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Analysis of a Prototypical Multiscale Method Coupling Atomistic and Continuum Mechanics

Thursday, April 14, 2005 - 11:15am - 12:15pm
EE/CS 3-180
Frédéric Legoll (University of Minnesota, Twin Cities)
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).