Symmetries of 2-lattices and second order accuracy of the Cauchy--Born Model

Brian Van Koten; Christoph Ortner

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arXiv · 1203.5854

Symmetries of 2-lattices and second order accuracy of the Cauchy--Born Model

Brian Van Koten·Christoph Ortner

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Abstract

We show that the Cauchy--Born model of a single-species 2-lattice is second order if the atomistic and continuum kinematics are connected in a novel way. Our proof uses a generalization to 2-lattices of the point symmetry of Bravais lattices. Moreover, by identifying similar symmetries in multi-species pair interaction models, we construct a new stored energy density, using shift-gradients but not strain gradients, that is also second order accurate. These results can be used to develop highly accurate continuum models and atomistic/continuum coupling methods for materials such as graphene, hcp metals, and shape memory alloys.

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Brian Van Koten, Christoph Ortner. 2012-03-27. Symmetries of 2-lattices and second order accuracy of the Cauchy--Born Model. https://arxiv.org/abs/1203.5854

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