Numerical Methods Across Scales

The traditional analytical framework in engineering mechanics has been that of a continuum. However, the mechanical deformation and failure of many engineering materials are inherently multi-scale. Indeed, the observed homogeneous macroscopic (continuum scale) behavior of the material is governed by physical processes that occur at a heterogeneous microscopic fine scale. The current challenge in several solid mechanics applications is to incorporate micro-structural and/or atomic details to improve model predictions. However, approximations need to be done since the explicit representation of billions of atoms is out of reach even for the largest computer ever built.

At LSMS we develop and implement such multi-scale approaches. We put particular emphasis on direct concurrent coupling between discrete and continuum models. Our main current efforts are directed towards finite temperature and dislocation defects management when coupling molecular dynamics, dislocation dynamics and continuum mechanics. These multi-scale methods find direct applications in fracture (e.g. fatigue) and contact mechanics, where dislocations originate at atoms (discrete representation) whereas bulk behavior is best described by continuum approaches.



Selected Publications