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Multiscale methods coupling atomistic and continuum mechanics: analysis of a simple case

The description and computation of fine scale localized phenomena arising in a material (during nanoindentation, for instance) is a challenging problem that has given birth to many multiscale methods. In this work, we propose an analysis of a simple one-dimensional method that couples two scales, the atomistic one and the continuum mechanics one. The method includes an adaptive criterion in order to split the computational domain into two subdomains, that are described at different scales.