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About an analytical approach to a quasicontinuum method via Γ‐convergence
Author(s) -
Schäffner Mathias,
Schlömerkemper Anja
Publication year - 2016
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201610261
Subject(s) - limiting , convergence (economics) , pairwise comparison , statistical physics , context (archaeology) , mathematics , physics , engineering , geology , mechanical engineering , paleontology , statistics , economics , economic growth
We report on an analytical study of a quasicontinuum method in the context of fracture mechanics in a one‐dimensional setting. To this end, we compare the asymptotic behaviour of a discrete model with pairwise interactions of Lennard‐Jones type and its quasicontinuum approximation via Γ‐convergence. In an elastic regime the limiting behavior of the orginal model and its quasicontinuum approximation coincide. In the case of fracture it turns out that it is necessary to coarse grain the quasicontinuum approximation in the continuum region and at the atomistic/continuum interface in order to capture the same behavior as the atomistic model. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)