Title: Analysis of a prototypical multiscale method coupling atomistic and continuum mechanics
 
Speaker: Frederic Legoll, University of Minnesota
                              
Date/Time: Thursday, July 14, 2005, 10:00-11:00 am (MT)

Location: Building 980, Room 95 (Sandia NM), Building 915, Room S145 (Sandia, CA)

Brief Abstract: In order to describe a solid which deforms smoothly in some region, but non smoothly in some other region, many multiscale methods have been recently proposed, that aim at coupling an atomistic model (discrete mechanics) with a macroscopic model (continuum mechanics). We present here a theoretical analysis for such a coupling in a one-dimensional setting. We study both the general case of a convex energy and a specific example of a nonconvex energy, the Lennard-Jones case.

In the latter situation, we prove that the discretization needs to account in an adequate way for the coexistence of a discrete model and a continuous one. Otherwise, spurious discretization effects may appear. We also consider the effect of the finite element discretization of the continuum model on the behaviour of the coupled model.

This work is joint with Xavier Blanc (Paris 6) and Claude Le Bris (CERMICS, ENPC).