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

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. (C) 2014 Elsevier Ltd. All rights reserved.