A Galerkin boundary integral method for multiple circular elastic inclusions with homogeneously imperfect interfaces

Abstract

A Galerkin boundary integral method is presented to solve the problem of an infinite, isotropic elastic plane containing a large number of randomly distributed circular elastic inclusions with homogeneously imperfect interfaces. Problems of interest might involve thousands of inclusions with no restrictions on their locations (except that the inclusions may not overlap), sizes, and elastic properties. The tractions are assumed to be continuous across the interfaces and proportional to the corresponding displacement discontinuities. The analysis is based on a numerical solution of a complex hypersingular integral equation with the unknown tractions and displacement discontinuities at each circular boundary approximated by truncated complex Fourier series. The method allows one to calculate the stress and displacement fields everywhere in the matrix and inside the inclusions. Numerical examples are included to demonstrate the effectiveness of the approach.