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Shearing of loose granular materials: a statistical mesoscopic model
János Török1, Supriya Krishnamurthy, János Kertész
1Department of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics, 8 Budafoki út, H-1111 Budapest, Hungary.
Summary
This study introduces a lattice model for shear band formation in granular materials. The model reveals slow compaction and pattern formation, leading to shear bands becoming trapped over time.
Area of Science:
- Physics
- Geophysics
- Materials Science
Background:
- Shear bands are crucial for understanding granular material deformation.
- Previous models often simplify the complex dynamics of shear band evolution.
- Granular media exhibit unique behaviors under stress due to particle interactions.
Purpose of the Study:
- To propose a novel two-dimensional lattice model for shear band formation and evolution.
- To investigate the dynamics of shear band localization and pattern development.
- To explore the relationship between local density variations and shear band trapping.
Main Methods:
- Developed a two-dimensional lattice model where each site has a local density variable.
- Simulated strain localization along a shear band identified by an extremum condition.
- Implemented dynamics involving random density changes along the shear band and path re-evaluation.
Main Results:
- Observed slow compaction and the emergence of nontrivial density patterns with high-density regions and low-density valleys.
- Demonstrated that shear bands become progressively trapped over time due to density fluctuations.
- Identified metastable states and slow evolution resembling glassy dynamics.
Conclusions:
- The proposed lattice model effectively captures key aspects of shear band formation and evolution in granular media.
- Density fluctuations play a critical role in shear band localization and trapping.
- The system exhibits complex dynamics, including metastability and glassy behavior, with significant system-size effects.