Asymptotic analysis for a mixed boundary-value contact problem

The variational solution of the nonlinear Signorini contact problem determi nes also the active contact zone Gamma (c). If the latter is known, then th e elastic field is a solution of a linear mixed boundary value problem in w hich on Gamma (c) the normal displacement and tangential traction are given , while on the non-contact part the total traction is zero. Such mixed boun dary conditions in general generate singularities of the solution's stress field at the points P-(k) where the boundary conditions change. For smooth data, however, the variational solution of the Signorini contact problem ac tually belongs to H-2(Ohm)(2), which implies the disappearance of these sin gularities, i.e., that the corresponding stress intensity factors vanish. This paper is devoted to the characterization of the active contact zone Ga mma (c) by the vanishing stress intensity factors including their sensitivi ty with respect to varying Gamma (c) for two-dimensional problems provided that Gamma (c) consists of a finite number of intervals. We use the method of asymptotic expansions and derive an explicit formula for the sensitivity , which is rigorously justified by employing weighted Sobolev spaces with d etached asymptotics. These results can be used to determine the points P-(k ) with a corresponding Newton iteration.