Steady shearing flows of deformable, inelastic spheres

Area of Science:

• Physics
• Mechanical Engineering
• Materials Science

Background:

• Granular flow models based on kinetic theory face challenges at high volume fractions.
• A critical volume fraction exists where rate-independent stress contributions emerge.
• Understanding stress evolution in dense granular media is crucial for engineering applications.

Purpose of the Study:

• To extend kinetic theory models for granular flows beyond the critical volume fraction.
• To incorporate particle interaction duration into stress calculations.
• To accurately predict stress components in both homogeneous and inhomogeneous granular flows.

Main Methods:

• Extended kinetic theory models for granular flows.
• Incorporated a measure of particle interaction duration before and after critical volume fraction.
• Developed a simple expression for collision duration to ensure smooth transitions between flow regimes.
• Applied the theory to steady, homogeneous, and inhomogeneous shearing flows.

Main Results:

• Stress components at low volume fractions are influenced by elastic collisions.
• At high volume fractions, stress includes static contributions from elasticity and dynamic contributions from force chain breakage.
• The extended model provides predictions in good agreement with numerical simulations for homogeneous flows.
• The theory successfully reproduces features of inhomogeneous flows observed in simulations and experiments.

Conclusions:

• The extended kinetic theory provides a unified framework for granular flow stress.
• The model captures the transition in stress behavior at critical volume fractions.
• This approach offers improved predictive capabilities for dense granular flows in diverse applications.