Heterogeneous solids - Part II: Numerical 2-D results on boundary and other relevant phenomena

This two-part study explores the consequences of material heterogeneity on the response of an externally loaded structure/specimen near its boundaries. The single deviation from the framework of classical (homogeneous) linear elasticity is that the elastic properties of the material form a stationary random field. In this second part, it is first shown how the internal variables like stresses, strains and energy are correlated with the Young's modulus, and conclusions about the effect of a local failure criterion upon global failure are drawn. Then, boundary effects for which an analytical solution is not straightforward are enlightened. The effects yet found in one dimension are now coupled with those of the free boundary effect. The consequences of the free boundary on size related phenomena and the implications of spatial correlations on failure are analyzed and discussed in relation to the so-called characteristic material length and nonlocal models.