Aufsatz
Continuous modelling of single layer 2D carbonnanostructures based on a modified Cauchy–Born rule
Zusammenfassung
Graphene is the thinnest known structure. It consists of a single layer of carbon atoms and has unique mechanical properties. The carbon atoms form bonds with neighbouring atoms that can be described by interatomic potentials. A simulation of molecular mechanical processes can be performed by applying the formalism of the finite element method to the interatomic potentials. Neglecting local effects, a continuum formulation is an efficient alternative to a discrete model. The continuum formulation requires a connection between the discrete atomic lattice and the continuum. One way of doing this is to use the Cauchy–Born rule. This paper reviews the extensions of the Cauchy–Born rule, in particular, the exponential Cauchy–Born rule, and adds an alternative approach. It is shown that all contributions dealing with the exponential Cauchy–Born rule inevitably lead to shell models with Kirchhoff–Love kinematics. The approach presented here instead uses a shell model with Reissner–Mindlin kinematics, which has the major advantage of a much simpler mesh generation and a simpler application of the boundary condition.
Zitierform
In: Proceedings in applied mathematics and mechanics : PAMM Volume 23 / Issue 2 (2023-09-08) eissn:1617-7061Förderhinweis
Gefördert im Rahmen des Projekts DEALZitieren
@article{doi:10.17170/kobra-202311018935,
author={Ochs, Julian and Wackerfuß, Jens},
title={Continuous modelling of single layer 2D carbonnanostructures based on a modified Cauchy–Born rule},
journal={Proceedings in applied mathematics and mechanics : PAMM},
year={2023}
}
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2023-11-01T14:41:53Z 2023-11-01T14:41:53Z 2023-09-08 doi:10.17170/kobra-202311018935 http://hdl.handle.net/123456789/15139 Gefördert im Rahmen des Projekts DEAL eng Namensnennung-Nicht-kommerziell 4.0 International http://creativecommons.org/licenses/by-nc/4.0/ Cauchy–Born hypothesis extension Cauchy–Born hypothesis graphene-based nanostructures homogenisation Reissner–Mindlin shell element 510 Continuous modelling of single layer 2D carbonnanostructures based on a modified Cauchy–Born rule Aufsatz Graphene is the thinnest known structure. It consists of a single layer of carbon atoms and has unique mechanical properties. The carbon atoms form bonds with neighbouring atoms that can be described by interatomic potentials. A simulation of molecular mechanical processes can be performed by applying the formalism of the finite element method to the interatomic potentials. Neglecting local effects, a continuum formulation is an efficient alternative to a discrete model. The continuum formulation requires a connection between the discrete atomic lattice and the continuum. One way of doing this is to use the Cauchy–Born rule. This paper reviews the extensions of the Cauchy–Born rule, in particular, the exponential Cauchy–Born rule, and adds an alternative approach. It is shown that all contributions dealing with the exponential Cauchy–Born rule inevitably lead to shell models with Kirchhoff–Love kinematics. The approach presented here instead uses a shell model with Reissner–Mindlin kinematics, which has the major advantage of a much simpler mesh generation and a simpler application of the boundary condition. open access Ochs, Julian Wackerfuß, Jens 9 Seiten doi:10.1002/pamm.202300197 Festkörpermechanik Kristallgitter Mindlin-Reissner plate theory Nanostruktur publishedVersion eissn:1617-7061 Issue 2 Proceedings in applied mathematics and mechanics : PAMM Volume 23 false e202300197
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