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A finite deformation membrane based on inter-atomic potentials for the transverse mechanics of nanotubes
(2003-03)
Article.
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Article.
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A finite deformation hyper-elastic membrane theory based on inter-atomic potentials for crystalline films composed of a single atomic layer is developed. For this purpose, an extension of the standard Born rule that exploits ...
Nonlinear mechanical response and rippling of thick multi-walled carbon nanotubes
(2003-11)
Article.
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Article.
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The measured drop of the effective bending stiffness of multiwalled carbon nanotubes (MWCNTs) with increasing diameter is investigated by a generalized local quasicontinuum method. The previous hypothesis that this reduction ...
Effective coarse-grained simulations of super-thick multi-walled carbon nanotubes under torsion
(2009-02)
Article.
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Article.
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Under torsion and beyond the buckling point, multi-walled carbon nanotubes (MWCNTs) develop a periodic wave-like rippling morphology. Here, we show that torsional rippling deformations can be accurately described by a ...
Size dependent nonlinear elastic scaling of multiwalled carbon nanotubes
(2008-02)
Article.
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Article.
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We characterize through large-scale simulations the nonlinear elastic response of multi-walled carbon nanotubes (MWNCNTs) in torsion and bending. We identify a unified law consisting of two distinct power-law regimes in ...
Elastic bending modulus of monolayer graphene
(2009-05)
Article.
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Article.
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An analytic formula is derived for the elastic bending modulus of monolayer graphene based on an empirical potential for solid-state carbon atoms. Two physical origins are identified for the non-vanishing bending stiffness ...
Finite crystal elasticity of carbon nanotubes based on the exponential Cauchy-Born rule
(2004-03)
Article.
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Article.
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A finite deformation continuum theory is derived from interatomic potentials for the analysis of the mechanics of carbon nanotubes. This nonlinear elastic theory is based on an extension of the Cauchy-Born rule called the ...
An atomistic-based finite deformation membrane for single layer crystalline films
(2002-09)
Article.
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Article.
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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 ...
Finite element methods for the non-linear mechanics of crystalline sheets and nanotubes
(Wiley and Sons, 2004-01)
Article.
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Article.
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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 ...
Rippling and a phase-transforming mesoscopic model for multiwalled carbon nanotubes
(2008-04)
Article.
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Article.
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We propose to model thick multiwalled carbon nanotubes as beams with non-convex curvature energy. Such models develop stressed phase mixtures composed of smoothly bent sections and rippled sections. This model is motivated ...