Plane Non-inertial Contact Problems

We consider, in the present chapter, problems involving moving or varying loads acting on the boundaries of viscoelastic materials, where plane strain (see Sect. 2.8) conditions prevail. Inertial effects are neglected. 

The case of stationary, unvarying loads on a viscoelastic medium reduces to an elastic problem. Moving or changing loads cause considerable extra complexity however, though elastic solutions, and the methods used to obtain these solutions, remain very relevant. This might be expected in view of the discussion in the early stages of Chap. 2. 

As pointed out in Sect. 2.2, the crux of the problem is the determination of certain functions on the boundary. This results in an apparent lack of emphasis on the behaviour of the interior of the material. In fact, however, once the boundary functions are known, everything else can be determined in a relatively straightforward manner, if there is an interest in doing so - which in some cases there is not. 

Attention is confined to isotropic materials. Also, we deal only with halfplane problems and rigid indentors. However, the results are applicable to mildly curved surfaces and, with certain modifications, to the case of contact between two viscoelastic bodies. This is the familiar argument used in the theory of Hertzian contact. The modifications mentioned are not trivial in the viscoelastic case, as they are in the elastic case, involving as they do, the combining of viscoelastic 

1 Kolosoy-Muskhelishvili Equations Adapted to the Half-Plane 

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