Micromechanical approach to determine the effects of surface and interfacial roughness in materials and structure under cosinusoidal normal pressure

Contact mechanics is a topic that performs the investigation of the deformation of solids that touch each other at one or more points. A principal distinction in contact mechanics is between stresses acting perpendicular to the contacting bodies' surfaces and stresses acting tangentially between the surfaces. This study focuses mainly on the normal stresses that are caused by applied forces. As a case study, the present work aims at investigating the bi-dimensional contact mechanics of wavy cosinusoidal anisotropic finite planes. To achieve this objective, results on the displacement and stress component are first calculated with the help of the Lekhnitskii formalism. Then, with the application of normal pressure at plane surface and by applying boundary conditions at depth h of solid we obtain solution for the contact pressure in closed form. In case of infinite anisotropic plane where the depth h tends to infinite, by using results obtained with finite h we derive the analytical solution for vertical displacement at the surface. As an illustration, behaviour of a monoclinic material under consinusoidal pressure is analyzed