Seminar: I&C Mathematics - Coarse-graining atomistic models for crystalline solids

Industrial and Computational Mathematics Seminar

Dr Christoph Ortner (Warwick)

Although continuum mechanics is one of the most successful branches of mathematical modelling, all of its models have a restricted region of validity. For example, we could model crystal elasticity using a nonlinear elasticity model (e.g., the Cauchy--Born model), however, such a continuum model is highly inaccurate in the neighbourhood of defects such as vacancies, dislocations, cracks, etc. By coupling atomistic models of the defects with continuum models for the elastic far field one can, in principle, obtain models with near-atomistic accuracy at significantly reduced computational cost. However, several pitfalls need to be overcome to find a reliable coupling mechanism.
I will first describe the construction of coarse-grained continuum models of atomistic solids. I will then present a general overview and introduction to atomistic/continuum coupling problem, followed by some recent developments on the construction and rigorous numerical analysis.