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Scale separation in granular packings: stress plateaus and fluctuations
C Goldenberg1, A P F Atman, P Claudin
1Laboratoire de Physique et Mécanique des Milieux Hétérogènes (CNRS UMR 7636), ESPCI, 10 rue Vauquelin, 75231 Paris Cedex 05, France. chayg@lpmcn.univ-lyon1.fr
Researchers found a specific range of scales where granular solid stress is independent of measurement resolution, allowing for objective field definition. System gradients, not just size, influence this scale range, which can be extended by ensemble averaging.
Area of Science:
- Computational physics
- Materials science
- Granular mechanics
Background:
- Defining stress tensor fields in granular materials is challenging due to inherent heterogeneity.
- Coarse-graining methods are often used but can introduce scale-dependent artifacts.
Purpose of the Study:
- To identify a scale range for objective stress tensor definition in granular solids.
- To investigate factors influencing the stability of this objective scale range.
Main Methods:
- Numerical simulations of two-dimensional (2D) assemblies of polydisperse disks.
- Analysis of stress tensor fields under various loading conditions (homogeneous forcing, localized load, gravity).
Main Results:
- A plateau of coarse-graining scales was identified where the stress tensor field is nearly resolution-independent.
- The width of this plateau is determined by the magnitude of gradients, not solely system size.
- Ensemble averaging extends the plateau to subparticle scales.
Conclusions:
- An objective definition of the stress tensor field in granular solids is achievable within specific coarse-graining scales.
- Understanding scale-dependent behavior is crucial for accurate constitutive modeling of granular materials.
- Numerical simulations provide a robust framework for investigating granular material properties.
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