Contact of a rigid cylinder indenting an elastic layer sliding over a rigid substrate

Details of the integral transform solution of the state of stress in a layer resting on but sliding over a rigid substrate, in the presence of interfacial friction, is studied. The free surface of the layer is subject to a localised contact, which is represented as a piecewise linear distribution of tractions, using the Bentall–Johnson procedure. The influence functions needed are derived and their properties discussed and compared with those already available for other interface conditions. Lastly, the procedure is applied to the problem of a shrink fit tyre which, under severe tyre/road tangential loading, can be ‘torn’ around the wheel (here, the substrate).