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Strain versus stress in a model granular material: A Devil's staircase
1Laboratoire Central des Ponts et Chaussees, 58 Boulevard Lefebvre, 75732 Paris Cedex 15, France.
Physical Review Letters
|October 13, 2000
Summary
Disordered disk packings under stress exhibit geometric-driven rearrangements. Their strain response to biaxial compression follows a Levy flight pattern, independent of granular dynamics assumptions.
Area of Science:
- Physics
- Materials Science
- Computational Physics
Background:
- Disordered granular materials exhibit complex behaviors under stress.
- Understanding the statistical mechanics of granular packings is crucial for predicting material properties.
Purpose of the Study:
- To investigate the equilibrium states of 2D disordered disk packings under varying stress.
- To determine the factors governing the statistical properties of configuration space trajectories.
- To analyze the strain response to biaxial compression in granular systems.
Main Methods:
- Numerical simulations of rigid, frictionless disks in two dimensions.
- Analysis of statistical properties of trajectories in configuration space.
- Examination of discrete rearrangement events under monotonic loading.
Main Results:
- Statistical properties of granular packing dynamics are geometry-dependent, not dynamics-dependent.
- Macroscopic loading induces discrete rearrangement events.
- Biaxial compression leads to a Levy flight strain dependence on stress direction due to large-magnitude rearrangements.
Conclusions:
- The geometry of granular packings dictates their mechanical response.
- Rearrangement events play a key role in the macroscopic behavior of granular materials.
- Levy flight statistics characterize the strain response in the thermodynamic limit for biaxial compression.
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