Premium
About an analytical approach to a quasicontinuum method via Γ‐convergence
Author(s) -
Schäffner Mathias,
Schlömerkemper Anja
Publication year - 2014
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201410362
Subject(s) - convergence (economics) , statistical physics , context (archaeology) , grain boundary , nearest neighbour , continuum mechanics , physics , materials science , classical mechanics , computer science , geology , microstructure , paleontology , economic growth , economics , metallurgy , artificial intelligence
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 nearest and next‐to‐nearest neighbour interactions of Lennard‐Jones type and its quasicontinuum approximation via Γ‐convergence. In case of fracture it turns out that one has to coarse grain in the continuum region and at the atomistic/continuum interface in order to capture the same behavior as the atomistic model, while this is not needed if the boundary conditions are such that the system behaves elastically. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)