Granular materials: Bridging damaged solids and turbulent fluids

Granular materials exhibit abundant dissipations due to fluctuations in both granular motions and configurations (i.e., granular skeleton) evolutions. Twin granular temperatures T_k and T_e are introduced accounting for two types of fluctuations, and the so-called twin granular temperatures theory is established as an extension of granular solid hydrodynamics. By using simulations, the nonaffine deformations in a 2D assembly are simulated by using discrete element methods. By analogizing with microdamages in deformed solids, double scalar damage variables, D_P and D_q, are proposed to describe the deformed granular solid under triaxial compressions. Granular flows are found intrinsically turbulent due to the presence of T_k and the Naiver–Stokes equation is obtained for granular flows.     

Prediction of segregation characterization based on granular velocity and concentration in rotating drum

In a binary granular system composed of two types of particles with different granule sizes and the same density, particle sorting occurs easily during the flow process. The segregation pattern structure is mainly affected by the granular velocity and granular concentration in the flow layer. This paper reports on the experimental velocity and concentration measurement results for spherical particles in a quasi-two-dimensional rotating drum. The relationship between the granular velocity along the depth direction of the flow layer and granular concentration was established to characterize structures with different degrees of segregation. The corresponding relationships between the granular velocity and concentration and the segregation pattern were further analyzed to improve the theoretical models of segregation (convection–diffusion model and continuous flow model) and provide a reference for granular segregation control in the production process.     

The influence of the drag force due to the interstitial gas on granular flows down a chute

Fully-developed steady flow of granular material down an inclined chute has been a subject of much research interest, but the effect of the interstitial gas has usually been ignored. In this paper, new expressions for the drag force and energy dissipation caused by the interstitial gas (ignoring the turbulent fluctuations of the gas phase) are derived and used to modify the governing equations derived from the kinetic theory approach for granular–gas mixture flows, where particles are relatively massive so that velocity fluctuations are caused by collisions rather than the gas flow. This new model is applied to fully-developed, steady mixture flows down an inclined chute and the results are compared with other simulations. Our results show that the effect of the interstitial gas plays a significant role in modifying the characteristics of fully developed flow. Although the effect of the interstitial gas is less pronounced for large particles than small ones, the flowfields with large particles are still very different from granular flows which do not incorporate any interactions with the interstitial gas.     

The role of a realistic volume constraint in modelling a two dimensional granular assembly

This paper presents a deceptively simple mathematical model for the deformation of granular materials composed of rigid particles. The model captures many of the diverse features of the behaviour of such a material and emphasises the importance of volume constraints in situations where the deformation is mainly by particle rearrangement. It is constructed using a simple dissipation function and a rather more complicated dilatancy rule containing an updateable reference strain. This allows the solid-like and fluid-like properties of granular materials to be reconciled in a single model.The model has been used to simulate experiments that use an analogue of an ideal granular material [Joer, H.A., Lanier, J., Fahey, M., 1998. Deformation of granular materials due to rotation of principal axes. Geotechnique 48 (5), 605-619] consisting of a two dimensional assembly of thin PVC rods. These experiments clearly illustrate: partially reversible dilatancy in direct shear tests; cyclic shearing leading to liquefaction in constant volume shear tests; and non-coaxiality of the principal axes of stress and strain increment in circular loading tests. These radically different modes of deformation provide a challenging data set that allows the model's potential to be clearly demonstrated.The authors believe that the comparison of these experimental results and our simulations give strong support to the assertion that volume changes associated with shear deformation are responsible for the rotational kinematic hardening seen in granular materials, and hence, the non-coaxiality of the stress and strain-rate tensors.     

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 ex- tension 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.     

