Interaction among a row of ellipsoidal inclusions

Abstract

In this paper the interaction among a row of N ellipsoidal inclusions of revolution is considered. Inclusions in a body under both (A) asymmetric uniaxial tension in the x-direction and (B) axisymmetric uniaxial tension in the z-direction are treated in terms of singular integral equations resulting from the body force method. These problems are formulated as a system of singular integral equations with Cauchy-type or logarithmic-type singularities, where unknowns are densities of body forces distributed in the r,θ,z directions. 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 polynomials. The present method is found to yield rapidly converging numerical results for interface stresses. When the elastic ratio E 1⇒E I/E M>1, the primary feature of the interaction is a large compressive or tensile stress σn on the interface θ=0. When E 1⇒E I/E M<1, a large tensile stress σθ or σt on the interface θ=1/2π is of interest. If the spacing b/d and the elastic ratio E I/E M are fixed, the interaction effects are dominant when the shape ratio a/b is large. For any fixed shape and spacing of inclusions, the maximum stress is shown to be linear with the reciprocal of the squared number of inclusions.