Elastic equilibrium of a medium containing a finite number of arbitrarily oriented spheroidal inclusions

An unbounded domain containing a certain number of spheroidal inclusions proves to be a suitable model for a wide class of heterogeneous materials. Elastic equilibrium of this model structure, in the case of aligned spheroids was studied, before by Kushch, who has obtained an accurate solution in series using the multiple expansion technique. The present paper expands this approach on the case of the arbitrarily oriented spheroids. The new formulae are obtained providing the re-expansion of the vectorial partial solutions of Lameʹs equation, due to the rotation of the coordinate system. The using of these formulae enables one to reduce a primary boundary-value problem to an infinite set of linear algebraic equations. Some numerical results are presented which demonstrate how the interfacial stress concentrations, caused by an interaction among the particles, vary with their relative position and orientation. © 1998 Elsevier Science Ltd.