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arXiv · 1108.2991

Consistent Energy-based Atomistic/Continuum Coupling for Two-body Potentials in Three Dimensions

Alexander V. Shapeev
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Abstract

Very few works exist to date on development of a consistent energy-based coupling of atomistic and continuum models of materials in more than one dimension. The difficulty in constructing such a coupling consists in defining a coupled energy whose minimizers are free from uncontrollable errors on the atomistic/continuum interface. In this paper a consistent coupling in three dimensions is proposed. The main achievement of this work is to identify and efficiently treat a modified Cauchy-Born continuum model which can be coupled to the exact atomistic model. The convergence and stability of the method is confirmed with numerical tests.

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Alexander V. Shapeev. 2012-09-10. Consistent Energy-based Atomistic/Continuum Coupling for Two-body Potentials in Three Dimensions. https://doi.org/10.1137/110844544

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