Averaging of a finely laminated elastic medium with roughness or adhesion on the contact surfaces of the layers

The governing relations of a laminated elastic medium with non-ideal contact conditions in the interlayer boundaries are obtained by an asymptotic averaging method. The interaction of rough surfaces is described by a non-linear contact condition which simulates the local deformation of the microroughnesses using a certain penetration of the nominal surfaces of the elastic layers. The cohesive forces, caused by the thin adhesive layer, are described within the limits of the Frémond model which includes a differential equation characterizing the change in the cohesion function. A piecewise-linear approximation of the initial positive segment of the Lennard–Jones potential curve is proposed to describe of the adhesive forces between smooth dry surfaces. A comparison is made with the solution obtained within the limits of the Maugis–Dugdale model based on a piecewise-constant approximation. Solutions of the above problems are constructed taking account of the possible opening of interlayer boundaries.