(285a) Unsteady Shear Flow Of Assemblies Of Cohesive Granular Materials

Authors: 
Aarons, L. R. - Presenter, Princeton University


In the present study we have examined through Discrete Element Method (DEM) simulations the dynamic response of dense assemblies of cohesive particles to time-varying shear flow. Such simulations reveal the essential characteristics that a dynamic continuum model for granular rheology should possess. For example, it is well known that in the quasistatic regime of flow the stresses in a dense granular assembly are independent of the steady shear rate. Thus, if a step change is made in the shear rate, the asymptotic values of the stresses before and after the change will not differ. However, there can be significant dynamic excursions and the nature and extent of such excursions are not well understood. The present study examines the dynamic response of the stresses and the microstructure to imposed changes in the shear rate.

We consider DEM simulations [1] of the plane shear flow of particle assemblies in periodic domains, employing Lees ? Edwards boundary conditions [2] across the faces. Simulations were performed for different strengths of cohesion, shear rates, and particle volume fractions. In these simulations, assemblies were subjected to oscillatory shear or step changes in shear rate, and we have tracked the response of the normal and shear stresses. All the simulations were done at small shear rates, representative of the ?quasistatic regime?.

Under constant shear [3], it was found that steady state was achieved for a given simulated system after shearing for a time equal to about the inverse of the shear rate. Similarly under oscillatory shear, we found that if the oscillation frequency was chosen to be larger than the maximum shear rate, the steady state stress achieved in the steady shear simulations was never achieved, regardless of the number of oscillations performed. At lower frequencies, the steady state stress value was achieved, and the stress fluctuated about that value until shear was reversed. Upon shear reversal, the normal stress rapidly dropped to a negative value, such that the assembly was in tension. Afterwards, the normal stress increased monotonically towards the steady state value until the shear reversal occurred again. As cohesion was increased, the normal stress started to drop off just before shear reversal (i.e. at very small shear rates), even if the steady state stress was reached and even though the shearing occurred in the quasistatic regime.

The behavior of cohesive materials subject to a step change in shear rate depended on the level of cohesion. At low levels of cohesion, the change in shear rate was followed by a large spike in the normal stress. Investigations into the microstructure of these systems have shown a distinct correlation between the behaviors of the force chains and the normal stress. After the change in shear rate but before the spike in stress, the majority of the stress is carried by the particles at the top and bottom of the simulated system. At the top of the spike, the stress became more evenly spread out across the assembly. After the stress spike, the majority of the stress was once again confined to force chains. At higher levels of cohesion, none of this happened. There was no large spike in stress and the force chains were virtually unaffected by the change in shear rate. Thus, cohesion serves to mitigate very large fluctuations that can occur under dynamic conditions, suggesting that one can beneficially exploit modest levels of cohesion to suppress stress fluctuations.

In this presentation, we will also compare these results with the hypoplastic model for slow flow of granular materials proposed by Wu et al. [4]. It will be shown that such models are miss important qualitative features.

[1] P. A. Cundall, O. D. L. Strack, A discrete numerical model for granular assemblies, Geotechníque 29 (1) (1979) 47-65.

[2] A. W. Lees, S. F. Edwards, The computer study of transport processes under extreme conditions, Physics C: Solid State Phys. 5 (1972) 1921-1929.

[3] L. Aarons, S. Sundaresan, Shear flow of assemblies of cohesive and non-cohesive granular materials, Powder Technol. 169 (1) (2006) 10-21.

[4] W. Wu, et al., Hypoplastic constitutive model with critical state for granular materials, Mechanics of Materials 23 (1) (1996) 45-59.