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Particle simulations reveal constitutive relations for deformable particles under shear flow. Unique relations merge fluid and solid regimes, capturing jamming transitions and granular temperature dependencies.

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Area of Science:

  • Physics of granular materials
  • Computational physics

Background:

  • Understanding the behavior of granular materials under shear is crucial for various engineering applications.
  • Previous studies often focused on hard particles, limiting insights into deformable particle dynamics.

Purpose of the Study:

  • To investigate homogeneous shear flows of frictionless, deformable particles using particle simulations.
  • To develop constitutive relations that accurately describe the behavior of these materials across different regimes, including jamming transitions.

Main Methods:

  • Particle simulations were employed to study simple homogeneous shear flows.
  • Analysis focused on large shear rates and varying particle stiffness.
  • Asymptotic scaling relations were inferred for pressure, shear stress, and granular temperature.

Main Results:

  • Unique constitutive relations were developed by merging fluid (unjammed) and solid (jammed) regimes.
  • These relations cover the transition zone near jamming density.
  • The shear stress ratio (μ) for deformable particles does not collapse solely on the inertial number (I), suggesting additional control parameters are needed.

Conclusions:

  • Continuous and differentiable phenomenological relations for stresses and granular temperature were established.
  • These relations depend on volume fraction, shear rate, particle stiffness, and proximity to jamming.
  • Unlike hard particles, shear stress in deformable particles shows slight rate and stiffness dependency in the solid regime.