Microstructural stress tensor of granular assemblies with volume forces

This paper focuses on the discrete expression of stress tensors of assemblies containing discrete particles with volumetric loads acting on them in addition to boundary forces. Instead of the concept of continuum point, a domain containing a finite number of grains is considered. This domain is replaced by a suitably chosen equivalent continuum whose average stress is expressed-assuming that the grains are in equilibrium-in terms of contact forces and properly defined branch vectors. Symmetry of the stress tensor is also analyzed.