Some Cases of Unrecognized Transmission of Scientific Knowledge: From Antiquity to Gabrio Piola’s Peridynamics and Generalized Continuum Theories

Abstract : The aim of this paper is to show some typical mechanisms in the transmission of scientific knowledge through the study of some examples. We will start by considering some ancient examples concerning Democritus, Heron, Galileo and the history of the theory of tides. Then we will mainly focus on the works of the Italian scientist Gabrio Piola (1794–1850). In particular: 1. we show clear similarities between Noll’s postulation of mechanics and the ‘ancient’ presentation by Piola of the ideas needed to found Analytical Continuum Mechanics; 2. we prove that non-local and higher gradient continuum mechanics were conceived (and clearly formulated) already in Piola’s works; 3. we explain the reasons of the unfortunate circumstances which caused the (temporary) erasure of the memory of many among Piola’s contributions to mechanical sciences. Moreover, we discuss how the theory which has recently been called peridynamics, i.e. a mechanical theory which assumes that the force applied on a material particle of a continuum depends on the deformation state of a neighbourhood of the particle, was first formulated in Piola’s works. In this way we argue that in the passage from one a cultural tradition to another the content of scientific texts may often be lost, and it is possible to find more recent sources which are scientifically more primitive than some more ancient ones.
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Francesco Dell'Isola, Alessandro Della Corte, Raffaele Esposito, Lucio Russo. Some Cases of Unrecognized Transmission of Scientific Knowledge: From Antiquity to Gabrio Piola’s Peridynamics and Generalized Continuum Theories. Generalized Continua as Models for Classical and Advanced Materials , Advanced Structured Materials (42), pp.77-128, 2016. ⟨hal-01316153v2⟩

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