Effects of size and boundary conditions on the yield strength of heterogeneous materials

Abstract

Studied is the apparent yield strength of a specimen consisting of an elastic-perfectly plastic heterogeneous material and being smaller than a representative volume element. The two fundamental variational principles of limit analysis, reformulated by means of dual gauge functions, are applied to qualitatively bring out effects of size and boundary conditions. It is shown that (i) the static apparent yield strength domain of any specimen is included in its kinematic one; (ii) the static apparent yield strength domain of any specimen includes the intersection of the static apparent yield strength domains of the smaller specimens resulting from the partition of the initial one; (iii) the kinematic apparent yield strength domain of any specimen is included in the volume fraction weighted convex combination of the kinematic apparent yield strength domains of the smaller specimens partitioning the initial one. These results give rise to a hierarchical chain of apparent yield strength domain inclusions.