The dependence of stresses on the elastic constants is explored in frictionless contact problems principally for the case when the contacting bodies are made of the same material and the deformations are induced by prescribed surface tractions. The strongest results can be obtained for problems with contacts that either recede or remain stationary upon loading. In such problems, the stresses are proportional to the applied tractions and the extent of contact is independent of the level of loading. Furthermore, it is shown that the Michell result regarding the dependence of stresses on Poisson’s ratio carries over to plane contact problems with receding and stationary contacts. In three and two-dimensional problems with advancing contacts, it is possible to establish certain rules for scaling displacements and stresses.

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