Non-local updated Lagrangian peridynamics model for granular flow with μ(I) rheology

Abstract

Granular materials exhibit complex behaviors in different flow states that feature nonlocality. In this study, we propose a non-local updated Lagrangian peridynamics model for granular flow. The model treats the granular flow as a weakly compressible fluid, governed by the framework of Navier–Stokes equation and incorporating the μ(I) rheology. The introduction of peridynamics with the Wendland C² kernel function enables this nonlocal feature. The proposed model is implemented to simulate granular collapse processes. Simulated flow velocities and deposition configurations are compared with experimental observations. It is the found that the proposed peridynamics method naturally includes non-local effects through considering the non-contact interaction between material points in the peridynamics horizon, specifically, slower static-to-flowing transitions and wider shear bands can be captured compared with the local model. Sensitive analysis indicates that increasing the peridynamic horizon enhance stress redistribution, widen shear band, and extend runout. In addition, the influence of the compressibility of granular properties and the adopted kernel functions is further investigated. In general, the updated Lagrangian nonlocal peridynamics model can reproduce simultaneously the behaviors exhibited by granular materials, especially in the quasi-static regime.