Contact problems for rough elastic solids being in nearly full contact or regarded as such for further elaboration

Abstract

Problems on nearly full contact between elastic bodies with nominally flat rough boundaries are considered, so that only relatively small crack-like no-contact areas are present. Such a case is of essential applied interest and has been considerably less examined than the case of comparatively small contact areas, when only relatively sparsely located "contact spots" appear. This case may really appear under sufficiently large loads and appropriate roughness and compliance conditions (e.g. when metallic and polymeric materials contact) or it may be regarded as a zero- approximation, when roughness is essentially multi-scale and a procedure of successive approximations (iterations) is applied to solve corresponding contact problems. The latter situation is mainly considered below for plane strain, and, in a lesser degree, for 3D conditions, assuming no shear interaction. Particularly, the case is considered, when there is a coarse-scale Λ and a fine-scale λ (λ<<Λ) of roughness extent. In zero approximation, only coarse-scale roughness is taken into account, assuming that it is presented by a correspondingly large solitary socket. Fine-scale roughness is considered in first approximation only based on the Greenwood-Williamson model [1]. Similarly, the situations, where bending of a layer or a multi-layer structure plays dominant role are considered.