Heterogeneous solids - Part I: Analytical and numerical 1-D results on boundary effects

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. It is shown that the consequences near boundaries can be quite adverse. Specifically, in the first part, investigation of a bar subjected to uniaxial load demonstrates that the strain field near the two ends is significantly and unfavorably different than in the bulk. Here, `unfavorably' concurs to fracture initiation. Further, it is shown that for brittle materials, both size effects and data scatter of peak strength are closely related to boundary phenomena. The (approximate) analytical solution of the problem provides significant insight, and allows examination of the efficiency of numerical solution schemes for problems of the type studied herein.