Abstract

Under the assumption of small contrast between the elasticity tensors of two materials, we derive an algorithm based on an approximate relaxation of a problem that minimizes the compliance under a constraint on stress. Numerical results are presented for the short cantilever problem, where we see that, for a 1 to 2 contrast in Young moduli, and when compared with a configuration that only minimizes compliance, one can get up to a 46 % reduction in peak stress, while compliance increases by only 1 %. The basis of the method is the small amplitude homogenization technique derived by Allaire and Guti,rrez, which relies on the use of H-measures introduced by Tartar to study the quadratic interaction of weakly convergent sequences of functions.