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

Francesco Dell'Isola 1 Ugo Andreaus 1 Luca Placidi 2
1 DISG - Dipartimento di Ingegneria Strutturale e Geotecnica
2 International Telematic University "Uninettuno"
Abstract : Gabrio Piola's scientic 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 scientic 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.
Document type :
Book sections
Complete list of metadatas

Cited literature [2 references]  Display  Hide  Download
https://hal.archives-ouvertes.fr/hal-00955904
Contributor : Christian Cardillo <>
Submitted on : Wednesday, March 5, 2014 - 3:36:30 PM
Last modification on : Wednesday, October 12, 2016 - 4:18:09 PM
Long-term archiving on : Thursday, June 5, 2014 - 11:41:28 AM

File

Cap_5_pery_20140222.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00955904, version 1

Citation

Francesco Dell'Isola, Ugo Andreaus, Luca Placidi. A still topical contribution of Gabrio Piola to Continuum Mechanics: the creation of peri-dynamics, non-local and higher gradient continuum mechanics. The complete works of Gabrio Piola: Volume I - , Volume 38, 2014, Advanced Structured Materials. ⟨hal-00955904⟩

Export

BibTeX TEI DC DCterms EndNote

Share

Metrics

Record views

212

Files downloads

200

Contact

CCSD