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In this commentary we try to make clearer the state of the art concerning therelation between mechanical contact interactions and the different notions ofstresses. 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 startingwith an expression of the power expended by internal stresses and deducing theform of contact interactions as when starting with some form of the contactinteractions and developping a representation theorem for these contactinteractions based on the Cauchy tetrahedron construction.

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