Qicheng Sun

Expression for the granular elastic energy

Granular solid hydrodynamics (GSH) is a broad-ranged continual mechanical description of granular media capable of accounting for static stress distributions, yield phenomena, propagation and damping of elastic waves, the critical state, shear band, and fast dense flow. An important input of GSH is an expression for the elastic energy needed to deform the grains. The original expression, though useful and simple, has some drawbacks. Therefore a slightly more complicated expression is proposed here that eliminates three of them: (1) The maximal angle at which an inclined layer of grains remains stable is increased from 26^{∘} to the more realistic value of 30^{∘}. (2) Depending on direction and polarization, transverse elastic waves are known to propagate at slightly different velocities. The old expression neglects these differences, the new one successfully reproduces them. (3) Most importantly, the old expression contains only the Drucker-Prager yield surface. The new one contains in addition those named after Coulomb, Lade-Duncan, and Matsuoka-Nakai-realizing each, and interpolating between them, by shifting a single scalar parameter.

Three-dimensional simulations of Bingham plastic flows with the multiple-relaxation-time lattice Boltzmann model

ABSTRACT This paper presents a three-dimensional (3D) parallel multiple-relaxation-time lattice Boltzmann model (MRT-LBM) for Bingham plastics which overcomes numerical instabilities in the simulation of non-Newtonian fluids for the Bhatnagar–Gross–Krook (BGK) model. The MRT-LBM and several related mathematical models are briefly described. Papanastasiou’s modified model is incorporated for better numerical stability. The impact of the relaxation parameters of the model is studied in detail. The MRT-LBM is then validated through a benchmark problem: a 3D steady Poiseuille flow. The results from the numerical simulations are consistent with those derived analytically which indicates that the MRT-LBM effectively simulates Bingham fluids but with better stability. A parallel MRT-LBM framework is introduced, and the parallel efficiency is tested through a simple case. The MRT-LBM is shown to be appropriate for parallel implementation and to have high efficiency. Finally, a Bingham fluid flowing past a square-based prism with a fixed sphere is simulated. It is found the drag coefficient is a function of both Reynolds number (Re) and Bingham number (Bn). These results reveal the flow behavior of Bingham plastics.

Entropy productions in granular materials

Granular materials display more abundant dissipation phenomena than ordinary materials. In this paper, a brief energyflow path with irreversible processes is illustrated, where the concept of granular temperature T g , initially proposed for dilute systems, is extended to dense systems in order to quantify disordered force chain configurations. Additionally, we develop the concept of conjugate granular entropy s g and its production equation. Our analyses find out that the granular entropy significantly undermined the elastic contact between particles, seriously affecting the transport coefficients in granular materials and creating new transport processes.

Energy dissipation of debris flow through pile group obstructions

Since the devastating Sichuan Earthquake on May 12, 2008, large-scale landslides and debris flows are predicted to occur in these populous areas over the next 10-30 years. In order to prevent and mitigate the geological disasters, it is of great importance to better understand the mechanism of granular flows and to predict their temporal and spatial scales in an efficient way. In this work, we develop a Roe-type finite volume model of the Savage-Hutter equations. Unstructured grid of either triangular or quadrilateral cells is used to match natural topography wells. After appropriately selecting bed and internal friction coefficients, we conduct a series of numerical flume experiments to simulate debris flow passing through pile group obstruction, which is commonly used in damping the kinetic energy of debris flows. Pile group of different spatial patterns are decorated in the downstream of the flume, and the influences of the spatial distributions of pile group obstruction to their damping effect are investigated.

Multi-scale modelling for granular materials using material \\point method and discrete element method

Granular materials are composed by discrete particles, which are often observed in geo-hazards, such as debris flows. It is difficult to establish unified constitutive relations to describe the multiple-state properties of granular materials, i.e., solid-and fluid-like states and in-between transitions. In this study, a hierarchical multi-scale modelling scheme is developed based on the concept of black box theme. The macroscopic behavior is modelled by using material point method (MPM), which is suitable for large deformation treatment, while the constitution relations at each material point are extracted from discrete element method (DEM) modelling. By using the MPM/DEM modelling, the collapse of a sand pile is simulated and compared with experiments. The correlations between macroscopic phenomenons and microscopic network of force chain are illustrated. This MPM/DEM multi-scale modelling does not need any constitutive relations, and facilitates effective cross-scale interpretation and understanding of granular flow behaviors. It provides a potential approach to study the multiple states and large deformations of granular materials, especially when the constitutive relations cannot be expressed explicitly.

Numerical study of a sphere descending along an inclined slope in a liquid

The descending process of a sphere rolling and/or sliding along an inclined slope in a liquid involves interactions between the hydrodynamic forces on the sphere and the contact forces between the sphere and the plane. In this study, the descending process of sphere in a liquid was examined using coupled LBM–DEM technique. The effects of slope angle, viscosity and friction coefficient on the movement of a sphere were investigated. Two distinct descending patterns were observed: (a) a stable rolling/sliding movement along the slope, and (b) a fluctuating pattern along the slope. Five dimensionless coefficients (Reynolds number (Re), drag coefficient, lift coefficient, moment coefficient and rolling coefficient) were used to analyze the observed processes. The vortex structure in the wake of the sphere gives a lift force to the sphere, which in turn controls the different descending patterns. It is found that the generation of a vortex is not only governed by Re, but also by particle rotation. Relationships between the forces/moments and the dimensionless coefficients are established.

Analysis of parameters in granular solid hydrodynamics for triaxial compression tests

Granular materials are omnipresent in industries and in nature. For small strains, elastic-plastic and hypoplastic constitutive relations are widely used in engineering practice, but they are not a significant reflection of the underlying physics. Under a unified thermodynamics framework explaining the physics of materials, granular solid hydrodynamics (GSH) was an extension towards describing granular materials, not only solid-like, but also fluid-like behaviors. In this paper, the fundamentals of GSH are briefly treated and then simplified to analyze quasi-static deformations in triaxial compressions. The calculated stress-strain relations and volumetric strain are compared with experimental results. The influences of the major parameters in GSH, especially their cross coupling influences, are analyzed and their physical meanings are further clarified. After parameters were calibrated, the calculated stress values in the characteristic stress state are found to be within 22% of tested values. Meanwhile, the energy dissipation during triaxial compression is analyzed. The above results support and partially quantify GSH.