From particle ensembles to Cosserat continua: homogenization of contact forces towards stresses and couple stresses

In the present contribution, a transition from the dynamics of single particles to a Cosserat continuum is discussed. Based on the definition of volume averages, expressions for the macroscopic stress tensors and for the couple stress tensors are derived. It is found that an ensemble of particles allows for a non-symmetric macroscopic stress tensor and, thus, for the existence of couple stresses, even if the single particles are considered as standard continua. Discrete element method simulations of a biaxial box are used for the validation of the proposed homogenization technique.