The propagation of moving surface inside a body is analysed within the frameworl of thermomechanical couplings, when the moving surface is associated with an irreversible change of mechanical properties. The moving surface is a surface of heat sources and of entropy production, intensities of which are related to particular energy release rates defined in terms of Hamiltonian gradients. As example, we analyse the evolutionof partial damage in a composite sphere and a modelfor study the contact wear phenomena.