Discussion on "The asymmetry of stress in granular media" by J.P. Bardet and I. Vardoulakis - [Int. J. Solids and Structures, Vol. 38, pp. 353-367 (2001)]

The paper introduces two possible definitions for microstructural stress in granular assemblies. A stress tensor is derived from direct statical considerations (this stress is always symmetric in the absence of contact moments), and another stress tensor is found by the principle of virtual displacements (the authors show that this stress may be asymmetric even in the absence of contact moments). The authors' formulation of results is misleading since it creates the false impression that the difference of the two results was caused by using two different methods. Well-known that the principle of virtual displacements is just a different expression of the statical (equilibrium) equations. If the same problem is analyzed, the work principle must lead to the same result as the direct statical equations. The aim of this discussion is to analyze why the authors found different results with the two different, but theoretically equivalent methods. The notations will be the same here as those used in the paper.