Evaluation of the in-plane effective elastic moduli of single-layered graphene sheet
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Evaluation of the in-plane effective elastic moduli of single-layered graphene sheet K. Alzebdeh
Received: 19 July 2011 / Accepted: 30 April 2012 / Published online: 15 May 2012 Ó Springer Science+Business Media, B.V. 2012
Abstract In this paper, an equivalent continuumstructural mechanics approach is used to characterize the mechanical behaviour of nanostructured graphene. The in-plane elastic deformation of armchair graphene sheets is simulated by using finite element modelling. The model is based on the assumption that force interaction among carbon atoms can be modelled by load-carrying beams in a representative two-dimensional honeycomb lattice structure. The elastic properties of beam elements are determined by equating the energies of the molecular structure and the continuum beam model subjected to small strain deformation. Then an equivalent continuum technique is adopted to estimate effective elastic moduli from which elastic constants are extracted. A comparison of elastic constants obtained from current modelling concur with results reported in literature. With the multifunctional properties of graphene sheets as manifested in a broad range of industrial applications, determination of their elastic moduli will facilitate a better design of the corresponding materials at macroscopic level. Keywords Nanostructure Finite element Graphene sheet Elastic moduli
K. Alzebdeh (&) Department of Mechanical and Industrial Engineering, College of Engineering, Sultan Qaboos University, P.O. Box 33, Al Khod 123, Muscat, Sultanate of Oman e-mail: [email protected]
1 Introduction Since emerging as a new method of production, planar nanostructured graphene sheets have attracted a tremendous interest, which can be attributed to their extraordinary mechanical and electric properties (Stankovich et al. 2006). A broad range of industrial applications of graphene which include design of advanced composites, innovative sensors, mechanical generators, semi-conducting devices have motivated a great deal of research to characterize its mechanical properties. Moreover, graphite, the familiar metal, is constructed by numbers of graphene layers (sheets) ˚ . Due to its high with interlayer spacing of around 3.4 A stiffness and strength, graphite is used as reinforcement in composite materials (Fukushima and Drzal 2002). Thus, understanding the behaviour of a single-layer graphene sheet will facilitate a better characterization of the resulting nanocomposites and will provide a competitive alternative to carbon (C) nanotubes, which are viewed as deformed graphene sheets. A plethora of research has been conducted to explore the transport properties of the single-layer graphene sheets. However, little attention has been paid to mechanical properties. Further studies are thus needed in order to develop a better characterization of the elastic properties of graphene. Experimental measurement of mechanical properties of graphene sheets is not an easy task. This is why there are only few corresponding reported works in literature.
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