The influence of 2D periodic surface texture on the partial slip problem for elastic bodies

We consider contact interaction of elastic bodies, one of which has a 2D texture, described by a sinusoidal function of 2n power, in partial slip conditions within two material models. The first approach based on the Cattaneo-Mindlin theory for linear elastic half-plane, the second is an elastic foundation model (EFM) which takes into account normal and tangential compliances. Analytical expressions for determining the size of the contact zone and the stick and slip zones for both models are obtained, as well as the expressions for the normal and tangential tractions. It is shown that for relatively small profile heights, both models give close results for the stick and slip zones sizes when the parameters of the EFM are selected from the developed half-plane solution. We analyze the influence of the geometric parameters (shape, profile height, and distance between the grooves) of the texture profile on the stick zone size while the tangential force increases. The EFM model allows capturing the dependence of the stick zone width on the profile height.