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Symmetries of 2-lattices and second order accuracy of the Cauchy--Born Model
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Koten, Brian Van and Ortner, Christoph (2012) Symmetries of 2-lattices and second order accuracy of the Cauchy--Born Model. Working Paper. ArXiv e-prints. (ArXiv e-prints).
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Official URL: http://arxiv.org/pdf/1203.5854v1.pdf
Abstract
We show that the Cauchy{Born model of a singlespecies 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.
| Item Type: | Working or Discussion Paper (Working Paper) |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Mathematics |
| Series Name: | ArXiv e-prints |
| Publisher: | ArXiv e-prints |
| Date: | 27 March 2012 |
| Number: | No.1203.5854v1 |
| Number of Pages: | 21 |
| Status: | Not Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Open Access |
| Funder: | PIRE, University of Minnesota Supercomputing Institute, Department of Energy, EPSRC |
| Grant number: | DMS-0757355, DMS-0811039, OISE-0967140, DE-SC0002085, EP/H003096 |
| Related URLs: | |
| URI: | http://wrap.warwick.ac.uk/id/eprint/48648 |
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