Contact interaction of a rigid die with an elastic layer during frictional heating

A formulation and solution are presented for the static thermoelastic problem of the sliding of a rigid die on the surface of an elastic layer with a fixed base. Frictional heating which occurs in accordance with Amonton's law is taken in account. With the assumption that the die is insulated, the problem Is reduced to a system of two integral equations for contact pressure and a function which is a linear combination of the temperature and heat flux on the contact surface. A numerical algorithm is proposed for solving the system. A study is made of the effect of the reduction brought about in the size of the contact area by the steady generation of heat during the interaction of the layer and die with parabolic and semicylindrical bases.