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Rheological Behavior of Quasi-Static Granular Flows Under Unsteady Simple Shear

Jin Sun, Lee R. Aarons, and Sankaran Sundaresan. Chemical Engineering, Princeton University, Princeton, NJ 08544

In our previous work, we have studied steady simple shear flow of nearly homogeneous assemblies of uniformly sized, spherical particles in periodic domains under constant volume and constant normal stress conditions using the discrete element method [1, 2]. In addition to confirming the flow regime map for non-cohesive granular materials as reported in [3, 4], we found a new scaling which permits collapse of all steady shear data at various strengths of cohesion and shear rates into a single master curve for each particle volume fraction and coefficient of friction.

As an extension to more complex flow conditions, we now investigate the stress responses of quasi-static granular flows subjected to unsteady shear under similar computational settings in the present work. In these simulations, the shear rate varies with time according to either a square wave or a sinusoidal wave function. We find that the stress response is rate-independent as shown by the collapsed stress-strain curves at different shear rates and patterns. More interestingly, strong history dependence of the stress response is found. It is evidenced by two phenomena. Firstly, the normal and shear stresses undergo a transition after shear reversal that requires a shear strain of order unity (between one and two) to evolve. In contrast, they reach the previous steady state stress level rapidly when shear is resumed in the same direction. This characteristic strain of order unity is a robust scale independent of shear rate, volume fraction, strength of cohesion and fiction coefficient. Secondly, for unsteady shear at strain amplitudes smaller than the characteristic strain, the stress after reversal is affected by shear history in the preceding half-cycle. We also study the microscopic origin of the history dependence. We characterize the microstructure by a fabric tensor, whose shear component is used as a measure of the microstructure anisotropy. The development of shear-induced anisotropy and the correlation of the stress transition after shear reversal with the microstructure rearrangement are observed. The small strain amplitude effect can also be explained by the different microstructure evolution pattern. Comparison of the simulation data with the hypoplastic constitutive model [5, 6] predictions shows that the model without incorporating the microstructure evolution cannot correctly capture the characteristic strain after shear reversal. Thus this study also directly provides a justification and a database for developing fabric-incorporated anisotropic constitutive models for quasi-static granular flows.


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[2] L. Aarons and S. Sundaresan. Shear flow of assemblies of cohesive granular materials under constant applied normal stress. Powder Technology, 183(3):340355, 2008.

[3] C. S. Campbell. Granular shear flows at the elastic limit. Journal of Fluid Mechanics, 465:261291, 2002.

[4] C. S. Campbell. Stress-controlled elastic granular shear flows. Journal of Fluid Mechanics, 539:273297, 2005.

[5] W. Wu, E. Bauer, and D. Kolymbas. Hypoplastic constitutive model with critical state for granular materials. Mechanics of Materials, 23(1):4569, 1996.

[6] D. Kolymbas. Introduction to Hypoplasticity. A. A. Balkema, 2000.