Vertically aligned carbon nanotube (VACNT) arrays are moderately dense ensembles of nominally vertical carbon nanotubes (CNT) tethered to a rigid substrate. Variations in their synthesis protocols translate to largely unpredictable fluctuations in height, density, tortuosity and stiffness of the individual CNTs. Consequently, experimental studies on compression of these VACNT arrays exhibit a variety of responses. Moreover, many experimental studies report concerted buckling behaviour of the CNTs under compression. Numerical modelling of such coordinated behaviour in VACNT arrays poses many challenges. Each CNT can be modelled as a flexible beam capable of large deformations, allowing for tortuous initial shapes, mutual and/or self interactions that can be repulsive or attractive and periodic boundary conditions. Confining ourselves to a set of minimally realistic 2-dimensional parametric studies, we attempt to address how geometry/property fluctuations in an array of interacting columns leads to different types of collective compressive responses. We model each CNT as a geometrically exact beam using an established framework. A novel contact formulation is employed to model their mutual van der Waals interactions. In all cases, we capture coordinated buckling and are able to negotiate the response in the post-buckling stages. We first model ideal vertical arrays of defect-free CNTs and then discuss the effects of fluctuations in height, density, stiffness and tortuosity on their compressive behaviour.

垂直排列碳纳米管（VACNT）阵列是由名义上垂直的碳纳米管（CNT）固定在刚性基板上的中等密度的集合体。合成方案的变化导致单个碳纳米管的高度、密度、曲折度和刚度的波动在很大程度上不可预测。因此，对这些 VACNT 阵列压缩的实验研究表现出多种响应。此外，许多实验研究报告了碳纳米管在压缩下的一致屈曲行为。VACNT 阵列中这种协调行为的数值建模提出了许多挑战。每个碳纳米管都可以建模为能够进行大变形的柔性梁，允许曲折的初始形状、相互和/或自相互作用（可以是排斥或吸引）以及周期性边界条件。我们将自己限制在一组最低限度真实的二维参数研究中，试图解决一系列相互作用的柱中的几何/属性波动如何导致不同类型的集体压缩响应。我们使用既定框架将每个碳纳米管建模为几何精确的梁。采用一种新颖的接触公式来模拟它们之间的范德华相互作用。在所有情况下，我们都会捕获协调屈曲，并能够协商屈曲后阶段的响应。我们首先对无缺陷碳纳米管的理想垂直阵列进行建模，然后讨论高度、密度、刚度和弯曲度的波动对其压缩行为的影响。