Contact between a Smooth Indenter and a Two-Layer Elastic Half-Space with Complicated Conditions on the Surface

The problem of loading a textured two-layer elastic foundation with a rigid smooth indenter is considered. At the interface between the textured layer and the half-space, the conditions for complete adhesion are specified. Relief elements are elastic cylinders, characterized by height and radius, located on the surface of the base with a given period. The one-dimensional Winkler model is used to describe the mechanical properties of relief elements. The contact problem is solved using the boundary element method. Pressure, displacements, and also the shape of the indenter are approximated by piecewise constant functions. The influence coefficients are constructed using a method based on double integral Fourier transforms. The analysis of the influence of the texture elements arrangement density and their compliance on the distribution of the contact pressure is carried out. It was found that in most cases contact is made only with the elements of the texture. For a relatively stiff textured layer, the combined effect of layer curvature and additional pliability imparted by texture elements is important. For relatively stiff and pliable textured layers, load-penetration curves were obtained depending on the texture period. Within the framework of the proposed setting, the limiting case of contact of an indenter with a Winkler layer completely covering the surface of a two-layer elastic half-space is also considered. Load-penetration curves are obtained and analyzed for an indenter in the form of a Berkovich pyramid.