PARTIAL SLIP CONTACT BETWEEN ELASTIC HALF-SPACE AND CIRCULAR PUNCH UNDER NORMAL AND TANGENTIAL LOADS - Streliaiev, Yu. M. (Computer Science and Applied Mathematics, 2021)
The article presents a new approach to solving the quasi-static spatial contact problem of interaction with friction between a rigid cylindrical punch with a flat base and an elastic half-space when monotonically increasing normal and tangential loads act on the punch sequentially. To account for friction, we used Coulomb’s law in the classical form. We considered the stick and slip zones to be unknown in advance, which must be obtained. We simulated the loading process with a finite number of equilibrium states – loading steps. The contact problem is reduced to the sequential solution of similar systems of nonlinear boundary integral equations at each step of the discrete loading process. The resulting integral equations are characterized by the fact that their form does not depend on the configurations of the stick and slip zones. To compose such equations, it is only necessary to specify a canonical bounded flat region, which includes unknown areas of adhesion and slippage at all stages of loading the bodies. To obtain approximate solutions of these systems, they are discretized. Converging iterative processes are constructed for the numerical solution of the systems of nonlinear scalar equations obtained as a result of this discretization. Using numerical calculations performed for various values of the tangential displacement of the punch, we investigated the process of changing the distributions of contact tractions acting on its base. We also investigated the relative displacements of the contact surfaces and the evolution of the shapes and sizes of the stick and slip zones when the shear load gradually increases. We found that the stick zone loses symmetry and shifts towards the front (in the direction of the movement) edge of the punch when the tangential force begins to act. With an increase in the external tangential force, the area of the stick zone decreases and becomes zero when the punch begins to slide along the boundary of the elastic half-space. The maximum values of tangential contact stresses and relative displacements of the contact surfaces are achieved at the back edge of the punch.