A boundary integral method for multiple circular inclusions in an elastic half-plane

This paper presents a numerical method for solving the problem of an isotropic elastic half-plane containing a large number of randomly distributed, non-overlapping, perfectly bonded circular elastic inclusions. The boundary of the half-plane is assumed to be traction free and a uniform far-field stress acts parallel to that boundary. In general, the inclusions may have different elastic properties and sizes. The analysis is based on a numerical solution of a complex singular integral equation with the unknown tractions at each circular boundary approximated by a truncated complex Fourier series. A system of linear algebraic equations is obtained by using a Taylor series expansion. The resulting numerical method allows one to calculate the elastic fields everywhere in the matrix and inside the inclusions. Numerical examples are included to demonstrate the effectiveness of the approach.