A still topical contribution of Gabrio Piola to Continuum Mechanics: the creation of peri-dynamics, non-local and higher gradient continuum mechanics

Gabrio Piola’s scientific papers are in some aspects still topical in the matematical-physics literature. Actually, even if some authors [10] dedicated many efforts to the aim of unveiling the true value of Gabrio Piola as a scientist, some deep parts of his scientific achievements remain not yet sufficiently illustrated. We start our considerations by discussing some of the phenomena which influence the storage and transmission of knowledge, being inspired by the work of Lucio Russo ([106]). Subsequently, our aim is to prove that non-local and higher gradient continuum mechanics is rigorously formulated already in Piola’s works and then we try to explain the reasons of the unfortunate circumstance which caused the erasure of the memory of this aspect of his contribution. Finally some relevant differential relationships obtained in Piola [Piola, 1848] are carefully studied, as they are still nowadays too often ignored in the continuum mechanics literature while indeed they can be considered as the starting point of Levi-Civita’s theory of Connection for Riemannian manifolds.