| Carbon nanotubes grown on a substrate form a turf---a complex structure of intertwined, mostly nominally vertical tubes, cross-linked by adhesive contact and few bracing tubes. The turfs are compliant and good thermal and electrical conductors. The objective of this work is to understand the deformation of turfs using computational models. We consider two approaches: (a) A phenomenological constitutive model of the turf developed from the micromechanical analysis of the turf deformation. We benchmark the developed model using a finite element implementation and compare using the results from nanoindentation tests on CNT turfs. The model includes: nonlinear elastic deformation, small Kelvin-Voigt type relaxation, caused by the thermally activated sliding of contacts, and adhesive contact between the turf and the indenter. The pre-existing (locked-in) strain energy of bent nanotubes produces a high initial tangent modulus, followed by an order of magnitude decrease in the tangent modulus with increasing deformation. The strong adhesion between the turf and indenter tip is due to the van der Waals interactions. The finite element simulations capture the results from the nanoindentation experiments, including the loading, visco-elastic relaxation, unloading and adhesive pull-off. (b) A detailed discrete model of the turf developed by discretizing the CNTs using inextensible elastica elements with their equivalent material properties obtained from molecular dynamic simulations. The model includes a Lennard Jones type force law and a frictional component to model the interaction between segments of neighboring tubes. The equations of motion are integrated using an explicit integration technique and the response of the turf to external loading is studied. Periodic boundary conditions are used to model infinitely large turfs. Under flat punch indentation, the tendency of the carbon nanotubes to coalesce together and undergo coordinated buckling similar to experimental observations is captured. We observe this behavior only when there is friction between the interacting segments and with the indenter surface. There is a strong qualitative agreement in the nominal stress-strain response between the numerical results and experiments. |
