A new approach to calculation of contact characteristics

A new method of calculation of contact characteristics for rough surfaces is proposed based on integral relations that express the normal contact stress as an explicit function of the surface shape. To produce calculations by this method, a region having a simple shape should be chosen first, where the contact is supposed to be nominally complete. An iterative procedure with regard to the shape is applied within the load-free surface portion, and allows the normal stresses, surface displacement and the real area of contact to be determined. The method is applicable to rough bodies of arbitrary shape for which the half-space formulation and equivalent roughness concepts apply; the real contact area should lie within the initially chosen contact region and can include a system of unconnected contact spots. Both 2D and 3D cases are considered in the present work. The 2D analysis is based on known integral relations for nonperiodic and periodic contact problems. In the 3D case, new analytical relations are obtained and their properties are analyzed. An iteration algorithm based on these relations and its efficient numerical implementation are described. Application of the method to the contact of real rough surfaces is discussed.