The effective conductivity of strongly heterogeneous composites

Abstract
A general solution is given for problems of generalized plane stress distributions in an infinite plate which contains circular holes of varying sizes in any positions, subject only to certain conditions of convergence of the solution. The method for extending the results to allow for the effect of one or two straight boundaries is indicated. As a particular case of the general solution the problem of the stress distribution in an infinite plate under tension containing three holes in a row, is discussed, and a few numerical results are given. These results are compared with experiments which were carried out by Mr. P. L. Capper. The comparison is incomplete as the experiments were done for a finite plate and the influence of the edges of the plate on the numerical values of the stresses is considerable. Agreement, however, is found for the general character of some of the stresses.