The stability of two-dimensional (2D) layers and membranes is subject of a long standing theoretical debate. According to the so called Mermin-Wagner theorem, long wavelength fluctuations destroy the long-range order for 2D crystals. Similarly, 2D membranes embedded in a 3D space have a tendency to be crumpled. These dangerous fluctuations can, however, be suppressed by anharmonic coupling between bending and stretching modes making that a two-dimensional membrane can exist but should present strong height fluctuations. The discovery of graphene, the first truly 2D crystal and the recent experimental observation of ripples in freely hanging graphene makes these issues especially important. Beside the academic interest, understanding the mechanisms of stability of graphene is crucial for understanding electronic transport in this material that is attracting so much interest for its unusual Dirac spectrum and electronic properties. Here we 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. We 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 stability of flexible membranes. This unexpected result seems to be due to the multiplicity of chemical bonding in carbon.

Intrinsic ripples in graphene

Nonlinear vibration of functionally graded graphene-reinforced composite laminated plates in thermal environments

In this paper, the free vibration of magnetoelectro-elastic (MEE) nanoplates is investigated based on the nonlocal theory and Kirchhoff plate theory. The MEE nanoplate is assumed as all edges simply supported rectangular plate subjected to the biaxial force, external electric potential, external magnetic potential, and temperature rise. By using the Hamilton's principle, the governing equations and boundary conditions are derived and then solved analytically to obtain the natural frequencies of MEE nanoplates. A parametric study is presented to examine the effect of the nonlocal parameter, thermo-magneto-electro-mechanical loadings and aspect ratio on the vibration characteristics of MEE nanoplates. It is found that the natural frequency is quite sensitive to the mechanical loading, electric loading and magnetic loading, while it is insensitive to the thermal loading.

Free vibration of size-dependent magneto-electro-elastic nanoplates based on the nonlocal theory

https://northumbria-test.eprints-hosting.org/id/document/268107

A review on the mechanics of nanostructures

This paper investigates the free vibration of magneto-electro-elastic (MEE) nanobeams based on the nonlocal theory and Timoshenko beam theory. The MEE nanobeam is subjected to the external electric potential, magnetic potential and uniform temperature rise. The governing equations and boundary conditions are derived by using the Hamilton principle and discretized by using the differential quadrature (DQ) method to determine the natural frequencies and mode shapes. A detailed parametric study is conducted to study the influences of the nonlocal parameter, temperature rise, external electric and magnetic potentials on the size-dependent vibration characteristics of MEE nanobeams.

Free vibration of size-dependent magneto-electro-elastic nanobeams based on the nonlocal theory

Nonlocal plate model for nonlinear bending of bilayer graphene sheets subjected to transverse loads in thermal environments

Prediction of nonlinear vibration of bilayer graphene sheets in thermal environments via molecular dynamics simulations and nonlocal elasticity

We report here the buckling phenomenon of a monolayer graphene with four free edges subjected to uniaxial tension by molecular dynamics simulations. We find that the buckling occurs when tension force is applied and is sufficiently large for both armchair and zigzag single layer graphene sheets. The maximum amplitude is increased and the maximum wavelength is decreased with increase in temperature.

Yu-Mou Xu

Papers

Nonlocal plate model for nonlinear bending of bilayer graphene sheets subjected to transverse loads in thermal environments

Prediction of nonlinear vibration of bilayer graphene sheets in thermal environments via molecular dynamics simulations and nonlocal elasticity

Graphene: Why buckling occurs?