Analytical, numerical and experimental analysis of continuous indentation of a flat hyperelastic circular membrane by a rigid cylindrical indenter

• The paper develops an original way to treat continuous indentation of flat membrane by cylindrical indenters through the principle of stationary potential energy.
• The study examines the numerical and analytical solutions for Neo-Hookean and Mooney–Rivlin materials.
• The study is validated by finite element and experimental solutions.
• The study shows that the analytical solution can be useful to determine the principal stress and the force necessary to penetrate the membrane.

Several researchers have studied the process of the indentation of a membrane by rigid objects, but there is currently a lack of continuous indentation studies and experimental data to validate the theoretical formulations that model membrane behaviour.This research presents a numerical and analytical formulation as well as a finite element model and experimental validation for the behaviour of a circular flat membrane subjected to continuous indentation by a rigid circular cylindrical indenter. The material of the membrane is modelled as a homogenous, isotropic, hyperelastic material. The model considered Neo-Hookean and Mooney Rivlin material behaviours. The contact between the membrane and the rigid cylindrical indenter is assumed to be frictionless. The numerical model divides the continuum into three stages, and the equilibrium equations and boundary conditions for each stage are obtained by the principle of stationary potential energy. The nonlinear equilibrium equations are solved using the symbolic software package Maple©. The model was validated with results from finite elements analysis as well as experimental results. The comparison of the numerical and analytical solutions gives interesting insights for researchers who are only interested in calculating maximum tension stresses.