Adhesion of an elastic sphere on a tensioned membrane

Abstract

<jats:p> 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. </jats:p>

Indentation mapping of stretched adhesive membranes

“…The first attempt to solve the problem of adhesive interaction between two elastic spheres was undertaken by Derjaguin [24], who has formulated the following principle: The vertical work done by the external load is equal to the sum of the virtual change of the potential elastic energy and the virtual work that will be consumed by the increase of the surface attractions. Since then, this variational principle has become the cornerstone of many studies of adhesive contact [25,26]. Let U T denote the total energy, which is obtained by summation of the stored elastic energy, U E , the mechanical energy of the applied load, U M , and the surface energy, U S , so that U T = U E + U M + U S .…”