Collective compression of VACNT arrays modelled as nominally vertical, mutually interacting beams

Abstract

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.