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A Still Topical Contribution of Gabrio Piola to Continuum Mechanics: The Creation of Peri-dynamics, Non-local and Higher Gradient Continuum Mechanics

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The complete works of Gabrio Piola: Volume I

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 38))

Abstract

Gabrio Piola’s scientific papers are in some aspects still topical in the mathematical-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.

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Authors and Affiliations

  1. Dipartimento di Ingegneria Strutturale e Geotecnica, Università di Roma La Sapienza, Via Eudossiana 18, 00184, Roma, Italy

    Francesco dell’Isola & Ugo Andreaus

  2. International Telematic University Uninettuno, C.so Vittorio Emanuele II, 39, 00186, Rome, Italy

    Luca Placidi

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  1. Francesco dell’Isola
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  2. Ugo Andreaus
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  3. Luca Placidi
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Editors and Affiliations

  1. Dipartimento di Ingegneria Strutturale e Geotecnica, Università di Roma "La Sapienza", Roma, Italy

    Francesco dell'Isola

  2. Department of Structural Engineering, Technical University of Milan, Milano, Italy

    Giulio Maier

  3. Dipartimento di Ingegneria Strutturale, Politecnico di Milano, Milano, Italy

    Umberto Perego

  4. Dipartimento di Ingegneria Strutturale e Geotecnica, Università degli Studi di Roma "La Sapienza", Roma, Italy

    Ugo Andreaus

  5. Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica, Università dell'Aquila, L'Aquila, Italy

    Raffaele Esposito

  6. Centre des Matériaux, MINES Paristech, Evry Cedex, France

    Samuel Forest

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dell’Isola, F., Andreaus, U., Placidi, L. (2014). A Still Topical Contribution of Gabrio Piola to Continuum Mechanics: The Creation of Peri-dynamics, Non-local and Higher Gradient Continuum Mechanics. In: dell'Isola, F., Maier, G., Perego, U., Andreaus, U., Esposito, R., Forest, S. (eds) The complete works of Gabrio Piola: Volume I. Advanced Structured Materials, vol 38. Springer, Cham. https://doi.org/10.1007/978-3-319-00263-7_5

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