A finite element implementation of the nonlocal granular rheology

Abstract

SUMMARYInhomogeneous flows involving dense particulate media display clear size effects, in which the particle length scale has an important effect on flow fields. Hence, nonlocal constitutive relations must be used in order to predict these flows. Recently, a class of nonlocal fluidity models have been developed for emulsions and subsequently adapted to granular materials. These models have successfully provided a quantitative description of experimental flows in many different flow configurations. In this work, we present a finiteelement-based numerical approach for solving the nonlocal constitutive equations for granular materials, which involve an additional, non-standard nodal degree-of-freedom -the granular fluidity, which is a scalar state parameter describing the susceptibility of a granular element to flow. Our implementation is applied to three canonical inhomogeneous flow configurations: (i) linear shear with gravity, (ii) annular shear flow without gravity, and (iii) annular shear flow with gravity. We verify our implementation, demonstrate convergence, and show that our results are mesh-independent.

Microscopic Origin of Nonlocal Rheology in Dense Granular Materials

“…To account for such nonlocal effects, the concept of granular fluidity was introduced [12][13][14][15][16], and continuum constitutive laws extending the inertial granular rheology to the quasistatic regime were proposed [14,[17][18][19]. Recently, using discrete element simulations in plane shear, gravitational and chute flows, a relation between granular fluidity and velocity fluctuations was exhibited [20].…”

Non-locality in Granular Flow: Phenomenology and Modeling Approaches

“…On issue (iii), the extent to which the different models have been tested varies quite a bit. NGF, with its own dedicated numerical solver [68], has been validated in the most geometries and conditions [78]. The NGF and the I−gradient models have each shown quantitative agreement with non-local creep in multiple 2D experiments [23,51,62], capturing proper flow spreading and the emergence of rate-independence.…”

“…Kinetic theory, partial fluidization, and NGF propose one additional PDE involving one new state variable. These can be solved numerically using the finite-element method (see for example, the implementation in [68]) and sometimes analytically in unidirectional flow cases [44,54,57,62,69]. Based on its mathematical form, it is not clear what the difficulty of numerical integration of the I−gradient model would be in arbitrary cases.…”

A hierarchy of granular continuum models: Why flowing grains are both simple and complex

“…The NGF model was then implemented in 3D [13]. This was done using a customized finite-element routine in Abaqus [50]. We first modeled the split-bottom cell geometry (Fig 2(a)), a flow environment that serves as a benchmark for flow rheologies, as no previous continuum model was able to correctly predict its flow fields.…”