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

Studied is the apparent yield strength of a specimen consisting of an elast ic-perfectly plastic heterogeneous material and being smaller than a repres entative volume element. The two fundamental variational principles of limi t analysis, reformulated by means of dual gauge functions, are applied to q ualitatively bring out effects of size and boundary conditions. It is shown that (i) the static apparent yield strength domain of any specimen is incl uded in its kinematic one; (ii) the static apparent yield strength domain o f any specimen includes the intersection of the static apparent yield stren gth domains of the smaller specimens resulting from the partition of the in itial one; (iii) the kinematic apparent yield strength domain of any specim en is included in the volume fraction weighted convex combination of the ki nematic apparent yield strength domains of the smaller specimens partitioni ng the initial one. These results give rise to a hierarchical chain of appa rent yield strength domain inclusions. (C) 2001 Elsevier Science Ltd. All r ights reserved.