考虑损伤的内变量黏弹-黏塑性本构方程

基于Rice 不可逆内变量热力学框架,在约束构型空间中讨论材料的蠕变损伤问题. 通过给定具体的余能密度函数和内变量演化方程推导出考虑损伤的内变量黏弹-黏塑性本构方程. 通过模型相似材料单轴蠕变加卸载试验对一维情况下的本构方程进行参数辨识和模型验证,本构方程能很好地描述黏弹性变形和各蠕变阶段.不同的蠕变阶段具有不同的能量耗散特点. 受应力扰动后,不考虑损伤的材料系统能自发趋于热力学平衡态或稳定态. 在考虑损伤的整个蠕变过程中,材料系统先趋于平衡态再背离平衡态发展. 能量耗散率可作为材料系统热力学状态偏离平衡态的测度;能量耗散率的时间导数可用于表征系统的演化趋势;两者的域内积分值可作为结构长期稳定性的评价指标.      

Nonlinear elasto-plastic model for dense granular flow

This work proposes a model for granular deformation that predicts the stress and velocity profiles in well-developed dense granular flows. Recent models for granular elasticity [Jiang, Y., Liu, M., 2003. Granular elasticity without the Coulomb condition. Phys. Rev. Lett. 91, 144301] and rate-sensitive fluid-like flow [Jop, P., Forterre, Y., Pouliquen, O., 2006. A constitutive law for dense granular flows. Nature 441, 727] are reformulated and combined into one universal elasto-plastic law, capable of predicting flowing regions and stagnant zones simultaneously in any arbitrary 3D flow geometry. The unification is performed by justifying and implementing a Kröner–Lee decomposition, with care taken to ensure certain continuum physical principles are necessarily upheld. The model is then numerically implemented in multiple geometries and results are compared to experiments and discrete simulations.     

Solution existence conditions for elastoplastic constitutive models of granular materials

In this paper, the conditions of solution existence for stress rates under given strain rates are investigated. The focus of the solution existence investigation is on the non-associated flow rule and elastic stress–strain relationship. Granular materials characterized with strong non-associated plastic flows are used as a particular example for analysis. Various flow rules for granular materials are analyzed, including Rowe’s, Roscoe’s flow rules and their modified versions. In the elastic stress–strain relationships of materials, the effects of Poisson’s ratio on solution existence are investigated. Both isotropic and anisotropic elasticity are considered. Given a granular material and its states, it is found that there exists a critical Poisson’s ratio for a particular non-associated flow rule. When the Poisson’s ratio of a material is above this critical Poisson’s ratio, its constitutive model is susceptible to solution non-existence. It is suggested that special attentions should be paid to the selection of material Poisson’s ratio and non-associated flow rule to ensure the existence of elastoplastic solutions.     

Thermodynamic fluctuations in canonical shock–turbulence interaction: effect of shock strength

In this work, we use numerical simulation and linear inviscid theory to study the thermodynamic field generated by the interaction of a shock wave with homogeneous isotropic turbulence. Fluctuations in density, pressure, temperature and entropy can play an important role in shock-induced mixing, combustion and energy transfer processes. Data from shock-captured direct numerical simulations (scDNS) are used to investigate the variation of thermodynamic fluctuations for varying shock strengths, and the results are compared with linear interaction analysis (LIA). The density, pressure and temperature variances attain large values at the shock, followed by, in general, a rapid decay in the downstream flow. The rapid variation behind the shock makes it difficult to compare numerical results with theoretical predictions. A threshold method based on instantaneous shock dilatation is used to overcome this problem, and it gives excellent match between scDNS and LIA. We find cases with non-monotonic variation with Mach number as well as local peaks in density fluctuations behind the shock. These are explained in terms of the contribution of the post-shock acoustic and entropy modes in the LIA solution and their cross-correlation. Budget of the transport equations reveals interesting insight into the physics governing the thermodynamic field behind the shock wave. It is found that the variances are primarily determined by the competing effects of dilatational and dissipation mechanisms. The dominant mechanisms are identified for a range of conditions, and their implication for developing predictive models is highlighted.     

Entropy productions in granular materials

Granular materials display more abundant dissipation phenomena than ordinary materials. In this paper, a brief energy flow 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.     

