Internal dissipation, relaxation property, and free energy in material with fading memory

This paper examines some features of the standard theory of materials with fading memory and emphasizes that the commonly-accepted notion of dissipation yields unexpected consequences. First, application of the Clausius-Duhem inequality to linear viscoelasticity shows that there is a free energy functional such that the so-called internal dissipation vanishes in spite of the dissipative character of the model. Second, upon the choice of a suitable function norm, the relaxation property is proved not to hold for viscoelastic solids. Finally, the particular case is considered when the relaxation function is a superposition of exponentials. Different descriptions of state are then possible which prove to be inequivalent as far as the free energy is concerned.