A Generalized Model of Viscoelastic Interlayer or Coating Taking into Account its Transverse Shear Deformation

Abstract

A generalized model of viscoelastic anisotropic interlayer or coating operating in compression and in transverse shear is constructed and examined. We solve the problem of action of a time-dependent normal distributed load on the isotopic viscoelastic layer on the rigid substrate and study the case of concentrated forces acting at the origin of coordinates.In contemporary machine building, civil engineering, and transport, the mechanical contact between solid bodies fairly often is realized through thin interlayers or coatings with their own physicomechanical properties and characteristics. Among these objects are pavements and foundations, damping layers in transport and in laying of pipelines, etc. In the design of objects of this kind, it is necessary to take into account their physicomechanical behavior under loads of different types for various loading modes and guarantee the adequate choice of the proper mathematical model. In [2, 3, 6], a large number of contact problems for bodies with thin coatings and interlayers described by elastic and viscoelastic models, including the linear and nonlinear Winkler models, were solved within the framework of the theory of creep and aging [2,3]. The Winkler viscoelastic foundation was considered within the framework of the Voigt model in [14]. However, the Winkler model does not take into account the resistance of the foundation to transverse shear and, hence, the displacements outside the region of action of the load are equal to zero. Thus, the two-parameter models of foundation taking into account its operation both in compression and in transverse shear were proposed in [4,9] and numerous problems were solved both for massive solids and for thin-walled structural elements. The subsequent development in this direction is described in [5,7,12,16]. In [1], in order to formulate the conjugation conditions in the tangential direction, the authors apply a second-order differential operator. However, the models of elastic interlayer considered in the cited work are not two-parameter models. The generalizations of the two-parameter model of foundation to the viscoelastic case in the dynamic and quasistatic statements can be found in [8,15]. Note that the surveys of the results on the models of elastic and viscoplastic foundations together with a large body of cited literature can be found in [5,7,13].The aim of the present paper is to study a generalized model of viscoelastic interlayer or coating that takes into account its operation both in compression and in transverse shear, in particular, on the example of a problem of action of normal loads on the viscoelastic layer joined with the rigid foundation. A Generalized Model of Viscoelastic Interlayer (Coating)Within the framework of the Kelvin-Voigt model [11], the generalized thermomechanical conditions of conjugation of solid bodies via a thermoelastic anisotropic interlayer of thickness 2h operating in compression