Singular Perturbation Solutions of a Class of Systems of Singular Integral Equations

A new class of systems of strongly singular integrodifferential equations is examined, which emerges in the study of the bridged interface crack growth, e.g., in fiber stitched layered composites. This work generalizes the asymptotic analysis of strongly singular integral equations by Willis and Nemat-Nasser [Quart. Appl. Math., 48 (1990), pp. 741–753]. Singular perturbation solutions up to the first-order in a small paramter are presented for a general case which corresponds to the elasticity problem of bridged interface cracks in general anisotropic bimaterials. In particular, detailed solutions are described for a special case which includes the problem of bridged interface cracks in isotropic bimaterials. Methods are illustrated by solving particular examples.