On the uniqueness of response stress functionals for purely mechanical continuous media, from the Mach Painleve point of view

This extended memoir is devoted to the axiomatics of media which respond to stresses (and no higher-order generalized forces). It therefore deals especially with the notion of contact forces and raises the question of whether these can be defined in terms of forces at-a-distance and kinematic notions along a path paved by Ernst Mach and Paul Painleve almost a century ago. This can also ´ be regarded as a contribution to a program proposed by C. A. Truesdell concerning the search for constitutive functionals (here the stress functional) which are compatible with a given class of thermomechanical processes.