颗粒材料剪切流动状态转变的环剪试验研究

颗粒材料的剪切流动行为广泛地存在于滑坡、泥石流等自然灾害以及矿物原料传输、泵送等工业过程中.颗粒材料在不同体积分数、剪切速率和应力约束下会表现出不同的流动状态并发生相互转化.对颗粒材料在剪切流动过程中力学特性的研究有助于加深理解其发生不同流动状态的内在机理,为解决相应的颗粒材料问题提供理论依据.为此,本文研制了颗粒材料剪切流动的中型环剪仪,并对颗粒材料在不同法向约束应力和剪切速率下的剪切应力和体积膨胀率进行了测试.结果表明,剪切应力和体积膨胀率均随剪切速率的增大而增大,但增长速率在临界剪切速率处发生转变,使其随剪切速率的平方呈分段式线性增长.通过对颗粒材料在不同剪切速率和惯性数下有效摩擦系数变化趋势的分析,讨论了颗粒材料由慢速流向快速流转化的基本规律,以及在临界剪切速率处发生流动状态转化的内在条件.此外,通过对不同法向应力下临界剪切速率以及快速流动下运动规律的测试,发现临界剪切速率随法向应力的增加而减小,即法向应力可促进颗粒材料由慢速流向快速流的转化,但在快速流动状态下的有效摩擦系数对法向应力不敏感.以上对颗粒材料在不同剪切速率、法向应力下流动状态的环剪试验研究有助于揭示其发生不同流动状态转化的内在机理.      

考虑等效曲率的超二次曲面单元非线性接触模型

基于连续函数包络的超二次曲面单元可有效地描述自然界和工业生产中的非球体颗粒形态, 并通过非线性迭代方法精确计算单元间的接触力. 对于具有复杂几何形态的超二次曲面单元, 线性接触模型不能准确地计算不同接触模式下的作用力. 考虑超二次曲面单元相互作用时不同颗粒形状及表面曲率的影响, 本文发展了相应的非线性黏弹性接触模型. 该模型将不同接触模式下的法向刚度和黏滞力统一表述为单元间局部接触点处等效曲率半径的函数; 切向接触作用则借鉴基于Mohr-Coulomb摩擦定律的球体单元非线性接触模型的计算方法. 为检验超二次曲面单元接触模型的可靠性, 对球形颗粒间的法向碰撞、椭球体颗粒间的斜冲击过程、圆柱体的静态堆积和椭球体的动态卸料过程进行离散元模拟, 并与有限元数值结果及试验结果进行对比验证. 计算表明, 考虑接触点处等效曲率半径的超二次曲面非线性接触模型可准确地计算单元间的接触碰撞作用, 并合理地反映非球形颗粒体系的运动规律. 在此基础上进一步分析了不同长宽比和表面尖锐度对卸料过程中颗粒流动特性的影响, 为非球形颗粒材料的流动特性分析提供了一种有效的离散元方法.      

考虑等效曲率的超二次曲面单元非线性接触模型

基于连续函数包络的超二次曲面单元可有效地描述自然界和工业生产中的非球体颗粒形态,并通过非线性迭代方法精确计算单元间的接触力.对于具有复杂几何形态的超二次曲面单元,线性接触模型不能准确地计算不同接触模式下的作用力.考虑超二次曲面单元相互作用时不同颗粒形状及表面曲率的影响,本文发展了相应的非线性黏弹性接触模型.该模型将不同接触模式下的法向刚度和黏滞力统一表述为单元间局部接触点处等效曲率半径的函数;切向接触作用则借鉴基于Mohr-Coulomb摩擦定律的球体单元非线性接触模型的计算方法.为检验超二次曲面单元接触模型的可靠性,对球形颗粒间的法向碰撞、椭球体颗粒间的斜冲击过程、圆柱体的静态堆积和椭球体的动态卸料过程进行离散元模拟,并与有限元数值结果及试验结果进行对比验证.计算表明,考虑接触点处等效曲率半径的超二次曲面非线性接触模型可准确地计算单元间的接触碰撞作用,并合理地反映非球形颗粒体系的运动规律.在此基础上进一步分析了不同长宽比和表面尖锐度对卸料过程中颗粒流动特性的影响,为非球形颗粒材料的流动特性分析提供了一种有效的离散元方法.     

