Brittle Fracture: From Elasticity Theory to Atomistic Simulations

Understanding the mechanical properties of materials with theory traditionally has been done by using continuum methods, ranging from elastic theory (in both linear and nonlinear regimes), to plastic theory, and to fracture mechanics. The computational counterpart of continuum modeling is represented by finite element analysis. Continuum theories have been extremely successful, as proved by the tremendous achievements reached in structural design of buildings, ships, bridges, air-/space crafts, nuclear reactors, and so on. Overall this represents the core of theoretical and computational solid mechanics. In the last 20 years or so, the technological rush toward nano-sized systems has forced researchers to investigate mechanical phenomena at a length scale in which matter no longer can be considered as a continuum. This is the case, for instance, of investigating the crack-related features in a material displaying elastic or structural complexity (or, equivalently, inhomogeneity or disorder) at the nanoscale. This problem of atomic-scale granularity immediately seems to be prohibitive for (standard) solid mechanics. To better elaborate on this