Friction and crack propagation in the indentation of flawed hyperelastic membranes

The indentation and puncturing of thin, soft membranes represent a complex non-linear mechanical problem characterized by finite strains, large displacements, frictional contact, and fracture. This work investigates the spherical-tipped indentation and subsequent failure of isotropic hyperelastic membranes containing a pre-existing crack-like defect, combining experimental results, analytical modelling, and finite element (FE) simulations. An axisymmetric semi-analytical solution for large-strain frictional indentation is coupled with a planar sub-model, describing failure of flawed membranes as the result of unstable crack propagation of an initial linear crack. The membrane’s constitutive behaviour is described by an Ogden incompressible strain–energy function, calibrated via uniaxial extension tests, while the Coulomb friction coefficient at the contact interface is determined through a dedicated experimental procedure. Following a hierarchical approach, the energy release rate is correlated with the pole stretch induced by membrane deflection, enabling prediction of critical indentation depth and stretch at failure as functions of initial crack size and friction. The framework is validated against indentation experiments on silicone rubber membranes, previously collected in our group, demonstrating excellent agreement. The results suggests that this integrated approach can be a robust predictive tool for assessing the fracture behaviour in soft hyperelastic membranes.