基于高阶Cauchy-Born准则的单壁碳纳米管本构模型

A higher order Cauchy-Born rule based constitutive model of SWNT

提出了一种基于高阶Cauchy-Born准则建立单壁碳纳米管本构模型的方法。通过引入高阶变形梯度,合理地修正了传统Cauchy-Born准则在描述纳米管变形几何关系时所存在的缺陷。利用原子间相互作用势以及能量等效原理,得到了基于广义连续介质模型的单壁碳纳米管的本构关系。由此得到的本构参数不仅与变形梯度张量F,而且与其梯度F相关,因此是一种广义连续介质模型。利用这样的本构模型,本文还对单壁碳纳米管的杨氏模量进行了预测,并与采用其他方法得到的结果进行了对比,从而证实了所提出方法的有效性。

Based on the higher order Cauchy-Born rule, a constitutive model of SWNT is established. In the present model, by including the second order deformation gradient tensor in the kinematic description, the limitation of the standard Cauchy-Born rule for the modeling of nanoscale crystalline films can be alleviated with less computational efforts. Based on the established relationship between the atomic potential and the macroscopic continuum strain energy density, analytical expressions for the tangent modulus tensors are derived. With the use of this model and the Tersoff-Brenner atomic potential for carbon, the size dependent mechanical properties of carbon nanotube are predicted. The obtained results agree well with those obtained by other experimental, atomic modeling and continuum concept based studies.