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On the Continuum Modelling of Carbon Nano Tubes

机译：碳纳米管的连续体建模

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A one-dimensional continuum endowed with internal structure, previously introduced by the authors, is extended and generalized by giving a procedure for constructing the constitutive functions. Starting from the reference configuration of a carbon nano sheet (CNS), a representative elementary volume (REV) is chosen. The deformation measures of the REV are identified with the change of the length of the carbon-carbon (C-C) bonds and angle variation between each pair of adjacent bonds. The strain energy density of the REV is given as a standard function of the microscopic strain measures. A relationship between the micro and the continuum strain measures is then established, this leading to an expression of the strain energy density of the REV in terms of the latter strains. Making the derivative of this energy with respect to its arguments the constitutive functions for the one-dimensional continuum are derived. The geometric and mechanical properties of a graphene nano sheet are used to construct its equivalent continuum and some numerical comparisons discussed. Although the procedure is established for a CNS, its extension to carbon nano tubes (CNTs) involves only simple geometric computations.
机译：作者先前介绍的具有内部结构的一维连续体，通过给出构造本构函数的过程进行了扩展和推广。从碳纳米片（CNS）的参考配置开始，选择代表性的基本体积（REV）。 REV的变形量度通过碳-碳（C-C）键长度的变化以及每对相邻键之间的角度变化来确定。 REV的应变能密度是微观应变测量的标准函数。然后建立了微观应变测量和连续应变测量之间的关系，这导致了REV的应变能密度以后者的应变表示。使该能量相对于其参数的导数成为一维连续体的本构函数。石墨烯纳米片的几何和机械性能用于构建其等效连续体，并讨论了一些数值比较。尽管已为CNS建立了程序，但将其扩展到碳纳米管（CNT）的过程仅涉及简单的几何计算。

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