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首页> 外文期刊>Proceedings of the institution of mechanical engineers >Stability of a single-layer graphene sheet with various edge conditions: a non-local plate model including interatomic potentials
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Stability of a single-layer graphene sheet with various edge conditions: a non-local plate model including interatomic potentials

机译：具有各种边缘条件的单层石墨烯片的稳定性：包含原子间电势的非局部板模型

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摘要

In this article, the biaxial buckling of a single layer graphene sheet is investigated. The model is established through the incorporation of an interatomic potential into non-local elastic plate theory to take into account the size effects and to circumvent the use of the Young's modulus of a single layer graphene sheet since there is no accurate value of this property available in the literature. The model links the strain energy density induced in the continuum to Eringen's non-local constitutive relations. By using the Galerkin method, explicit formulas for the critical buckling stresses of a single layer graphene sheet with arbitrary edge supports are derived from its static deflection due to a uniformly distributed load. The influences of the small size of the system and boundary conditions on the critical buckling load of the single layer graphene sheet are studied. It is found that the critical buckling load at large side lengths is almost independent of the type of boundary condition and compressive loading and is nearly immune to size effects. The analytical expressions provide a simple and quick way to evaluate accurate values of the critical buckling load. Indeed, the lack of complexity in the formulas allows a simple prediction of the value of the scale parameter that closely matches the one obtained using the complex molecular dynamics simulation technique.
机译：在本文中，研究了单层石墨烯片的双轴屈曲。该模型是通过将原子间电势并入非局部弹性板理论中而建立的，以考虑尺寸效应并避免使用单层石墨烯片的杨氏模量，因为尚无此特性的准确值在文学中。该模型将连续体中感应的应变能密度与艾林根的非局部本构关系联系起来。通过使用Galerkin方法，从具有均匀分布载荷的静态挠度导出具有任意边缘支撑的单层石墨烯片的临界屈曲应力的显式公式。研究了系统小尺寸和边界条件对单层石墨烯片临界屈曲载荷的影响。发现在较大边长处的临界屈曲载荷几乎与边界条件和压缩载荷的类型无关，并且几乎不受尺寸影响。解析表达式提供了一种简单快速的方法来评估临界屈曲载荷的准确值。实际上，公式中缺乏复杂性，因此可以简单地预测比例参数的值，该值与使用复杂分子动力学模拟技术获得的参数非常匹配。

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