Two-dimensional grained composites of minimum stress concentration

In this paper, we consider a regular two-phase microstructure which is formed by identical foreign inclusions spaced periodically in an elastic matrix. The optimization problem of finding the inclusion shape that minimizes the stress concentration over the whole region is solved explicitly (without recourse to approximate or numerical methods) when both materials have the same shear modulus differing only in Poissonʹs ratios. It is rigorously shown that the stress concentration reduces to the absolute minimum (dictated only by a global part of a given average stress tensor) if the inclusions have equi-stress boundaries identified before in the closely-related context of energy-wise optimization. The stress concentration factors at non-optimal circular inclusions are also found in a closed form to estimate the gain from applying optimal contours. Copyright © 1997 Elsevier Science Ltd