Spherical indentation of freestanding circular thin films in the membrane regime

We present theoretical and experimental results to describe the mechanics of indentation of a clamped circular membrane with a frictionless spherical indenter. Analytical expressions and numerical simulations are presented for the relationships between contact radius, finite indentation strains (and stresses), pre-stretch, loads and deflection. These closed-form solutions are contrasted with point-load models that neglect the contact size (i.e. classical Schwerin-type solutions), and lead to important differences in the indentation strain and load–deflection response. The accuracy of these closed form expressions is illustrated by comparisons with detailed numerical results and experiments on thin elastomer films. We show that the closed-form solutions can be used to extract mechanical properties from indentation testing of freestanding films, with important implications for developing new tests on nanoscale films and/or compliant materials such as polymers and biological substances.