Modelling of materials with long memory

We deduce the Lagrangian motion and energy conservation equations for thermoviscoelastic materials with long memory and with strongly dependent temperature stresses. For this purpose, the Eulerian conservation equations are written in terms not only of the classical thermodynamical variables such as the deformation gradient and the temperature, but also of an internal variable which gives the viscoplastic history of the material. For these materials, we also obtain some linearized conservation equations. As example of this type of materials we present the Maxwell–Norton ones.