Brittle Fracture and Plastic Slip in Materials: from the Atomistic to the Engineering Scale
May 26, 2008 — May 30, 2008
Coordinators:
- Antonio De Simone (SISSA, Trieste, Italy)
- Luciano Colombo (Univ. d. Studi di Cagliari, Monserrato (CA), Italy)
In recent years new techniques – complementing the traditional approaches based on experiment and on continuum theories – have become available to study, understand, and control those mechanical phenomena occurring when deformations organize in spatially localized patterns. On the one hand, atomistic simulations have reached the scale and resolution necessary to perform numerical experiments describing extended defects and their interaction. On the other hand, new mathematical tools have made it possible to model in microscopic detail the evolution of those singularities (dislocations, shear bands, cracks), which control the inelastic response of solids at the macroscopic level.
The occurrence of such conceptually diverse developments has led to a new generation of numerical models, aimed at interfacing the atomistic and continuum description. Here, the wide range of length and time scales that need to be resolved creates a situation where a single set of methods/approaches cannot be used. Rather, different tools are employed to deal with a hierarchy of sub-problems. In such a multiscale theoretical device, phenomenological models are typically used to incorporate the properties at a finer scale within calculations at a larger scale. The ability to couple atomic-scale (or, even, electronic-level) simulations with macroscopic modeling represents a revolutionary step forward towards the ability to predict bulk material properties from first principles, so that constitutive laws need no longer to be postulated for describing the mechanical behaviour of a given system. Similarly, the incorporation of microstructural inhomogeneities and the explicit resolution of cracks and shear bands in finite element simulations at the continuum scale have led to significant improvements in our understanding of material response.
The aim of this course is to present the above recent developments by highlighting both strengths and limitations of each single method, and emphasizing the necessity of bridging between different time and length scales. Focus will be put on:
i. advances in atomistic simulations offering the possibility to span time intervals typical of some interesting mechanical phenomena;
ii. coarsening of spatial degrees of freedom, namely, a key issue for bridging disparate lengths;
iii. mechanisms of fracture in brittle solids and of plastic deformation in amorphous materials (in particular, shear banding in metallic glasses), examined both at the atomistic and at the continuum scale.
The course is addressed to Master and Ph.D. students, post-docs and research associates in applied mathematics, physics, materials science, mechanical sciences, and structural (e.g., civil, mechanical,…) engineering.