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

Abstract

This paper deals with 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 the body forces distributed in the γ, θ, z directions are unknown functions. In order to satisfy the boundary conditions along the boundaries, the unknown functions are approximated by a linear combination of fundamental density functions and polynomials. The present method is found to yeild rapidly converging numerical results and smooth stress distributions along the boundaries. For hard inclusions(E_I/E_M>1), the interaction appears as a large compressive stress σ_n;however, the maximum tensile stress is almost independent of the interaction. For soft inclusions(E_I/E_M<1), the interaction appears as a large tensile stress σ_θ.