(18a) A Constitutive Model for Quasi-Static and Intermediate Granular Flows

Granular materials composed of discrete solid particles are ubiquitous in nature and in industries. They exhibit complex dynamical behaviors that mimic molecular solid, liquid and gas depending on external excitation to the systems. Conventionally, these different behaviors are classified into quasi-static, intermediate and rapid flow regimes. A continuum rheological model, capable of describing granular flows over all regimes, remains an open problem. This presentation will present a constitutive model that is capable of capturing rheological behaviors in both quasi-static and intermediate regimes.

We conduct computational rheological experiments of monodisperse spherical particles under homogeneous deformations using the discrete element method (DEM). We then identify flow characteristics, stress responses and microstructure evolution at continuum level under different flow conditions [1]. It will be shown that the flow behaviors can be better understood by identifying its jamming transition [2] in a flow map of stress versus scaled shear rate; at low shear rates, stress is independent of shear rate for assemblies with volume fractions above a critical value, while it is proportional to the second power of shear rate otherwise. At higher shear rates, stress scales as a single power law of shear rate regardless of volume fractions. A constitutive model is constructed using these insights; it consists of a plasticity model and a power-law viscous model for the quasi-static and intermediate regimes, respectively. The plastic stress equation is composed of a pressure term, a deviatoric term with a macroscopic friction coefficient, and two terms to account for normal stress differences. The closures for the stress equation are linked to microstructure through evolution equations for coordination number and fabric. The stress contribution from the plasticity model vanishes naturally according to the microstructure evolution at higher shear rates and is instead given by the power-law model. The material constants in the model are linked to particle-level properties, such as particle friction coefficient and elasticity modulus, and are calibrated using computational data. It will be demonstrated that the model is capable of predicting complex rheological behaviors when applied to steady and cyclic flows.

References

[1] L. R. Aarons, J. Sun, and S. Sundaresan. Unsteady shear of dense assemblies of cohesive granular materials under constant volume conditions. Industrial & Engineering Chemistry Research, 11 2009.

[2] C. S. O'Hern, L. E. Silbert, A. J. Liu, and S. R. Nagel. Jamming at zero temperature and zero applied stress: The epitome of disorder. Physical Review E, 68(1), 011306-1--19, 2003.