Stress Concentrations in Elastic Composites with Limiting Shear Properties

Abstract

A circular elastic inclusion, embedded in an elastic matrix under plane strain or generalized plane stress conditions, produces a particular kind of stress concentration, if the shear moduli of matrix and inclusion are equal. In this case, the state of stress around the inclusion depends solely on a dimensionless parameter, and the sum of principal stresses is constant at all points of the stress field. This sum, in the matrix side in particular, does not depend on the material properties at all, while in the inclusion it depends solely on Poisson's ratio. As a result, lateral contraction of the matrix is not affected by the stress concentration field. Thus, an equal shear modulus, but higher Poisson's ratio, filler material can be dispersed in the matrix, to produce a higher E-modulus composite under conditions of minimal stress concentration.