Particle and Continuum Rotations of Granular Materials: Discrete-Element Method Simulations and Experiment

Abstract

For granular materials, the kinematic degrees of freedom at the microscale of particles are the particles’ displacements and rotations. In classical continuum mechanics, the kinematic degree of freedom at the macroscale is the (local) displacement field. The rotation of a material element is not independent but is determined by the antisymmetric part of the displacement gradient. The objective of this study is to investigate, mainly by means of discrete-element method simulations, whether the average particle rotation is equal to the continuum rotation determined from the average displacement gradient. In the three-dimensional discrete-element method simulations of shear tests (with nonzero average continuum rotation), simulations with and without contact couples have been analyzed. The simulation results show that the average particle rotation is effectively equal to the continuum rotation, over the whole range of strains. Additionally, the results of an X-ray tomography test of a rounded granular soil under triaxial compression are analyzed. The average rotation of soil particles inside shear bands agrees well with the average continuum rotation determined from the particle displacements. Comparison of simulation results with contact couples to those where contact couples were not considered reveals that the presence of contact couples has a significant effect on the stress ratio and on the volumetric strain. The stress tensor is symmetric, even when contact couples are included.