Simulation of partial closure of a variable width slot with interfacial bonds in end zones in an isotropic medium

By the methods of elasticity theory, we construct a mathematical model of partial closure in isotropic medium of a variable width slot with end zones at which the cohesive forces of the material act. It is assumed that the interaction of surfaces of the slot under the action of applied volumetric and surface loads may lead to origination of the contact zones of their surfaces. We study the case of origination of several contact areas of the slot faces. Herewith, it is assumed that at some part of the contact area, there arises stick of faces; in the remaining part, slippage may occur. The problem on equilibrium of a slot with partially contacting faces is reduced to the problem of linear conjugation of analytic functions. Definition of the unknown parameters characterizing the partial closure of a variable thickness slot is reduced to the solution of the system of singular integrodifferential equations. The integral equations are transformed into the system of nonlinear algebraic equations solved by the successive approximations method. The contact stresses, the tractions in the interfacial bonds, the sizes of the contact areas, the cohesive zones, and end zones were determined.