碎石料直剪实验的组合颗粒单元数值模拟

通过构造三维组合颗粒单元来描述颗粒间的互锁效应,对非规则颗粒材料的力学行为进行了离散元数值模拟,并通过碎石料的直剪实验进行了验证.该组合颗粒的质量与碎石块具有相同的概率分布特性,其几何形态则由不同数目、镶嵌尺寸、组合方位和粒径的球形颗粒进行随机构造.组合颗粒单元在局部与整体坐标之间的转动、力矩和方位关系通过四元素方法进行确定;颗粒之间的作用力采用具有Mohr-Coulomb摩擦定侓的Hertz-Mindlin 非线性接触模型,并考虑了非线性法向粘滞力的影响.在不同的法向应力下,对碎石料在直剪实验中的剪切应力和剪胀现象进行了离散元模拟,计算结果与实测结果相吻合;此外,在不同的法向应力和接触摩擦系数下,对碎石料的有效摩擦系数进行了计算和讨论.本文工作验证了组合颗粒单元在非规则颗粒材料的离散元模拟中的可行性.     

考虑颗粒转矩的接触网络诱发各向异性分析

颗粒材料的宏观力学行为与接触网络的组构各向异性密切相关, 根据接触点的滑动与否、转动与否和强弱力情况, 可以将颗粒间的接触系统分为不同的子接触网络. 一般而言, 不同的子接触网络在颗粒体系中的传力机制不同, 对宏观力学响应的贡献也有不同. 采用离散单元法(discrete element method, DEM)模拟了不同抗转动系数$\mu_r$下颗粒材料三轴剪切试验, 分析了剪切过程中不同子接触网络的组构张量的演变规律, 并探究了颗粒抗转动效应对子接触网络各向异性指标演变规律的影响. 研究发现: 剪切过程中转动、非转动接触的组构张量变化不是独立的, 受到颗粒间滑动与否的影响; 非滑动、强接触网络是颗粒间的主要传力结构, 非滑动接触网络的接触法向和法向接触力各向异性均随$\mu_r$的增大而增大, 其对宏观应力的贡献程度随$\mu_r$的增大而减小;强接触网络的接触法向各向异性随$\mu_r$的增大而增大, 但法向接触力各向异性随$\mu_r$的增大无明显变化, 强接触网络对宏观应力的贡献程度在不同$\mu_r$情况下均相同.      

不同围压作用下非均匀岩石水压致裂过程的数值模拟

从岩石细观非均匀性的特点出发，提出一个描述非均匀材料渗流和破裂相互作用的数值模型。在这个数值模型中，单元的力学、水力学性质根据统计分布而变化，以体现材料的随机不均质性，材料在开裂破坏过程中流体压力传递通过单元渗流，损伤耦合迭代来实现。算例表明，该模型能较好地模拟出岩石类材料在水力压裂作用下，微结构非均匀分布和不同围压比对破裂模式、失稳压力的影响，非均匀性导致试件的开裂压力、失稳压力明显不同，裂纹扩展路径不规则发展，模拟结果和实验结果较为一致。     

颗粒材料内部滑动变形局部化的离散元模拟

颗粒材料在加载过程中表现出非常复杂的变形性质.在微观尺度上,单个颗粒的运动、单个孔隙胞元内的变形都是非均匀的,但也不是完全随机、没有规律可循的,而是呈现一定结构性的分布,如微带、剪切带等.本文用基于孔隙胞元的离散元方法对颗粒体进行双轴加载数值试验,模拟了以滑动变形表征的变形局部化现象.数值结果发现,对应加载过程中的不同...     

