From particle ensembles to Cosserat continua: definition of the macroscopic variables

摘要

In the current contribution, the transition from the dynamics of single particles to a Cosserat continuum is briefly repeated and the expressions for the macroscopic stress tensors and the couple stress tensors are supplemented with analogous expressions for the macroscopic kinematic variables, here the displacement gradient and the rotation gradient. To evaluate these definitions, in contrast to the previous publications with polygonal-shaped particles, the geometry for circular particles was implemented. To set a numerical example, biaxial tests with particles organized on a regular grid are simulated. It is found that only a representative volume with size of a particle and its direct neighbours is sufficiently small to reflect the macroscopic variables of the couple stress and the rotation field.