Interaction Effect between Ellipsoidal Inclusions is an Infinite Body under Asymmetric Uniaxial Tension

This paper deals with numerical solution of singular integral equations of the body force method in an interaction problem of two ellipsoidal inclusions under asymmetric uniaxial tension. The problem is solved on the superposition of two auxiliary loads ; (i) biaxial tension and (ii) plane state of pure shear. These problems are formulated as a system of singular integral equations with Cauchy-type or logarithmic-type singularities, where the densities of body forces distributed in the γ, θ, z directions are unknown functions. In order to satisfy the boundary conditions along the ellipsoidal boundaries, the unknown functions are approximated by a linear combination of fundamental density functions and polynominals. The present method is found to yield rapidly converging numerical results for stress distributions along the boundaries