Constitutive equations for quasi-processes of local pure-jump in simple materials with fading memory. Part 1-Theory with the Clausius-Duhem inequality. Part 2- A more general theory in which only the dynamic part of entropy is primitive.

By “quasi-processes of local pure jump” in simple materials with fading memory the author means certain thermodynamically admissible processes which are constant up to time t−ε (ε > 0). Such processes are characterized by a number of field equations including constitutive equations that depend on ε. When ε → 0, the constitutive functionals may suffer jumps at time t. The paper is devoted to a study of properties of such functionals. Emphasis is placed on the definitions of basic concepts such as the stress, internal energy, entropy and heat flux fields. One of the requirements for a good definition is that a field be defined uniquely within a class of physically admissible fields. Such a uniqueness should not be confused, however, with a uniqueness theorem for an initialboundary value problem for the field. The paper consists of two parts. Part 1 includes (1) purejump histories which are limits of smooth histories, (2) generalized sets of response functionals, (3) pure jump-functions associated with response functionals, (4) uniqueness theorems for a stress-functional, (5) restrictions on the response functionals resulting from the Clausius-Duhem inequality, and (6) indetermination of the heat flux response functional. Part 2 deals with splitting of a response functional into its pure-jump and dynamic parts, and with existence of a response function for the entropy of pure jump