Asymptotic modelling of an elastic roller crossing a scratch

The paper presents asymptotic modelling of the generalized Greenwood problem for an elastic cylinder (considered as a bounded two-dimensional elastic body) pressed between two rigid punches one of them with the dented surface having a scratch. The method of matched asymptotic expansions is used to obtain analytic approximations for the mutual displacement of the punches and the relative displacement of the rollerʹs center.