Analysis of a prototypical multiscale method coupling atomistic and continuum mechanics

Blanc, Xavier ; Bris, Claude Le ; Legoll, Frédéric

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 39 (2005), p. 797-826 / Harvested from Numdam

Résumé

In order to describe a solid which deforms smoothly in some region, but non smoothly in some other region, many multiscale methods have recently been proposed. They aim at coupling an atomistic model (discrete mechanics) with a macroscopic model (continuum mechanics). We provide here a theoretical ground for such a coupling in a one-dimensional setting. We briefly study the general case of a convex energy, and next concentrate on 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 provide a numerical analysis of the approach.

Détail

Publié le : 2005-01-01

MR 2165680 | Zbl pre02213940 | 4 citations dans Numdam

DOI : https://doi.org/10.1051/m2an:2005035
Classification:  65K10,  74G15,  74G70,  74N15

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