Theoretical Modeling of Surface Asperity Depression Into an Elastic Foundation Under Static Loading

A theoretical analysis is carried out in closed-form to quantitatively describe the pressing of an individual surface asperity into its elastic bulk when subjected to normal loads. To this end, a single asperity is simulated by a paraboloid of revolution of an arbitrary even power. The investigation is based on theory of elastic contact as originally developed by Shtaerman. It is shown that additional pressing of an individual asperity into the elastic bulk essentially depends upon four parameters: the elastic compression of its apex, the initial magnitude of the height of the asperity, a constant that characterizes the shape of the asperity peak, and the elastic properties of the materials involved in the contact. The analysis shows that the impression of the asperity into the elastic bulk increases for decreasing smoothness of the paraboloid. It will be demonstrated that the impression of the asperity into the elastic bulk, if both are made of the same material, typically reaches 50 percent of the value of elastic compression of the asperity peak.