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Nonlinear bending and stretching of a circular graphene sheet under a central point load

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TLDR
It is shown herein that, with properly selected parameters, the von Kármán plate theory can provide a remarkably accurate prediction of the graphene sheet behavior under linear and nonlinear bending and stretching.
Abstract
Understanding of the bending and stretching properties of graphene is crucial in guiding its growth and applications. In this paper, we investigate the deformation of a single layer, circular, graphene sheet under a central point load by carrying out molecular mechanics (MM) simulations. The bending and stretching of the graphene sheet are characterized by using the von Karman plate theory. Stress concentrations near the loaded region and the boundary due to bending rigidity of the graphene sheet are highlighted. It is shown herein that, with properly selected parameters, the von Karman plate theory can provide a remarkably accurate prediction of the graphene sheet behavior under linear and nonlinear bending and stretching.

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Citations
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Intrinsic ripples in graphene

TL;DR: In this paper, the authors address the nature of these height fluctuations by means of straightforward atomistic Monte Carlo simulations based on a very accurate many-body interatomic potential for carbon and find that ripples spontaneously appear due to thermal fluctuations with a size distribution peaked around 70 \AA which is compatible with experimental findings (50-100 \AA) but not with the current understanding of flexible membranes.
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Mechanical properties of bilayer graphene sheets coupled by sp3 bonding

TL;DR: In this article, the sp3 bonds exert a strengthening influence on the interlayer shear modulus as well as the load transfer rate, thereby enhancing the stability capacity of bilayer graphene sheets under axial compression.
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Effects of functional groups on the mechanical and wrinkling properties of graphene sheets

TL;DR: In this paper, the effects of the degree of functionalization, molecular structure and molecular weight of functional groups on the Young's modulus of graphene sheets were investigated through molecular dynamics and molecular mechanics simulations.
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Mechanical properties of monolayer graphene under tensile and compressive loading

TL;DR: In this article, the mechanical properties of zigzag graphene and armchair graphene nanoribbon under tensile and compressive loading are studied by the use of quantum mechanics as well as quantum molecular dynamics (MD) method based on the Roothaan-Hall equation and the Newton motion laws.
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A review on the flexural mode of graphene: lattice dynamics, thermal conduction, thermal expansion, elasticity and nanomechanical resonance

TL;DR: This review focuses on exploring the relationship between the flexural mode and thermal and mechanical properties of graphene, and describes how the Young's modulus of graphene can be extracted from its thermal fluctuations, which are dominated by theflexural mode.
References
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Journal ArticleDOI

Electric Field Effect in Atomically Thin Carbon Films

TL;DR: Monocrystalline graphitic films are found to be a two-dimensional semimetal with a tiny overlap between valence and conductance bands and they exhibit a strong ambipolar electric field effect.
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The rise of graphene

TL;DR: Owing to its unusual electronic spectrum, graphene has led to the emergence of a new paradigm of 'relativistic' condensed-matter physics, where quantum relativistic phenomena can now be mimicked and tested in table-top experiments.
Book

Theory of elasticity

TL;DR: The theory of the slipline field is used in this article to solve the problem of stable and non-stressed problems in plane strains in a plane-strain scenario.
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Detection of individual gas molecules adsorbed on graphene

TL;DR: In this paper, it was shown that micrometre-size sensors made from graphene are capable of detecting individual events when a gas molecule attaches to or detaches from graphene's surface.
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