HETEROGENEOUS SOLIDS .1. ANALYTICAL AND NUMERICAL 1-D RESULTS ON BOUNDARY EFFECTS

This two-part study explores the consequences of material heterogeneit y on the response of an externally loaded structure/specimen near its boundaries. The single deviation from the framework of classical (homo geneous) linear elasticity is that the elastic properties of the mater ial 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 t he strain field near the two ends is significantly and unfavorably dif ferent than in the bulk. Here, ''unfavorably' concurs to fracture init iation. Further, it is shown that for brittle materials, both size eff ects and data scatter of peak strength are closely related to boundary phenomena. The (approximate) analytical solution of the problem provi des significant insight, and allows examination of the efficiency of n umerical solution schemes for problems of the type studied herein.