煤仓内煤散料流动状态与力学行为影响因素

针对煤仓内煤散料流动问题及其力学行为,采用三维颗粒流模拟程序PFC3D建立了某型号煤仓与某种煤散料的离散元模型,简述了其力学模型与求解步骤,模拟分析了煤仓内煤散料卸料流动状态。通过分析水平向侧压力、颗粒速度场和接触力场,重点讨论了煤仓下部锥体内壁面摩擦系数、锥仓倾角和卸料口径等对煤散料颗粒流动状态和力学行为的影响。结果显示,深仓卸料流动为整体流动与中心流动混合状态,煤仓内壁摩擦系数、锥体倾角和卸料孔开口半径均对煤散料流动和水平侧压力有较大影响。     

点载荷作用下密集颗粒物质的传力特性分析

利用颗粒离散元商业软件PFC3D, 模拟了在2m*1m*0.01m容器中直径分别为0.01m, 0.008m和0.006m的颗粒各1*10$^4$个, 受重力作用下的静态密集堆积; 以此为初始条件, 在表层随机选择7个颗粒分别施加5.2*10$^{ - 2}$N(100倍最大颗粒重量)的点载荷, 进行应力传播特点研究. 结果表明: 力的传递在局部范围内呈现很强的各向异性; 应力涨落随着距离的增加呈指数下降; 在大于5倍最大颗粒粒径时, 其分布可以使用弹性力学理论来计算. 探讨了摩擦系数$\mu =0$, 0.2, 1对应力传递的影响, 随着摩擦系数的增加, 各向异性范围减小.     

Segregation of particulate solids＂ Experiments and DEM simulations

Segregation of granular materials is a complex phenomenon, difficult to measure quantitatively and to predict. Discrete element method （DEM） can be a useful tool to predict segregation effects and to support the industrial design. In this context, a very challenging idea is the characterization of the granular solids to provide the key parameters needed for a successful DEM simulation of segregation processes. Rolling friction, sliding friction and the coefficient of restitution are the critical parameters to be studied. These microscopic simulation parameters are calibrated by comparing the macroscopic behavior of granular matter in standard bulk experiments, which have the advantage of being highly repeatable and reliable. An experimental method is presented to characterize free surface segregation. The effects of different particle properties, particularly, shape and size, on segregation of cohesionless materials were investi- gated. From the experiments, particle size demonstrated a stronger effect on segregation than particle shape. Finally, the corresponding DEM simulations of the segregation experiments were presented. The parameters obtained by calibration were validated by the comparison of the modeled segregation behav- ior with the experimental results. Thus, calibrated DEM simulations are capable of predicting segregation effects.     

Density-induced granular segregation in a slurry rotating drum

We experimentally investigated the effects of interstitial fluid density and viscosity on density-induced granular segregation in a rotating drum. Image processing and a particle-tracking method were used for determining the segregation index and dynamic properties of granular materials. The results indicate that the interstitial fluid density has a crucial role in density-induced granular segregation. A dimensionless factor was defined for quantifying the effect of interstitial fluid density on density-induced granular segregation. The segregation intensity increased as the interstitial fluid viscosity increased. In addition, the Stokes number associated with density-induced granular segregation was discussed in this study.     

Representative elementary volume analysis of polydisperse granular packings using discrete element method

The representative elementary volume (REV) for three-dimensional polydisperse granular packings was determined using discrete element method simulations. Granular mixtures of various sizes and particle size distributions were poured into a cuboid chamber and subjected to uniaxial compression. Findings showed that the minimum REV for porosity was larger compared with the REV for parameters such as coordination number, effective elastic modulus, and pressure ratio. The minimum REV for porosity and other parameters was found to equal 15, 10, and 5 times the average grain diameter, respectively. A study of the influence of sample size on energy dissipation in random packing of spheres has also confirmed that the REV size is about 15 times the average grain diameter. The heterogeneity of systems was found to have no effect on the REV for the parameters of interest for the narrow range of coefficient of uniformity analyzed in this paper. As the REV approach is commonly applied in both experimental and numerical studies, determining minimum REV size for polydisperse granular packings remains a crucial issue.     

