Indentation of a circular membrane on an incompressible liquid

Abstract

A model of the indentation of a circular elastic membrane (neo-Hookean material) on an incompressible liquid layer and an effective numerical solution method are presented. For the interface between the indenter and the membrane, stick or slip contact conditions are considered. The solution procedure identifies the liquid pressure and, for slip contact, the radius in the reference configuration displaced to the edge of the indenter. Assuming a range of material and test performance parameters regarding deep tonometry of soft subcutaneous tissue, the predictions for the distributions of stretches, line tensions and profiles of the indented membrane are analyzed. Among the key results of this work are the dependencies of the total indentation force and the liquid pressure on the Young’s modulus of the membrane’s material that appeared to be approximately linear for a range of Young’s modulus values. The profiles of the membrane for different indentation depths are close to parabolic and can be used to relate the longitudinal line tension at the edge of the indenter to the total indentation force.