Geometrically consistent approximations of the energy in the quasi-continuum framework
Résumé
This paper addresses the issue of consistent and generic energy-based passing from a discrete model with finite-range interactions to a surrogate discrete model with nearest neighbor interactions only. For this purpose, we introduce a transition zone that defines a volume interface between the two models and enables us to deal with incompatibilities between these models. Over the transition zone, a geometrically consistent approximation of the energy of the discrete system is defined; it sets up energies in an automatic manner and for a large set of configu- rations. In this framework, two possible schemes are then presented and analyzed, and performances of these schemes are compared on several numerical experiments in statics or dynamics regimes.