ABSTRACT
As discussed in an extensive review article (Bazant and Chen, 1997), the onset and evolution of structural failure are related to size effects at different scales due to the different features of micro-, meso-, and macrostructures such as molecular, grain, cluster, and macroscopic structures. Inelastic deformation can be described as a prompt stress-controlled process if the deformation can occur in a nearly point-wise manner such as dislocation motions. However, the evolution of inelastic deformation appears to be a diffusion process if the deformation involves a length scale and can only occur in an essentially random-walk (disordered) manner subject to geometric constraints. From a continuum viewpoint, the stress state at any material point depends on not only the strain at that point but also the strain distribution around that point during the evolution of failure, that is, a failure criterion must be formulated as a nonlocal one with a suitable length scale (size effect). As shown by Chen (1996), a complete failure evolution process could be characterized by the nonlocal transition between discontinuities of different degrees, depending on the structural scale. At the microscale, experiments with crystalline materials have demonstrated that sample dimensions inuence the material strength and crystal plasticity due to the geometric constraints (surface-to-volume ratios) (Uchic et al., 2004). Nix and Gao (1998) have predicted the indentation size effect for crystalline materials based on the concept of geometrically necessary dislocations. The depth-dependent hardness is also related to the indenter shape due to different levels of stress concentration involved. Hence, geometric constraints appear to play a key role in characterizing the size effects at different scales. However, there is a lack of understanding of the
link between different size effects. Research efforts have been mainly made on the size effect at different structural levels.
