A non-linear wear-contact problem for a Winkler foundation with an increasing contact area

A wear-contact problem for a Winkler foundation is considered in the case when the rate of wear depends nonlinearly on the contact pressure and the contact area increases. The corresponding integral and differential equations are obtained. A successive approximation procedure is proposed which enables an exact solution of the problem in the space of continuous functions to be found. The property of non-negativity of the contact pressure when it has non-negative initial values is established. It is shown, using a qualitative analysis and calculations, that the non-linearity of the wear law can have a considerable effect on the behaviour of the contact pressure during the wear process.