Computational analysis of modeling error for the coupling of particle and continuum models by the Arlequin method

We propose in this paper a 1D model problem to study the convergence of surrogate approximations, using an atomistic-to-continuum coupling method, towards the solution of a full particle model. The 1D problem consists of a collection of springs that exhibits a local defect, materialized by a sudden...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2008-07, Vol.197 (41), p.3399-3409
Main Authors: Prudhomme, S., Ben Dhia, H., Bauman, P.T., Elkhodja, N., Oden, J.T.
Format: Article
Language:English
Subjects:
Atomistic-to-continuum coupling method
Engineering Sciences
Error analysis
Homogenization
Materials and structures in mechanics
Mechanics
Modeling error in quantities of interest
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Summary:We propose in this paper a 1D model problem to study the convergence of surrogate approximations, using an atomistic-to-continuum coupling method, towards the solution of a full particle model. The 1D problem consists of a collection of springs that exhibits a local defect, materialized by a sudden change in the spring properties. The surrogate model is obtained by the Arlequin approach which introduces an overlap region in which the continuum and particle models are coupled together using Lagrange multipliers. The objective of the present work is to show, via numerical experiments, that the modeling error does indeed converge to zero as the distance of the overlap region from the defect and/or its size are increased.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2008.03.014