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The Quasicontinuum Method: Theory and Applications

Kochmann, Dennis M. and Amelang, Jeffrey S. (2016) The Quasicontinuum Method: Theory and Applications. In: Multiscale Materials Modeling for Nanomechanics. Springer Series in Materials Science. No.245. Springer , Cham, Switzerland, pp. 159-193. ISBN 978-3-319-33478-3.

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The quasicontinuum (QC) method has become a popular technique to bridge the gap between atomistic and continuum length scales in crystalline solids. In contrast to many other concurrent scale-coupling methods, the QC method only relies upon constitutive information on the lowest scale (viz., on interatomic potentials) and thus avoids empirical constitutive laws at the larger scales. This is achieved by the application of a seamless coarse-graining scheme to the discrete atomistic ensemble and the careful selection of a small set of representative atoms. Since its inception almost two decades ago, many different variants and flavors of the QC method have been developed, not only to study the mechanics of solids but also to describe such physical phenomena as mass and heat transfer, or to efficiently describe fiber networks and truss structures. Here, we review the theoretical fundamentals and give a (non-exhaustive) overview of the state of the art in QC theory, computational methods, and applications. We particularly emphasize the fully nonlocal QC formulation which adaptively ties atomistic resolution to moving defects, and we illustrate simulation results based on this framework. Finally, we point out challenges and open questions associated with the QC methodology.

Item Type:Book Section
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Kochmann, Dennis M.0000-0002-9112-6615
Additional Information:© 2016 Springer International Publishing Switzerland. First Online: 31 August 2016. The authors gratefully acknowledge support from the National Science Foundation (NSF) under grant number CMMI-123436.
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Series Name:Springer Series in Materials Science
Issue or Number:245
Record Number:CaltechAUTHORS:20170705-075708170
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78747
Deposited By: Tony Diaz
Deposited On:07 Jul 2017 17:10
Last Modified:03 Oct 2019 18:11

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