一种用于材料高应变率剪切性能测试的新型加载技术

高应变率下的冲击剪切实验技术是材料动态力学行为及其微观机理研究的重要基础.采用分离式霍普金森压杆(split Hopkinson pressure bar)装置一般可以获得材料在104s-1以内应变率的动态力学性能.在超过104s-1的应变率下对材料进行冲击剪切测试时,通常需要采用高速压剪飞片技术或由气炮发射子弹对试样进行直接加载.本文提出一种可用于传统霍普金森压杆技术的新型双剪切试样,可以在103~105s-1剪应变率范围实现对材料剪切性能的精确测量;同时,可以对材料的变形及失效过程进行直接观测.试样与压杆之间避免了复杂的界面或连接装置,通过转接头可以保证试样与压杆直接接触,提高测试精度,同时可以防止因试样的横向位移而导致的非均匀变形.获得了紫铜在1400~75000s-1应变率下的剪应力-剪应变曲线,并采用计算软件"ABAQUS/Explicit"对双剪切试样的动态加载过程进行了数值模拟和结果验证.分析表明,剪切区的主要区域内剪切成分占主导地位,其应力应变场沿厚度及宽度方向基本呈均匀分布.实验得到的剪应力-剪应变曲线与模拟结果吻合较好,说明所提出的基于分离式霍普金森压杆系统的双剪切试样可以为材料的高应变率力学性能测试提供一种方便有效的加载技术.      

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.      

冲击载荷作用下颗粒材料动态力学响应的近场动力学模拟

颗粒材料在冲击载荷作用下的动态力学行为是学术界关注的热点问题. 新近问世的近场动力学(peridynamics)理论将材料视为由大量有限体积和有限质量的物质点组成,基于非连续性和非局部作用假定建模,建立空间积分形式的运动方程,自然适应于颗粒材料动态力学行为的描述与分析. 发展了描述颗粒间接触作用的物质点尺度的排斥力模型,考虑近场动力学方法中非局部长程力特征,改进了近场动力学中的初始微观弹脆性(prototype microelastic brittle, PMB) 模型的本构力函数,并消除了原PMB 模型中存在的“边界效应” 问题. 计算分析了冲击载荷作用下碳化钨陶瓷颗粒体系的动态力学响应,得到了不同冲击速度下颗粒体系的冲击波速,PD计算结果与试验结果高度一致;通过颗粒物质点尺度作用描述单颗粒尺度的接触作用,很好地再现了颗粒的转动与平动、颗粒挤压变形以及颗粒破碎等现象;刚性冲击板附近同时存在严重的颗粒破碎与轻微的颗粒损伤,远离冲击板的部分颗粒出现破损,且颗粒破碎主要是由颗粒间挤压、碰撞以及相对滑动剪切作用造成的. 研究结果表明,所发展的计算模型和分析方法能很好地反映颗粒材料动态力学行为,具有广泛的应用价值.      

Force and flow characteristics of an intruder immersed in 3D dense granular matter

The motion of a projectile impact onto a granular target results in both the resistance force exerted on the projectile and rheology of granular media. A horizontal arrangement of cylinder quasistatically and dynamically intruding into granular media under different velocities and angles is simulated using discrete element method. Three distinguished drag force regimes are exhibited, including hydrostatic-like force independent of velocity, viscous force related to velocity, and inertial drag force proportional to the square of velocity. Meanwhile, the influence of penetration angles on drag force is examined for these three regimes, and a force model, which is related to penetration depth and angle, is proposed for quasi-static penetration. Then, flow characteristics of the granular media, such as velocity field, pressure field, packing fraction etc., are traced, and a rheology model of packing fraction and inertial number is established.     

