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Stochastic flow rule for granular materials.

Ken Kamrin1, Martin Z Bazant

  • 1Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 01239, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 16, 2007
PubMed
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This study introduces a novel stochastic flow rule (SFR) for dense granular flow, accounting for material discreteness and randomness. The model successfully predicts various granular flow behaviors without fitting parameters, offering a general framework for plasticity in amorphous materials.

Area of Science:

  • Physics
  • Materials Science
  • Engineering

Background:

  • Continuum models for dense granular flow lack a general theory.
  • Classical plasticity principles like coaxiality are insufficient for granular materials.

Purpose of the Study:

  • To develop a general theory for dense granular flow.
  • To propose a "stochastic flow rule" (SFR) that incorporates granular material discreteness and randomness.

Main Methods:

  • Utilized Mohr-Coulomb plasticity for stress and slip plane calculations.
  • Introduced a "stochastic flow rule" (SFR) replacing coaxiality, modeling plasticity carriers as diffusing "spots" performing biased random walks.
  • Derived a continuum limit using a Fokker-Planck equation for spot concentration.

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Main Results:

  • The SFR model accurately predicts diverse granular flow profiles (silos, Couette cells, heaps, plate-dragging) with minimal parameters.
  • Demonstrated a transition to Bagnold rheology for specific cases like inclined plane flow.
  • Established the SFR as a versatile framework for multiscale plasticity modeling in amorphous materials.

Conclusions:

  • The stochastic flow rule offers a robust and generalizable approach to modeling dense granular flow.
  • The model bridges continuum, mesoscale, and microscopic descriptions of plasticity.
  • This work advances the understanding and prediction of granular material behavior in various engineering applications.