Three-dimensional Contact of a Rigid Roller Traversing a Viscoelastic Half Space

In this paper, the authors consider a nontrivial three-dimensionalviscoelastic contact problem which has some physical significance.(Although the subject of the analysis is an elliptical roller,it is only a small step onward to the consideration of a crownedcylindrical roller.) Generally, it is the intractability of the mathematics whichhinders analytic solution of true three-dimensional problemsin (visco)elasticity. The traditional method of surmountingthis difficulty is to reduce the problem to two dimensions,either by choosing a suitable geometry, or by using an appropriateco-ordinate system. The elastic line integral theory representsanother approach; certain approximations are used to simplifythe governing equations, thus allowing the solution of the problem. After the development of a viscoelastic analogue of the Boussinesqequation valid for the solution of quasi-steady state viscoelasticcontact problems, analysis proceeds making use of near fieldand extended line integral approximations. Results are generatedshowing the velocity dependence of several physical parameters,including the size and shape of the contact zone. One additionalpoint of interest is uncovered, namely the presence of a pressurepeak near the leading edge of the contact zone.