Transient Interaction of Rigid Indenter with Elastic Half-plane with Adhesive Force

Abstract

The transient interaction of a rigid convex indenter with elastic half-plane boundary is investigated in this paper. At the initial time point, the rigid indenter and half-plane have some distance between them. Indenter moves towards the half-plane on arbitrary law of motion. The indenter and half-plane interaction is considered in two stages: contactless interaction, which includes only adhesive forces, and the stage with mechanical contact between indenter and half-plane’s boundary. On the second stage, the adhesive force also takes place. In this paper the first stage of interaction is considered. To obtain the normal displacement of the half-plane, the superposition principle is used. For this method, the Lamb problem solution is considered as a Green function. However, the adhesive force function’s support is unknown. In this article the original numerical and analytical algorithm is constructed and realized, the solution for considered problem is obtained. Graphical results for half-plane boundary normal displacements space-time distribution are presented. Also graphical results for adhesive force support boundary position and velocity on time dependence are shown.