An atomistic-based foliation model for multilayer graphene materials and nanotubes

We present a three-dimensional continuum model for layered crystalline materials made out of weakly interacting two-dimensional crystalline sheets. We specialize the model to multilayer graphene materials, including multi-walled carbon nanotubes (MWCNTs). We view the material as a foliation, partiti...

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Veröffentlicht in:	Journal of the mechanics and physics of solids Jg. 61; H. 1; S. 235 - 253
Hauptverfasser:	Ghosh, Susanta, Arroyo, Marino
Format:	Journal Article Verlag
Sprache:	Englisch
Veröffentlicht:	Elsevier Ltd 01.01.2013
Schlagworte:	74 Mechanics of deformable solids 74B Elastic materials 90 Operations research, mathematical programming 90B Operations research and management science Buckling Classificació AMS Continuums Crystal structure Elasticitat Elasticity Graphene Investigació operativa Leaves Matemàtica aplicada a les ciències Matemàtiques i estadística Mathematical models Multi-walled carbon nanotubes Multilayers Operations research Programació matemàtica Quasicontinuum Resistència de materials Strength of materials Van der Waals forces Walls Àrees temàtiques de la UPC Multi-walled carbon nanotubes Graphene Quasicontinuum Buckling
ISSN:	0022-5096
Online-Zugang:	Volltext
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Zusammenfassung:	We present a three-dimensional continuum model for layered crystalline materials made out of weakly interacting two-dimensional crystalline sheets. We specialize the model to multilayer graphene materials, including multi-walled carbon nanotubes (MWCNTs). We view the material as a foliation, partitioning of space into a continuous stack of leaves, thus loosing track of the location of the individual graphene layers. The constitutive model for the bulk is derived from the atomistic interactions by appropriate kinematic assumptions, adapted to the foliation structure and mechanics. In particular, the elastic energy along the leaves of the foliation results from the bonded interactions, while the interaction energy between the walls, resulting from van der Waals forces, is parametrized with a stretch transversal to the foliation. The resulting theory is distinct from conventional anisotropic models, and can be readily discretized with finite elements. The discretization is not tied to the individual walls and allows us to coarse-grain the system in all directions. Furthermore, the evaluation of the non-bonded interactions becomes local. We test the accuracy of the foliation model against a previously proposed atomistic-based continuum model that explicitly describes each and every wall. We find that the new model is very efficient and accurate. Furthermore, it allows us to rationalize the rippling deformation modes characteristic of thick MWCNTs, highlighting the role of the van der Waals forces and the sliding between the walls. By exercising the model with very large systems of hollow MWCNTs and suspended multilayer graphene, containing up to 109 atoms, we find new complex post-buckling deformation patterns.
Bibliographie:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	0022-5096
DOI:	10.1016/j.jmps.2012.07.002