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The material characterization of ultra-thin solid sheets, includingtwo-dimensional materials like graphene, is often performed through indentationtests on a flake suspended over a hole in a substrate. While this `suspendedindentation' is a convenient means of measuring properties such as thestretching (two-dimensional) modulus of such materials, experiments onostensibly similar systems have reported very different material properties. Inthis paper, we present a modelling study of this indentation process assumingelastic behaviour. In particular, we investigate the possibility that thereported differences may arise from different geometrical parameters and/ornon-Hookean deformations, which lead to the system exploring nonlinearitieswith geometrical or material origins.

Indentation of two-dimensional solids: The signatures of geometrical and material nonlinearity