Commentary about the paper "Continuum Mech. Thermodyn. (2010) 22:163-176" by Podio Guidugli and Vianello and some related papers on higher gradient theories

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. [59], [45], or [12], [13]) 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 developping a representation theorem for these contact interactions based on the Cauchy tetrahedron construction.