Microstresses and effective elastic moduli of a solid reinforced by periodically distributed spheroidal particles

The particle composite consisting of a continuous matrix with the spheroidal particles arranged in several triply periodic arrays is considered. The problem on macroscopically uniform stressed state of this composite is solved accurately. The essence of the method used is the representation of a displacement vector by a series of triply periodic partial vectorial solutions of Lame’s equation written in a spheroidal basis. Exact satisfaction of the interfacial boundary conditions reduces the primary boundary-value problem to an infinite set of linear algebraic equations. By solving it numerically the displacements, strains and stresses at an arbitrary point of composite can be determined with any desirable accuracy. Analytical averaging of the strain and stress tensors gives the exact expressions for all components of effective elasticity tensor of composite considered. The influence on stress concentration and effective moduli of the structural parameters of composite is investigated and the comparison is made with known approximate solutions. 0 1997 Elsevier Science Ltd. All rights reserved