On the thermodynamics of viscosity and plasticity

The thermodynamic theory for viscosity and plasticity phenomena, given by the author in some previous papers, is further developed. A rather general Theological equation is derived from which the rheological equations for Poynting-Thomson, Jeffreys, Maxwell, Kelvin, Hooke, Newton, Prandtl-Reuss, and Bingham media may be considered as degeneracies. The physical meaning of these degeneracies is discussed. In particular it is seen that a Bingham medium may be considered as a special case of a Jeffreys medium. Explicit expressions are given for the free energy, the internal energy, and the entropy of the substances just mentioned. Temperature phenomena are taken into account. Some higher order effects (Poynting effect, structural viscosity, and thixotropy) are discussed from the point of view of the developed theory. A generalization of the Von Mises yield criterion is proposed. With the help of this criterion the Bauschinger effect may be explained as a consequence of memory phenomena. For media without memory this new criterion and the Von Mises criterion coalesce. It will be seen that for plastic media with memory a rheological equation holds, which may be considered as a generalization of the Poynting-Thomson equation. Both distortional and volumetric phenomena are considered. It is assumed that the deformations and rotations are small