The propagation of moving surface inside a body is analysed within the framework 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 examples, we analyse the evolution of partial damage in a composite sphere and a model for study the contact wear phenomena between two bodies.