Strain versus stress in a model granular material: A Devil's staircase

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.