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Atomistic-continuum coupled model for nonlinear analysis of single layer graphene sheets

机译：单层石墨烯片非线性分析的原子-连续体耦合模型

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摘要

In this paper, atomistic-continuum coupled model for nonlinear flexural response of single layer graphene sheet is presented considering von-Karman geometric nonlinearity and material nonlinearity due to atomic interactions. The strain energy density function at continuum level is established by coupling the deformation at continuum level to that of at atomic level through Cauchy-Born rule. Strain and curvature dependent tangent in-plane extensional, bending-extension coupling, bending stiffness matrices are derived from strain energy density function constructed through Tersoff-Brenner potential. The finite element method is used to discretize the graphene sheet at continuum level and nonlinear bending response with and without material nonlinearity is studied. The present results are also compared with Kirchhoff plate model and significant differences at higher load are observed. The effects of other parameters like number of atoms in the graphene sheet, boundary conditions on the central/maximum deflection of graphene sheet are investigated. It is also brought out that the occurrence of bond length exceeding cutoff distance initiates at corners for CFCC, CFCF, SFSS, SFSF graphene sheets and near center for SSSS and CCCC graphene sheets. (C) 2015 Elsevier Ltd. All rights reserved.
机译：本文提出了考虑原子相互作用引起的von-Karman几何非线性和材料非线性的单层石墨烯片非线性挠曲响应的原子连续体耦合模型。连续能级的应变能密度函数是通过柯西-伯恩定律将连续能级的变形与原子能级的变形耦合而建立的。应变和曲率相关的切线面内延伸，弯曲-延伸耦合，弯曲刚度矩阵来自通过Tersoff-Brenner势构造的应变能密度函数。使用有限元方法在连续水平上离散化石墨烯片，并研究了有无材料非线性的非线性弯曲响应。还将当前结果与Kirchhoff平板模型进行比较，并观察到较高载荷下的显着差异。研究了其他参数（如石墨烯片中的原子数，边界条件）对石墨烯片中心/最大挠度的影响。还得出结论，对于CFCC，CFCF，SFSS，SFSF石墨烯片，在拐角处开始出现键长超过截止距离的现象，而对于SSSS和CCCC石墨烯片，则在中心附近开始发生。 （C）2015 Elsevier Ltd.保留所有权利。

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