Constitutive relations in dense granular flows

Scaling theory of shear-induced inhomogeneous dilation in granular matter

Shearing with a finite shear rate a compressed granular system results in a region of grains flowing over a compact, static assembly. Perforce this region is dilated to a degree that depends on the shear rate, the loading pressure, gravity, various material parameters, and the preparation protocol. In spite of numerous studies of granular flows a predictive theory of the amount of dilation is still lacking. Here, we offer a scaling theory that is focused on such a prediction as a function of shear rate and the dissipative parameters of the granular assembly. The resulting scaling laws are universal with respect to changing the interparticle force laws.

Local fluctuations and spatial correlations in granular flows under constant-volume quasistatic shear

We investigate the local fluctuations in dense granular media subjected to athermal, quasistatic shearing, based on three-dimensional discrete element method simulations. By shearing granular assemblies of different polydispersities under constant-volume constraint, we quantify the characteristics of local structures (in terms of local volume and local anisotropy) and local deformation (using local shear strain and nonaffine displacement). The distribution of the local volume in a granular medium is found unchanged during the entire shearing process, which indicates a constant temperaturelike compactivity for the material. The compactivity is not, however, equilibrated among different particle groups in a polydisperse assembly. The local structures of a disordered granular assembly are inherently anisotropic. The fluctuations in local anisotropy can be well captured by a gamma or mixed-gamma distribution function, which is also unchanged during the shear. The local anisotropic orientation evolves towards the coaxial direction of the stress anisotropy with shear. The deformation characteristics of a jammed granular medium have their origins in the structural amorphousness. The local shear strain field depicts clear shear transformation zones which act as plasticity carriers. The spatial correlation of the local shear strains exhibits a fourfold pattern which is stronger in the stress deviatoric planes than in the stress isotropic plane. The fluctuations of nonaffine displacement suggest an isotropic granular temperature and an isotropic spatial correlation independent of the stress state. Both the local strain and the nonaffine displacement exhibit a power-law decayed distribution with a long-range correlation. We further modify the shear-transformation-zone theory to predict the pressure-dependent constitutive behavior of a sheared granular material and compare its prediction with our simulation data.