A constitutive law for dense granular flows

A constitutive law for dense granular flows

2006 | Pierre Jop, Yoël Forterre, Olivier Pouliquen
The paper by Jop, Forterre, and Pouliquen presents a new constitutive law for dense granular flows, which is a significant advancement in understanding and predicting the behavior of granular materials under various conditions. The authors propose a three-dimensional (3D) rheology that captures the complex flow patterns observed in granular materials, particularly in the intermediate dense regime where the material flows like a liquid. This regime is characterized by a yield criterion and a complex shear rate dependence, similar to classical visco-plastic fluids like Bingham fluids. The proposed rheology is based on the assumption that the granular material can be described as an incompressible fluid, with the internal stress tensor given by a function of the shear rate and isotropic pressure. The friction coefficient, which depends on a dimensionless inertial number, is derived from experimental data and numerical simulations. The model predicts that the effective viscosity diverges to infinity as the shear rate approaches zero, ensuring the existence of a yield criterion. To test the model, the authors conducted experiments on granular flows between rough sidewalls, where a complex 3D flow pattern develops. The model accurately predicts the flow shape and velocity profiles without any fit parameters, demonstrating its quantitative accuracy. The results support the idea that a simple visco-plastic approach can effectively capture the properties of granular flows, making it a valuable tool for modeling geophysical and industrial applications. The study also highlights the importance of considering the yield criterion, which is currently described using a Coulomb criterion. However, the authors note that more complex yield features, such as shear bands, intermittent flows, and hysteretic phenomena, need to be incorporated into a more comprehensive rheology. Despite these limitations, the proposed rheology represents a minimal model that captures the basic features of granular flows, providing a foundation for further development.The paper by Jop, Forterre, and Pouliquen presents a new constitutive law for dense granular flows, which is a significant advancement in understanding and predicting the behavior of granular materials under various conditions. The authors propose a three-dimensional (3D) rheology that captures the complex flow patterns observed in granular materials, particularly in the intermediate dense regime where the material flows like a liquid. This regime is characterized by a yield criterion and a complex shear rate dependence, similar to classical visco-plastic fluids like Bingham fluids. The proposed rheology is based on the assumption that the granular material can be described as an incompressible fluid, with the internal stress tensor given by a function of the shear rate and isotropic pressure. The friction coefficient, which depends on a dimensionless inertial number, is derived from experimental data and numerical simulations. The model predicts that the effective viscosity diverges to infinity as the shear rate approaches zero, ensuring the existence of a yield criterion. To test the model, the authors conducted experiments on granular flows between rough sidewalls, where a complex 3D flow pattern develops. The model accurately predicts the flow shape and velocity profiles without any fit parameters, demonstrating its quantitative accuracy. The results support the idea that a simple visco-plastic approach can effectively capture the properties of granular flows, making it a valuable tool for modeling geophysical and industrial applications. The study also highlights the importance of considering the yield criterion, which is currently described using a Coulomb criterion. However, the authors note that more complex yield features, such as shear bands, intermittent flows, and hysteretic phenomena, need to be incorporated into a more comprehensive rheology. Despite these limitations, the proposed rheology represents a minimal model that captures the basic features of granular flows, providing a foundation for further development.
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