General Elasticity Theory for Graphene Membranes Based on Molecular Dynamics
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1057-II10-20
General Elasticity Theory for Graphene Membranes Based on Molecular Dynamics Kaveh Samadikhah1, Juan Atalaya2, Caroline Huldt1, Andreas Isacsson1, and Jari Kinaret1 1 Department of Applied Physics, Chalmers University of Technology, Kemigården 1, Gothenburg, SE-41296, Sweden 2 Department of Physics, University of Gothenburg, Kemigården 1, Gothenburg, SE-412 96, Sweden ABSTRACT We have studied the mechanical properties of suspended graphene membranes using molecular dynamics (MD) and generalized continuum elasticity theory (GE) in order to develop and assess a continuum description for graphene. The MD simulations are based on a valence force field model which is used to determine the deformation and the elastic energy of the membrane (EMD) as a function of external forces. For the continuum description, we use the expression Econt = Estretching + Ebending for the elastic energy functional. The elastic parameters (tensile rigidity and Poisson ratio) entering Econt are determined by requiring that Econt = EMD for a set of deformations. Comparisons with the MD results show excellent agreement. We find that the elastic energy of a supported graphene sheets is typically dominated by the nonlinear stretching terms whereas a linear description is valid only for very small deflections. This implies that in some applications, i.e. NEMS, a linear description is of limited applicability.
INTRODUCTION The recent progresses in fabricating single graphite layers (graphene) [1] have considerably boosted the attention for this material. Among its unique features are remarkable electronic properties [2], which make graphene of considerable interest both for fundamental science and for technological applications. Moreover, its exceptionally large mechanical strength [3] and its ability to sustain large electrical currents can be of great future value in the broad field of nanodevices. In particular, in the field of nanoelectromechanical systems (NEMS), graphenebased mechanical resonators were recently demonstrated [3]. In the context of NEMS, a reliable and efficient description of the mechanical properties of graphene is essential. One approach is to use atomistic numerical modeling techniques such as density functional theory or molecular dynamics (MD) [5]. However, atomistic numerical methods are restricted to small systems and their use become cumbersome for structures of experimentally relevant sizes. An alternative route is based on generalized continuum elasticity theory (GE). This approach has the advantage of better scaling, and it lends itself to analytical treatment as well. On the other hand, elasticity theory relies on the continuum approximation as well as a series of other approximations. The validity of continuum theory for a material only one atomic layer thick can be questioned. It is therefore important to identify the appropriate constitutive equations and elastic parameters, and to investigate carefully the theory’s range of applicability. Due to their high resilience to plastic deformations, many
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