An atomistic-based finite deformation membrane for single layer crystalline films
A general methodology to develop hyper-elastic membrane models applicable to crystalline films one-atom thick is presented. In this method, an extension of the Born rule based on the exponential map is proposed. The exponential map accounts for the fact that the lattice vectors of the crystal lie al...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2002 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/8545 |
| Acceso en línea: | https://hdl.handle.net/2117/8545 https://dx.doi.org/10.1016/S0022-5096(02)00002-9 |
| Access Level: | acceso abierto |
| Palabra clave: | Finite element method Nanotubes, Carbon Buckling Constitutive behavior Shells and membranes Finite elements Atomistic models Elements finits, Mètode dels Nanotubs de carboni Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits |
| Sumario: | A general methodology to develop hyper-elastic membrane models applicable to crystalline films one-atom thick is presented. In this method, an extension of the Born rule based on the exponential map is proposed. The exponential map accounts for the fact that the lattice vectors of the crystal lie along the chords of the curved membrane, and consequently a tangent map like the standard Born rule is inadequate. In order to obtain practical methods, the exponential map is locally approximated. The effectiveness of our approach is demonstrated by numerical studies of carbon nanotubes. Deformed configurations as well as equilibrium energies of atomistic simulations are compared with those provided by the continuum membrane resulting from this method discretized by finite elements. |
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