Author(s)

A. N. Galybin & S. M. Aizikovich

Abstract

The paper deals with derivation of a system of singular integral equations for slightly heterogeneous media. The system is derived in terms of complex potentials by introducing a small parameter by the perturbation method. The resulting system of integral equations is of the Cauchy type with the correction terms that address inhomogeneity of the media, they are presented in the form somewhat similar to the problem with body forces. Therefore the numerical methods developed for the homogeneous crack problems can directly be applied for the further numerical analysis. Keywords: heterogeneous media, plane elasticity, singular integral equations. 1 Introduction Elastic properties of many natural and artificial materials have slight fluctuations. They can be produced during formation of a material (e.g., metal sheets or concrete consolidation), loading history (rocks) or non-homogeneity of structure (ceramics). They can also be imposed for the sake to improve performance of particular materials as in fractionally graded materials, FGM. Non-homogeneity is often neglected for the determination of the fracture resistance of such materials. However, in some cases the effect induced by moduli fluctuations can create significant fluctuations of material fracture toughness, which is the case for FGM. It should be noted that by introducing non-homogeneity of the fracture toughness one can model influence of stress fluctuations. However this case is fully not the fluctuations of material characteristics. They cannot be considered to be independent of applied load and therefore the direct superposition of two

Keywords

heterogeneous media, plane elasticity, singular integral equations