On virtual work and stress in granular media

A granular medium can be treated as an equivalent continuum. Appropriate representative stresses can be derived from the virtual work principle. However, the expression of virtual work is not unique and therefore may lead to different results of stress expressions in terms of discrete quantities—contact forces, contact moments, and branch vectors. In this paper, we introduced a generalized expression of virtual work that includes the restriction of boundary conditions. To show the advantages of the current expression, the virtual work expression is applied to derive expressions for stress, couple stress, a higher-order stress, and the stress moment. A distinction is made between the average stress within a granular volume and the representative stress that is conjugate with the representative strain of the volume. The current work is compared with that of [International Journal of Solids and Structures 38 (2) (2001) 353–367], and the current stress expressions are shown to satisfy three essential conditions of a stress measure.