Stress constrained compliance minimization by means of the small amplitude homogenization method

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 Gutiérrez, which relies on the use of H-measures introduced by Tartar to study the quadratic interaction of weakly convergent sequences of functions.