颗粒介质固-流态转变的理论分析及实验研究

颗粒介质由大量离散的颗粒聚集而成,因而与传统固体和流体不同,运动过程中的颗粒介质中可能同时存在多种流态及其相互间复杂的转换过程. 颗粒介质弹性失稳机理、不可恢复应变量化是研究颗粒介质固态和流态及固-流态转变的关键. 在前期建立的双颗粒温度热力学(two-granular-temperature, TGT) 理论基础上,确定了颗粒介质的弹性稳定性条件,建立了不可恢复应变流动法则,搭建了描述颗粒固态-液态及其相互转化的简单模型. 颗粒堆积体坍塌过程是典型的颗粒介质固态和流态及其转变过程,因此本文首先开展了25 167 个陶颗粒堆积体坍塌过程的实验研究,并使用基于TGT 理论的物质点方法和离散元方法对物理实验进行了模拟. 结果表明,模型数值结果与物理实验在颗粒堆坍塌过程中的形态、速度分布等细节上吻合很好,同时也发现了现阶段所使用的物质点方法和TGT 理论的不足. 初步说明TGT 理论可以实现颗粒介质固态和流态,以及状态转变的描述.      

On mechanics of saturated granular materials

A continuum theory of saturated granular materials is formulated. The basic balance laws for the solid phase as well as for the fluid phase are presented. The constitutive equations are derived and the basic equations of motion of the solid and fluid continua are obtained. Several cases of interest, such as incompressible granules saturated with liquids are discussed. It is shown that the theory contains, as its special cases, the Mohr-Coulomb criterion for a granular material as well as Darcy's law of flow through porous media.     

一种改进的颗粒移动床μ(I)拟流体模型及应用

颗粒移动床在工业领域应用广泛, 发展实用可靠的颗粒移动床模型具有理论和应用价值. 本文基于颗粒流μ(I)模型, 补充局部颗粒体积分数与颗粒局部压力和局部颗粒流密度的关系式, 将移动床内密集颗粒处理成可压缩拟流体, 建立了颗粒流单相可压缩流μ(I)模型, 并建立了颗粒流?壁面摩擦条件, 在计算中对颗粒流拟黏度和拟压力项进行正则化处理. 采用上述模型与方法对3种典型散料在移动床缩口料仓内的流动进行模拟, 与实验对比, 得到了玻璃珠、刚玉球和粗沙的μ(I)模型参数, 分析了3种不同散料在料仓内的颗粒速度、体积分数等分布特性, 模拟结果较好地揭示了料仓内不同物料的整体流和漏斗流特性; 进而以玻璃珠为例, 对移动床颗粒单管绕流流动进行了模拟, 所得结果合理揭示了管流附近的流动特性. 计算结果表明, 对于本文的计算工况, 颗粒体积分数变化最大范围为0.510 ~ 0.461, 绝大部分区域流动惯性数小于0.1, 改进的单相μ(I)模型能合理预测出密集颗粒流移动床内的流动特性, 方法可行且较多相流算法能明显减小计算量.      

Fabric and connectivity as field descriptors for deformations in granular media

Granular materials involve microphysics across the various scales giving rise to distinct behaviours of geomaterials, such as steady states, plastic limit states, non-associativity of plastic and yield flow, as well as instability of homogeneous deformations through strain localization. Incorporating such micro-scale characteristics is one of the biggest challenges in the constitutive modelling of granular materials, especially when micro-variables may be interdependent. With this motivation, we use two micro-variables such as coordination number and fabric anisotropy computed from tessellation of the granular material to describe its state at the macroscopic level. In order to capture functional dependencies between micro-variables, the correlation between coordination number and fabric anisotropy limits is herein formulated at the particle level rather than on an average sense. This is the essence of the proposed work which investigates the evolutions of coordination number distribution (connectivity) and anisotropy (contact normal) distribution curves with deformation history and their inter-dependencies through discrete element modelling in two dimensions. These results enter as probability distribution functions into homogenization expressions during upscaling to a continuum constitutive model using tessellation as an abstract representation of the granular system. The end product is a micro-mechanically inspired continuum model with both coordination number and fabric anisotropy as underlying micro-variables incorporated into a plasticity flow rule. The derived plastic potential bears striking resemblance to cam–clay or stress–dilatancy-type yield surfaces used in soil mechanics.     

