Adhesion of an elastic sphere on a tensioned membrane

Abstract

Inspirited by the fact that classical models of adhesion contact (such as the Johnson–Kendall–Roberts model, Young’s equation or the Neumann equation) cannot be directly applied to adhesion of an elastic sphere on a membrane, the present work aims to develop an explicit general model for axisymmetric adhesion mechanics of an elastic sphere on a tensioned circular membrane. An explicit expression for the potential energy of the sphere–membrane system is derived, and explicit equations are given to determine the adhesion equilibrium state. The validity and accuracy of the proposed model are verified by good agreement between the predicted results and known results on both adhesion of a rigid sphere on a membrane and the critical condition for full wrapping of a rigid sphere by a membrane of non-zero bending rigidity.