Lower bound of effective yield strength domain for random heterogeneous materials

A random heterogeneous material is represented by a finite family of microstructures, the environment of each microstructure being subjected to a perfect mix condition whose validity is justified both theoretically and numerically. Necessary conditions, satisfied by any permissible strain rate field on a representative and unlimited domain of the material, are highlighted. They enable one to obtain, by solving a discrete infmax problem, a lower bound of the effective yield strength domain of the material, that is rigorous and more predictive than the classical bound of Reuss. An analytical application on a porous medium illustrates the methodology.

► A randomheterogeneousmaterialisrepresented by a finitefamily of microstructures. ► Theirdisposal the mostlikelyisdescribed by a perfectmixing condition. ► This conditionallows to found a lowerbound of the effective yieldstrengthdomain. ► This boundisrigorous and more predictivethan the classicalbound of Reuss. ► An application on a porousmaterialis made.