Integral Equations For Crack Systems In A
Slightly Heterogeneous Elastic Medium
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
Related Book
Other papers in this volume
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