Effective yield strengths of random materials by an ε-self-consistent method

Abstract

The problem of determining the effective yield strength domain of a material containing random distributed heterogeneities is dealt with. This material is represented by a set of microstructures, each occupying a volume of the order of the heterogeneities. A homogeneous comparison material is used, characterized by its own yield strength domain, in which these microstructures are placed. The equivalent homogeneous material is envisaged as the solution of a system of self-consistent equations. The problems of non-existence or non-uniqueness of the solutions of this system lead to modifying it, using an equality to “within ε”. “Extremal” solutions are highlighted for each of the equations of the system transformed in this way, which bound the effective domain sought for. The proposed homogenization method is applied to a defect material and the result is compared with a structure calculation.