On the first attempts to write non-local constitutive equations

In the twenties of the last century Navier, Poisson and Cauchy built the continuum mechanics starting from molecular models of matter. The continuum was a first gradient approximation of microscopic phenomena, like molecular relative displacements (or velocities) and interactions. Hints about higher gradients approaches appeared in Poisson's and Cauchy's. It is in the sixties of that century that the first attempts to set forth higher order theories come out in the literature, after Kleitz and Levy. Saint-Venant positively discouraged further investigations "for half a century or more" [Truesdell, 1965]. We analyse the early authors' sources and their hypotheses on the molecular nature of matter.