A Cattaneo-Mindlin problem for a rigid punch with tangential load applied above the interface line

We study the contact between a rigid flat punch and an elastic half-space using Coulomb friction for a normal load followed by a tangential load applied at a certain height above the interface line. The study is inspired by recent experiments by the group of Jay Fineberg in Israel. Three regimes are found in the evolution of slip at the interface depending on a dimensionless parameter =<mml:mfrac>a2h</mml:mfrac> , the ratio between the halfwidth of the contact and the product of twice friction coefficient and height of the loading point. Normal pressure and shear tractions are plotted for each case. It is shown that the effect of height does not collapse the data, contrary to the experimental data of Fineberg's setup. However, this is not surprising given the many deviations from the ideal configuration we have studied, namely the finite thickness of the bottom block, the presence of vertical surfaces on the upper block (both not permitting the assumption of halfspace elasticity) and finally local effects due to concentrated tangential load which give rise to local and not only global induced moment.