Numerical moving mesh solution for the JKR adhesive contact between an incompressible layer and an axisymmetric rigid indenter

Recent research extended the non-adhesive contact problems between an incompressible layer and a rigid indenter to adhesive cases in the limit of the Johnson–Kendall–Roberts (JKR) model, where it simply changes the boundary condition. The governing equation of this problem is in the form of Poisson’s equation, and there are two boundary conditions, one of which serves to determine the extent of the contact area. This makes it possible to develop a numerical solution of an adhesive thin incompressible layer indentation problem. For a numerical implementation, we have devised a finite element formulation with a moving mesh technique satisfying the slope boundary condition, which determines the actual extent of the contact area. We shall apply the proposed numerical method to an adhesive contact problem by a spherical rigid indenter to demonstrate the validity of the method. Furthermore, we will compare the characteristics of the JKR indentation solutions between a half-space and a thin incompressible layer.