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

TL;DR

This paper clarifies the relationship between contact interactions and stress notions in continuum mechanics, emphasizing the significance of virtual displacements in understanding internal stresses and contact forces.

Contribution

It provides a clearer overview of the state of the art regarding contact interactions and stresses, highlighting the role of virtual displacements in continuum mechanics.

Findings

Emphasizes the importance of virtual displacements in stress analysis.

Clarifies the relation between contact interactions and stress notions.

Highlights the role of the Cauchy tetrahedron construction in representation theorems.

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. [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.