Contact interaction of rough elasic solids in the presence of two highly different scales of roughness extent

Abstract

Using the method of successive approximations (iterations), the problem of contact interactions of squeezed semi-infinite elastic solids with rough surfaces characterized by two highly different scales of roughness extent, Λ and λ << Λ , is considered. In zero approximation, only the coarse-scale roughness (i.e., of scale Λ of its extent) is taken into account, so that the contact between the solids may be considered as full. The effects of fine-scale roughness are studied only in first approximation. The consideration in zero approximation is performed in the case when there is a single coarse-scale element in the form of a socket simulating a defect elongated in a certain direction. The solution of the corresponding problem obtained earlier by the authors is applied. The fine-scale roughness effects are considered by means of the Greenwood-Williamsom model. The conditions for application of the proposed approximate treatment are investigated. Examples of calculations are presented.