Mechanics of Indentation into Micro- and Nanoscale Forests of Tubes, Rods, or Pillars

The force-depth behavior of indentation into fibrillar-structured surfaces such as those consisting of forests of micro- or nanoscale tubes or rods is a depth-dependent behavior governed by compression, bending, and buckling of the nanotubes. Using a micromechanical model of the indentation process, the effective elastic properties of the constituent tubes or rods as well as the effective properties of the forest can be deduced from load-depth curves of indentation into forests. These studies provide fundamental understanding of the mechanics of indentation of nanotube forests, showing the potential to use indentation to deduce individual nanotube or nanorod properties as well as the effective indentation properties of such nanostructured surface coatings. In particular, the indentation behavior can be engineered by tailoring various forest features, where the force-depth behavior scales linearly with tube areal density (⁠$m$⁠, number per unit area), tube moment of inertia $(I)$⁠, tube modulus $(E)$⁠, and indenter radius $(R)$ and scales inversely with the square of tube length $(L2)$⁠, which provides guidelines for designing forests whether to meet indentation stiffness or for energy storage applications in microdevice designs.