'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

摘要

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 Theorie des Corps Deformables, Herman, Paris, 1909; Cosserat and Cosserat in Note sur la theorie 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.