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Finite element methods for the non-linear mechanics of crystalline sheets and nanotubes
dc.contributor.author | Arroyo Balaguer, Marino |
dc.contributor.author | Belytschko, T. |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III |
dc.date.accessioned | 2010-08-02T08:06:12Z |
dc.date.available | 2010-08-02T08:06:12Z |
dc.date.created | 2004-01 |
dc.date.issued | 2004-01 |
dc.identifier.citation | Arroyo, M.; Belytschko, T. Finite element methods for the non-linear mechanics of crystalline sheets and nanotubes. "International journal for numerical methods in engineering", 21 Gener 2004, vol. 59, núm. 3, p. 419-456. |
dc.identifier.issn | 0029-5981 |
dc.identifier.uri | http://hdl.handle.net/2117/8526 |
dc.description | The definitive version is available at http://www3.interscience.wiley.com/journal/106569279/abstract |
dc.description.abstract | The formulation and finite element implementation of a finite deformation continuum theory for the mechanics of crystalline sheets is described. This theory generalizes standard crystal elasticity to curved monolayer lattices by means of the exponential Cauchy-Born rule. The constitutive model for a two-dimensional continuum deforming in three dimensions (a surface) is written explicitly in terms of the underlying atomistic model. The resulting hyper-elastic potential depends on the stretch and the curvature of the surface, as well as on internal elastic variables describing the rearrangements of the crystal within the unit cell. Coarse grained calculations of carbon nanotubes (CNTs) are performed by discretizing this continuum mechanics theory by finite elements. A smooth discrete representation of the surface is required, and subdivision finite elements, proposed for thin-shell analysis, are used. A detailed set of numerical experiments, in which the continuum/finite element solutions are compared to the corresponding full atomistic calculations of CNTs, involving very large deformations and geometric instabilities, demonstrates the accuracy of the proposed approach. Simulations for large multi-million systems illustrate the computational savings which can be achieved. |
dc.format.extent | 38 p. |
dc.language.iso | eng |
dc.publisher | Wiley and Sons |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits |
dc.subject | Àrees temàtiques de la UPC::Física::Física de l'estat sòlid::Propietats mecàniques |
dc.subject.lcsh | Nanotubes, Carbon |
dc.subject.lcsh | Finite element method |
dc.subject.other | carbon nanotubes |
dc.subject.other | continuum surface model |
dc.subject.other | hyperelasticity |
dc.subject.other | finite elements |
dc.title | Finite element methods for the non-linear mechanics of crystalline sheets and nanotubes |
dc.type | Article |
dc.subject.lemac | Elements finits, Mètode dels |
dc.subject.lemac | Nanotubs de carboni |
dc.contributor.group | Universitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria |
dc.identifier.doi | 10.1002/nme.944 |
dc.description.peerreviewed | Peer Reviewed |
dc.relation.publisherversion | https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.944 |
dc.rights.access | Open Access |
local.identifier.drac | 2631001 |
dc.description.version | Postprint (author’s final draft) |
local.citation.author | Arroyo, M.; Belytschko, T. |
local.citation.other | The definitive version is available at http://www3.interscience.wiley.com/journal/106569279/abstract |
local.citation.publicationName | International journal for numerical methods in engineering |
local.citation.volume | 59 |
local.citation.number | 3 |
local.citation.startingPage | 419 |
local.citation.endingPage | 456 |
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