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“Hypertractions and hyperstresses convey the same mechanical information Continuum Mech. Thermodyn. (2010) 22:163–176” by Prof. Podio Guidugli and Prof. Vianello and some related papers on higher gradient theories

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Abstract

In this commentary, we try to make clearer the state of the art concerning the relation between mechanical contact interactions and the different notions of stresses. We emphasize the importance of the concept of virtual displacements. Its role has been recognized in Mechanics and in Continuum Mechanics long ago (see e.g., Vailati in Il principio dei lavori virtuali da Aristotele a Erone d’Alessandria, 113–128, 1987; Russo in The forgotten revolution, Springer, Berlin, 2003, or Cosserat and Cosserat in Sur la Théorie des Corps Déformables, Herman, Paris, 1909; Cosserat and Cosserat in Note sur la théorie de l.action euclidienne, Gauthier-Villars, Paris, 1908), and it is central as well when starting with an expression of the power expended by internal stresses and deducing the form of contact interactions as when starting with some form of the contact interactions and developing a representation theorem for these contact interactions based on the Cauchy tetrahedron construction.

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Authors and Affiliations

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

    Francesco dell’Isola

  2. Laboratorio Strutture e Materiali Intelligenti Fondazione Tullio Levi-Civita, Via S. Pasquale snc Cisterna di Latina, Latina, Italia

    Francesco dell’Isola

  3. Institut de Mathématiques de Toulon U.F.R. des Sciences et Techniques, Université de Toulon et du Var, Avenue de l’Université, BP 132, 83957, La Garde Cedex, France

    Pierre Seppecher

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  1. Francesco dell’Isola
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Correspondence to Francesco dell’Isola.

Additional information

Communicated by Stefan Seelecke.

In memory of Prof. Carlo Gavarini, who recently passed away. He assured a visiting grant to Rome for P.S. in 1996, during which the paper [13] was written.

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dell’Isola, F., Seppecher, P. “Hypertractions and hyperstresses convey the same mechanical information Continuum Mech. Thermodyn. (2010) 22:163–176” by Prof. Podio Guidugli and Prof. Vianello and some related papers on higher gradient theories. Continuum Mech. Thermodyn. 23, 473–478 (2011). https://doi.org/10.1007/s00161-010-0176-3

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