Multiscale methods coupling atomistic and continuum mechanics: analysis of a simple case
Frederic Legoll, ENPC LAMI

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 a particle model (discrete mechanics) with a macroscopic model (continuum mechanics). One such mehod is the Quasi-Continuum method. 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.

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