Dense Granular Flow Described by Micropolar Fluid and Its Peridynamic Implementation

Abstract

This work presents a nonlocal mesh-free peridynamic model for micropolar fluids that describe fluids enriched with the micro-rotational and length scale effects. The stabilized force state is applied to remedy the zero-energy mode instability in the micropolar viscous term. The present model is validated with the planar Couette flow and Poiseuille flow simulation. Considering the natural inheritance of micro-spinning and microstructures in granular flows, the peridynamic micropolar fluid model is also applied to simulate the dense, dry granular flow with a modified µ(I) rheology flow law. The effects of the coupling number, the micro-inertia, and the characteristic length on the granular µ(I) flow are discussed in a two-dimensional column collapse example. The numerical results of column collapse show that the micropolar coupling number can significantly affect column collapse behavior. A larger coupling number can slow down the translational movement of the granular flow, resulting in a larger angle of repose. The micro-rotational velocity increases by enlarging the coupling number. The micro-inertia and characteristic length have a significant influence on the micro-rotational behavior of the granular flow. Increasing either micro-inertia or characteristic length value decreases the micro-rotational velocity. However, the characteristic length and micro-inertia have an insignificant influence on the translational behavior. Slight differences are observed in the translational velocity distribution or free surface profile.