Thermodynamic restrictions, free energies and Saint-Venant's principle in the linear theory of viscoelastic materials with voids

This paper examines the thermodynamic restrictions imposed by the second la w of thermodynamics upon the relaxation functions in the linear theory of v iscoelastic materials with voids. On this basis the existence of a maximal free energy is proved by means of a constructive method. Further, we use su ch a maximal free energy in order to establish a principle of Saint-Venant type in the dynamics of viscoelastic materials with voids. A uniqueness the orem is proved for finite and infinite bodies and we note that it is free o f any kind of a priori assumptions concerning the orders of growth of solut ions at infinity. (C) 1999 Elsevier Science Ltd. All rights reserved.