Analysis of uniaxial compression of vertically aligned carbon nanotubes

We carry out axisymmetric, finite deformation finite element analyses of the uniaxial compression of cylindrical bundles of vertically aligned carbon nanotubes (VACNTs) firmly attached to a Si substrate. A compressible elastic–viscoplastic constitutive relation with a piecewise, linear hardening–softening–hardening flow strength is used to model the material. Calculations are performed for VACNTs both with uniform properties and with axially graded properties. We show that, with uniform properties, sequential buckling initiates at the substrate and propagates away from it, in agreement with previous experimental findings. We investigate the dependence of the magnitude and wavelength of the buckles on characteristics of the function defining the flow strength. When a property gradient giving a more compliant response at the end opposite to the substrate is specified, we find that sequential buckling initiates at that end and propagates toward the substrate. Results of the analyses are compared with the experimental observations and capture many of the experimentally obtained stress–strain and morphological features. The proposed model serves as a promising foundation for capturing the underlying energy absorption mechanisms in these systems. Comparison of the model predictions with the experimental results also suggests directions for model improvement.