finite domain problem of a single cell. Appropriate far-field boundary conditions in the transform domain are applied in conjunction with the high-fidelity generalized method of cells micromechanical model which forms the second approach. The third approach consists of the application of the higher-order theory for the computation of the elastic field in the transform domain. An inverse transform provides the actual field. The effect of damage is included in the analysis in the form of eigenstresses which are a priori unknown. Hence an iterative procedure is employed to obtain a convergent solution. Several verifications of the proposed theory by comparisons with closed-form solutions have been presented. Results show the effect of stationary damaged regions as well as the development of cracks in the composite. It is demonstrated that standard micromechanical analysis based on the analysis of the repeating unit cell of the periodic composite with evolving damage cannot predict its actual behavior when a localized damage is involved.