Interaction effect between ellipsoidal inclusions in an infinite body under asymmetric uniaxial tension

This paper deals with an interaction problem of two ellipsoidal inclusions under asymmetric uniaxial tension. The problem is solved on the superpositi on of two auxiliary loads; (i) biaxial tension and (ii) plane state of pure shear. These problems are formulated as a system of singular integral equa tions with Cauchy-type or logarithmic-type singularities, where the densiti es of the body forces distributed in the r, theta, z directions are unknown functions. In order to satisfy the boundary conditions along the boundarie s, the unknown functions are approximated by a linear combination of fundam ental density functions and polynomials. The present method is found to yie ld rapidly converging numerical results and smooth stress distributions alo ng the boundaries. For hard inclusions (E-I/E-M>1), the interaction appears as a large compressive stress (rn; 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 sigma(theta).