Solution of the contact problem on indentation of rectangular punch in an elastic roughnesses half-space in the presence of coulomb friction

The numerical solution of the static three-dimensional contact problem of the indentation of a rectangular stamp with a flat base in an elastic rough half-space in the presence of Coulomb friction and previously unknown adhesion and slip zones is obtained. Accounting for surface roughness in this problem is carried out based on the spherical model of microroughnesses by introducing the nonlinear terms describing surface microroughnesses crushing and shearing to the expression of relative displacement of the interacting bodies. The influence of the values of the friction coefficient and the parameters of the microscopic irregularities on the size and shape of the zone of adhesion and the distribution of the tangential contact stresses are analyzed. It is shown that the inclusion of surface microroughness shear forming roughness can lead to a substantial increase in the size of the zone of adhesion.