Plane Contact and Adhesion of Two Elastic Solids With an Interface Groove

A systematic study is performed on the plane contact and adhesion of two elastic solids with an interface groove. The nonadhesion and Johnson–Kendall–Roberts (JKR) adhesion solutions for a typical groove shape are obtained in closed form by solving singular integral equations and using energy release rate approaches. It is found that the JKR adhesion solution depends solely on a dimensionless parameter $α$ and the groove is predicted to be unstably flattened with no applied load when $α≥0.535$⁠. Furthermore, the corresponding Maugis–Dugdale adhesion model has been revisited with three possible equilibrium states. By introducing the classical Tabor parameter $μ$⁠, a complete transition between the nonadhesion and the JKR adhesion contact models is captured, which can be recovered as two limiting cases of the Maugis–Dugdale model. Depending on two nondimensional parameters $α$ and $μ$⁠, where $α2$ represents the ratio of the surface energy in the groove to the elastic strain energy when the grooved surface is flattened, different transition processes among three equilibrium states are characterized by one or more jumps between partial and full contact. Larger values of $α$ and $μ$ tend to induce more energy loss due to adhesion hysteresis. Combination values of $α$ and $μ$ are also suggested to design self-healing interface grooves due to adhesion.