Phonon, Cauchy-Born and homogenized stability criteria for a free-standing monolayer graphene at the continuum level

Sfyris, D.

doi:10.1016/j.euromechsol.2015.08.011

Cited by 10 publications

(13 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This approach is fairly classical, at least in the case of infinite crystals, where a number of different stability criteria has been set forth, essentially by prescribing specific set of admissible perturbations [14,15]. The reader is referred to the discrete-to-continuous analysis in [12,13] and the recent comparison in [36] of such different stability concepts at the continuum level for free-standing graphene. Our approach here is that of possibly considering all small perturbations, where such smallness is exclusively aimed at preserving the local coordination of the atomic bonds.…”

Section: Introductionmentioning

confidence: 99%

Carbon-Nanotube Geometries as Optimal Configurations

Mainini¹,

Murakawa²,

Piovano³

et al. 2017

Multiscale Model. Simul.

View full text Add to dashboard Cite

The fine geometry of carbon nanotubes is investigated from the viewpoint of Molecular Mechanics. Actual nanotube configurations are characterized as being locally minimizing a given configurational energy, including both two-and three-body contributions. By focusing on so-called zigzag and armchair topologies, we prove that the configurational energy is strictly minimized within specific, one-parameter families of periodic configurations. Such optimal configurations are checked to be stable with respect to a large class of small nonperiodic perturbations and do not coincide with classical rolled-up nor polyhedral geometries.2010 Mathematics Subject Classification. 82D25.

show abstract

Section: Introductionmentioning

confidence: 99%

Carbon-Nanotube Geometries as Optimal Configurations

Mainini¹,

Murakawa²,

Piovano³

et al. 2017

Multiscale Model. Simul.

View full text Add to dashboard Cite

show abstract

“…The mathematical framework for describing the graphene-substrate system is presented in the work by Sfyris et al [4]. There, we consider simple loading/deformation histories for three classes of problems within the linear framework [5,6] of modeling graphene as a hexagonal 2-lattice [7][8][9][10][11]. The first class of problems pertains to in-surface motions only, while the second class are where we also have out-of-surface motions.…”

Section: Introductionmentioning

confidence: 99%

Influence of partial blistering on the global and the local stress and couple stress field for a monolayer graphene resting on substrate

Sfyris

2017

Mathematics and Mechanics of Solids

View full text Add to dashboard Cite

Partial delamination of a thin film attached on a substrate is a phenomenon which is likely to occur in many film/substrate systems. Such a delamination strongly affects the developed stress and couple stress field of the film. The objective of this work is to accurately determine the effect of delamination on the stress and the couple stress field of a monolayer-thick graphene film bonded on a polymeric substrate. The theoretical framework we adopt is restricted to the materially and geometrically linear case; graphene is modeled as a hexagonal 2-lattice, while the substrate is assumed to behave in an isotropic linearly elastic manner. The present approach expands significantly on recent findings [4] for the case of partial blistering of the film resting on a substrate. We investigate the influence of the perfect bonding parameter, the substrate material and the size of the specimen, on stresses and couple stresses. Various stress and couple stress profiles illustrate the effect of the above on the local stress and couple stress fields. We also explore the effect on the global stress and global couple stress measures that we define by integrating the local stress and couple stress field along the surface of the film. Selected diagrams illustrate the effect delamination has on these global measures. Our theoretical analysis shows that the effect of delamination is of cardinal importance for the developed stress and couple stress fields of monolayer graphene.

show abstract

“…Note that various concepts of crystal stability are available. We refer the reader to [14] for a discussion of the connections between phononstability, homogenized-continuum stability, and Cauchy-born stability in the case of three-dimensional crystals and [43] for an application at the continuum level for freestanding graphene. The validity of the Cauchy-Born assumption for crystalline solids has been also discussed in [13] and [17].…”

Section: Introductionmentioning

confidence: 99%

The Geometry of $C_{60}$: A Rigorous Approach via Molecular Mechanics

Friedrich¹,

Piovano²,

Stefanelli³

2016

SIAM J. Appl. Math.

View full text Add to dashboard Cite

Abstract. Molecular Mechanics describes molecules as particle configurations interacting via classical potentials. These configurational energies usually consist of the sum of different phenomenological terms which are tailored to the description of specific bonding geometries. This approach is followed here to model the fullerene C 60 , an allotrope of carbon corresponding to a specific hollow spherical structure of sixty atoms. We rigorously address different modeling options and advance a set of minimal requirements on the configurational energy able to deliver an accurate prediction of the fine three-dimensional geometry of C 60 as well as of its remarkable stability. In particular, the experimentally observed truncated-icosahedron structure with two different bond lengths is shown to be a strict local minimizer.

show abstract

Phonon, Cauchy-Born and homogenized stability criteria for a free-standing monolayer graphene at the continuum level

Cited by 10 publications

References 40 publications

Carbon-Nanotube Geometries as Optimal Configurations

Carbon-Nanotube Geometries as Optimal Configurations

Influence of partial blistering on the global and the local stress and couple stress field for a monolayer graphene resting on substrate

The Geometry of $C_{60}$: A Rigorous Approach via Molecular Mechanics

Contact Info

Product

Resources

About