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 \(\mu (I)\) rheology flow law. The effects of the coupling number, the micro-inertia, the characteristic length, and the peridynamic horizon size on the granular \(\mu (I)\) 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 translational velocity. Slight differences are observed in the translational velocity distribution or free surface profile. For the horizon size, we find it affects the granular flow only on the micro-rotational velocity and runout distance.