Non-slipping adhesive contact of an elastic cylinder on stretched substrates

The plane strain problem of an elastic cylinder in adhesive contact with a stretched substrate is studied via a generalized JKR model taking into account the transmission of both tangential and normal tractions across the contact interface. The width of the contact region is determined from the Griffith energy balance near the contact edge. In the absence of external loading, the tangential traction is found to have a negligible effect on the contact size. As an external stress is applied to stretch the substrate, the contact solution exhibits three distinct regimes characterized by two threshold strains: (i) the size of the contact region is hardly affected by the applied loading when the substrate strain is below the first threshold level; (ii) the contact size decreases quickly with stretch as the substrate strain increases to between the two threshold levels; (iii) the contact size approaches zero when the substrate strain exceeds the second threshold level. Interestingly, these results share a number of common features with the experimentally observed cell reorientation on a cyclically stretched substrate. An approximate solution is presented in an appendix to represent the numerical results in closed form.