On the concepts of state and free energy in linear viscoelasticity (Q1362186)

The authors study systematically the concepts of state, process, work, and free energy in linear viscoelasticity, whose constitutive equation is a Boltzmann-Volterra equation, by using the approach by \textit{B. D. Coleman} and \textit{D. R. Owen} [Arch. Ration. Mech. Anal. 54, 1-104 (1974; Zbl 0306.73004)]. The paper is of a high mathematical level and is of great interest to anyone seriously involved in the theory of materials with memory. Contents: 1. Introduction; 2. Histories and segments; 3. States and processes; 4. Work; 5. Free energy; 6. Relaxation functions of exponential type; 7. Completely monotonic relaxation functions.