The analysis of periodic composites with randomly damaged constituents

A new method is offered for the modeling of periodic composites in which some damaged constituents are randomly distributed. The representative volume element for such composites consists of many repetitive cells, and its direct analysis by standard methods is an expensive computational task. The proposed approach allows to diminish significantly the volume of calculations. It is based on the representative cell method and the higher-order theory. In the former, the problem of the periodic composite with randomly located damages is reduced, in conjunction with the discrete Fourier transform, to a single cell problem, formulated in the transform domain. The solution of this boundary value problem is obtained by the latter one. The inversion of the transform, in conjunction with an iterative procedure, establishes the elastic field at any point of the damaged composite. The method is employed for the evaluation of the effective properties and field distribution for a specified loading of unidirectional fiber-reinforced composites with numerous randomly located defective fibers such as lost, missing, and damaged fibers. In addition, porous materials with random distributions of pores and unidirectional composites with fibers that are randomly located within the matrix can be considered. Furthermore, random distributions of matrix cracks in composites can be simulated, and the resulting behavior can be predicted. Finally, broken layers and interfacial cracks in periodically layered composites in which the cracks are randomly located can be similarly analyzed.