岩土类颗粒物质宏-细观力学研究进展

岩土类颗粒物质在自然界、工程建设以及日常生活中普遍存在,其运动特性的研究在力学界已经开展了几十年.在近20年开展的一系列小尺寸物理实验中,颗粒物质表现出许多新奇现象,人们从物理角度开展了系统研究,在统计力学中,颗粒固体的流体动力学等理论研究以及实验检测技术等方面都取得突破性进展,深刻地揭示了颗粒材料的物理机制,促使力学...     

Modulation of solitary waves and formation of stable attractors in granular scalar models subjected to on-site perturbation

Present work concerns the propagation of solitary waves in the array of coupled, uncompressed granular chains subjected to onsite perturbation. We devise a special analytical procedure depicting the modulation of solitary pulses caused by the inter-chain interaction as well as by the on-site perturbations of a general type. The proposed analytical procedure is very efficient in depicting both the transient response characterized by significant energy fluctuations between the chains as well as in predicting the formation of stable attractors corresponding to a steady state response. We confirm the validity of a general analytical procedure with several specific setups of granular scalar models. In particular we consider the response of the array of coupled granular chains free of perturbation as well as the arrays subject to the basic type of on-site perturbations such as the ones induced by the uniform and random elastic foundation, dissipation. Additional interesting finding made in the present study corresponds to the granular arrays subject to a special type of on-site perturbation containing the terms leading to the two opposing effects namely dissipation and energy sourcing. Interestingly enough this type of perturbation may lead to the formation of stable attractors. By the term attractors we refer to the stable, stationary pulses simultaneously forming on all the coupled chains and propagating with the same phase speed. It is important to emphasize that the analytical procedure developed in the first part of the study predicts the formation of stable attractors through a typical saddle–node bifurcation. Moreover, results of the reduced model are found to be in a spectacular agreement with those of the direct numerical simulations of the true model.     

Segregation of particulate solids: Experiments and DEM simulations

Segregation of granular materials is a complex phenomenon, difficult to measure quantitatively and to predict. Discrete element method (DEM) can be a useful tool to predict segregation effects and to support the industrial design. In this context, a very challenging idea is the characterization of the granular solids to provide the key parameters needed for a successful DEM simulation of segregation processes. Rolling friction, sliding friction and the coefficient of restitution are the critical parameters to be studied. These microscopic simulation parameters are calibrated by comparing the macroscopic behavior of granular matter in standard bulk experiments, which have the advantage of being highly repeatable and reliable.An experimental method is presented to characterize free surface segregation. The effects of different particle properties, particularly, shape and size, on segregation of cohesionless materials were investigated. From the experiments, particle size demonstrated a stronger effect on segregation than particle shape. Finally, the corresponding DEM simulations of the segregation experiments were presented. The parameters obtained by calibration were validated by the comparison of the modeled segregation behavior with the experimental results. Thus, calibrated DEM simulations are capable of predicting segregation effects.     

椭球颗粒体系剪切过程中自由体积的分布与演化

颗粒材料是一种复杂的多体相互作用体系, 由大量离散的颗粒和其周围的自由体积组成. 虽然颗粒的自由体积与颗粒材料的力学性能和变形特征的相关性已得到证实, 但是由于表征上的困难, 目前对非球形颗粒体系的局部自由体积的认识还不够充分. 本文采用连续离散耦合分析方法进行了不同主轴长度的椭球颗粒试样的三轴剪切数值模拟, 基于Set Voronoi算法对剪切过程中的颗粒试样进行了Voronoi元胞分割, 分析了颗粒试验在剪切过程中自由体积的统计分布特性和演化规律, 研究了颗粒形态对自由体积的影响. 剪切过程中Voronoi元胞的各向异性逐渐增强, 且各项异性增强程度随颗粒非球度的增加而增大, 表明非球颗粒在剪切过程中经历更加强烈的重排列. 具有不同非球度的椭球颗粒体系的局部孔隙比均服从k?Γ分布, 且这个分布仅与颗粒体系的全局孔隙比相关, 不受颗粒形态和剪切状态的影响. 局部孔隙比的波动呈现非对称拉普拉斯分布, 非对称参数刻画了局部自由体积收缩和膨胀的博弈, 其与全局孔隙比呈线性关系.