On the response functions of a thermo-elastic body, from the Mach-Painleve' point of view

This paper is a sequel to a paper by A. Bressan and the author [same journal Cl. Sci. Fis. Mat. Natur. Mem. (9) Mat. Appl. 1 (1990), no. 3, 59–94]. It extends this work by including thermodynamical effects. That is, thermoelastic bodies are considered instead of purely elastic ones. No notions of contact forces, heat flux, internal energy, and entropy are primary concepts at the outset. Following ideas put forward by E. Mach and P. Painleve early in this century, these notions can be defined ´ in terms of forces at a distance, absolute temperature, and some purely mechanical notions. This is made possible on the basis of uniqueness theorems for the corresponding response functions (stress, entropy, heat flux).