On the rheology of dilative granular media: Bridging solid- and fluid-like behavior

A new rate-dependent plasticity model for dilative granular media is presented, aiming to bridge the seemingly disparate solid- and fluid-like behavioral regimes. Up to date, solid-like behavior is typically tackled with rate-independent plasticity models emanating from Mohr–Coulomb and Critical State plasticity theory. On the other hand, the fluid-like behavior of granular media is typically treated using constitutive theories amenable to viscous flow, e.g., Bingham fluid. In our proposed model, the material strength is composed of a dilation part and a rate-dependent residual strength. The dilatancy strength plays a key role during solid-like behavior but vanishes in the fluid-like regime. The residual strength, which in a classical plasticity model is considered constant and rate-independent, is postulated to evolve with strain rate. The main appeal of the model is its simplicity and its ability to reconcile the classic plasticity and rheology camps. The applicability and capability of the model are demonstrated by numerical simulation of granular flow problems, as well as a classical shear banding problem, where the performance of the continuum model is compared to discrete particle simulations and physical experiment. These results shed much-needed light onto the mechanics and physics of granular media at various shear rates.     

Simulated configurational temperature of particles and a model of constitutive relations of rapid-intermediate-dense granular flow based on generalized granular temperature

In gas–solid flat-base spout bed with a jet, the flow of particles must go through an intermediate regime where both kinetic/collisional and frictional contributions play a role. In this paper, the statistical framework is proposed to define the generalized granular temperature which sums up the configurational temperature and translational granular temperature. The configurational temperature, translational and rotational granular temperatures of particles are simulated by means of CFD-DEM (discrete element method) in a 3D flat-base spout bed with a jet. The configurational temperatures of particles are calculated from instantaneous overlaps of particles. The translational and rotational granular temperatures of particles are calculated from instantaneous translational and angular velocities of particles. Roughly, the simulated translational and rotational granular temperatures increase, reach maximum, and then decrease with the increase of solids volume fractions. However, the configurational temperature increases with the increase of solids volume fractions. At high solid volume fraction, the predicted configurational temperatures are larger than the translational and rotational granular temperatures, indicating that the rate of energy dissipation do contributes by contact deformation of elastic particles. The generalized granular temperature is proposed to show the relation between the variance of the fluctuation velocity of deformation and the variance of the translational fluctuation velocity of particles. The constitutive relations of particle pressure, viscosity, granular conductivity of fluctuating energy and energy dissipation in rapid-intermediate-dense granular flows are correlated to the generalized granular temperature. The variations of particle pressure, shear viscosity, energy dissipation and granular conductivity are analyzed on the basis of generalized granular temperature in a flat-base spout bed with a jet. The axial velocities of particles predicted by a gas–solid two-fluid model of rapid-intermediate-dense granular flows agree with experimental results in a spout bed.     

Discrete simulation and micromechanical analysis of two-dimensional saturated granular media

In this study, a novel approach to incorporate the pore water pressure in the discrete element method (DEM) to comprehensively model saturated granular media was developed. A numerical model was constructed based on the DEM by implanting additional routines in the basic DEM code; pore water pressure calculations were used with a two-dimensional (2D) model to simulate the undrained behavior of saturated granular media. This model coupled the interaction of solid particles and the pore fluid in saturated granular media. Finally, several 2D undrained shear tests were simulated. The test results showed that the model could predict the response of the saturated granular soil to shear loading. The effect of initial compaction was investigated. Biaxial tests on dense and loose specimens were conducted, and the effect of the initial density on the change in shear strength and the volume change of the system was investigated. The overall behavior of loose and dense specimens was phenomenologically similar to the real granular material. Constant volume tests were simulated, and the results were compared to those from the coupled model. Induced anisotropy was micromechanically investigated by studying the contact force orientation. The change in anisotropy depended on the modeling scheme. However, the overall responses of the media obtained using the coupled and constant volume methods were similar.