Koten, Brian Van and Ortner, Christoph (2013) Symmetries of 2-lattices and second order accuracy of the Cauchy-Born model. Multiscale Modeling & Simulation, Volume 11 (Number 2). pp. 615-634. doi:10.1137/120870220 ISSN 1540-3459.
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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 multispecies 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: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics |
| Library of Congress Subject Headings (LCSH): | Lattice theory, Multiscale modeling, Continuum mechanics |
| Journal or Publication Title: | Multiscale Modeling & Simulation |
| Publisher: | World Scientific Publishing Co. Pte. Ltd. |
| ISSN: | 1540-3459 |
| Official Date: | 2013 |
| Dates: | Date Event 2013 Published |
| Volume: | Volume 11 |
| Number: | Number 2 |
| Page Range: | pp. 615-634 |
| DOI: | 10.1137/120870220 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| Date of first compliant deposit: | 26 December 2015 |
| Date of first compliant Open Access: | 26 December 2015 |
| Funder: | National Science Foundation (U.S.) (NSF), University of Minnesota. Supercomputer Institute, United States. Department of Energy, Engineering and Physical Sciences Research Council (EPSRC) |
| Grant number: | DMS-0757355 (NSF), DMS-0811039 (NSF), OISE-0967140 (NSF), DE-SC0002085 (DOE), EP/H003096 (EPSRC) |
| URI: | https://wrap.warwick.ac.uk/59236/ |
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