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 (No.1203.5854v1).

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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, Engineering and Medicine > Science > Mathematics
Series Name:	ArXiv e-prints
Publisher:	ArXiv e-prints
Official Date:	27 March 2012
Dates:	Date Event 27 March 2012 ["eprint_fieldopt_dates_date_type_available" not defined]
Number:	No.1203.5854v1
Number of Pages:	21
Institution:	University of Warwick
Status:	Not Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access (Creative Commons)
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:	Publisher

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