The Concept of a Minimal State in Viscoelasticity: New Free Energies and Applications to PDEs

We show here the impact on the initial-boundary value problem, and on the evolution of viscoelastic systems of the use of a new definition of state based on the stress-response (see, e.g., [48, 16, 41]). Comparisons are made between this new approach and the traditional one, which is based on the identification of histories and states. We shall refer to a stress-response definition of state as the minimal state [29]. Materials with memory and with relaxation are discussed.