PARADOXES IN THE APPLICATION OF THERMODYNAMICS TO STRAINED SOLIDS

This paper identifies the difficulties encountered in extending thermostatics to the description of irreversible processes in solid materials, and compares the resolutions proposed for them. The difficulties stem from the requirement of a continuum formulation of. the theory in view of the nonuniform fields accompanying processes, and also from the paradoxes which arise in a casual adaption of the theoretical framework to the description of state for inelastic behavior such as plasticity, creep, and relaxation. The discussion is in terms of the classical theory of irreversible processes. Basic concepts and results are compared with the more recent nonlinear field theory, employing memory functional representations. Finally, the role of internal variables is examined in bringing inelastic behavior within the framework of the classical theory. One noteworthy result, for a wide class of rate-dependent materials, is the existence of a potential function of stress, at each set of · internal variables, from which the inelastic strain rate may be derived. 1.