Definition and Symmetry of Averaged Stress Tensor in Granular Media and its 3D DEM Inspection Under Static and Dynamic Conditions

Yan, Beichuan; Regueiro, Richard A

Citeable URL: https://scholar.colorado.edu/concern/articles/vm40xs73f

Abstract

The paper aims to clarify the stress tensor definition and its symmetry property that applies to granular media, and conducts 3D Discrete Element Method (DEM) inspection of the stress tensor definitions provided in the literature. Various stress tensor formulas under static and dynamic conditions are summarized, compared and numerically inspected through different types of simulation, such as gravitational deposition, isotropic/oedometer compression and high-strain-rate (HSR) oedometer impact. The stress tensor symmetry is particularly discussed from the perspective of applying classical continuum mechanics to granular media. It is proved analytically and numerically that the stress tensor should be calculated by Bagi’s formula, not Weber’s formula or Drescher’s formula, for a particle assembly or representative volume element (RVE) in static equilibrium. We propose to modify the De Saxcé and Nicot formulas by incorporating the boundary-radius-gap term such that they are consistent with Bagi’s formula, which is particularly well-suited for studying granular phenomena that transition between static, quasi-static and dynamic conditions. It is shown from the perspective of stress tensor calculation that the number of particles in the RVE does not need to be large. Symmetry of averaged stress tensor can be accurately satisfied in static equilibrium of the granular DEM RVE, however it cannot in quasi-static or dynamic states due to imbalance of angular momentum of the granular DEM RVE (in comparison to the balance of angular momentum which is always satisfied in classical continuum mechanics). When the stress tensor definition is extended to “discontinuous” state with regard to discrete granular DEM RVEs, the calculated values need to be treated with caution.

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