2-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 elas tic matrix. The optimization problem of finding the inclusion shape th at minimizes the stress concentration over the whole region is solved explicitly (without recourse to approximate or numerical methods) a he n both materials have the same shear modulus differing only in Poisson 's ratios. It is rigorously shown that the stress concentration reduce s to the absolute minimum (dictated only by a global part of a given a verage stress tensor) if the inclusions have equi-stress boundaries id entified before in the closely-related context of energy-wise optimiza tion. The stress concentration factors at non-optimal circular inclusi ons are also found in a closed form to estimate the gain from applying optimal contours. Copyright (C) 1997 Elsevier Science Ltd.