基于颗粒物质流体动力学的三轴力学分析

构建了颗粒体系热力学特征函数, 确定了宏观尺度不可逆过程的迁移系数, 将颗粒物质流体动力学理论应用于密砂的三轴加载力学性质分析, 得到了应力-应变关系和体积应变-应变关系, 还得到了颗粒温度演化过程.      

颗粒材料三维应力路径下的接触组构特性

颗粒材料的宏观应力变形特征与其微观接触力、组构等紧密相关.一般而言,强接触系统属于颗粒内部体系的传力结构,其对应的组构张量是影响宏观应力性质的重要因素.细观数值方法(如离散单元法)能够反映物理试验的基本规律,并且可以方便地提取宏微观数据来研究颗粒体系的应力变形机制.采用离散单元法(discrete element method,DEM)进行一系列等$p$等$b$应力路径下颗粒材料的真三轴试验,在此基础上研究了三维应力路径下颗粒材料的宏微观力学参数的演化过程、三维组构张量与应力张量多重联系以及强接触体系反映的宏观应力特征.研究表明:颗粒体系偏应力峰值状态和临界状态均存在与加载路径无关的宏微观特征;三维应力路径下组构张量与应力张量存在非共轴性,但其联合不变量演化过程表现出加载路径无关的特征;与弱接触系统的组构张量相比,强接触系统的组构张量更能反映宏观应力张量的特征;强弱接触体系的组构张量对颗粒体系宏观响应的贡献不同,其分界点存在一定取值范围,但采用平均接触力较为简单合理.      

密集颗粒物质的介观结构

密集颗粒物质由大量颗粒组成的多体相互作用体系,在一定条件下,颗粒互相连接,形成相对稳定的介观尺度结构,其几何和动力学性质较大程度上决定了颗粒体系的宏观物理和力学性质,因此开展颗粒的介观结构研究具有重要的理论价值,是科学的前沿之一.自然界的堆石坝、堰塞体和碎屑流,以及工程中的高温气冷堆堆芯颗粒流和先进核裂变能系统(ADS嬗变)的颗粒散裂靶等都是典型的颗粒体系,研究颗粒体系宏观力学性质是灾害预测和调控技术的关键.本文首先介绍颗粒接触力理论和简化模型的研究进展,接着介绍介观尺度结构分析方法与测量技术,颗粒体系Jamming转变、软点和颗粒微位移测量技术等,最后列举了几个关键的科学问题.颗粒介质中很多基本力学问题的解决需要借鉴物理和数学等学科的最新成果,建立新的概念和范式,从新的角度、思路、理念去认识颗粒介质的基本问题.同时,颗粒介质的基础研究还要紧密结合工程应用领域的大量相关的核心技术,与工程领域专家共同合作,使得颗粒介质的研究有的放矢,更具生命力.     

颗粒材料破碎演化路径细观热力学机制

颗粒材料在高应力环境下会发生颗粒破碎现象,颗粒破碎不仅影响颗粒材料的力学特性,同时与大量工程问题密切相关.目前的相关研究主要集中在唯象地描述颗粒破碎的演化以及破碎对力学特性的影响层面,对颗粒破碎演化路径的物理机制研究较少.本文基于热力学框架,采用细观力学中细观-宏观的均匀化方法推导了颗粒体系弹性能和破碎能量耗散,并在最大能量耗散的假设下,在热力学框架内,建立了理想化的无摩擦球体颗粒等向压缩过程的弹性-破碎模型,阐述了颗粒材料破碎演化路径细观热力学机制.由于模型的推导不依赖任何唯象的经验公式,因此模型中包含的参数均有明确的物理意义.模型预测与前人试验结果对比表明,材料的初始级配对弹性压缩模量和破碎应力的影响并不相同:不同分形维数级配对应的弹性体变模量存在极大值,而破碎应力却随着分形维数的增大单调递增;颗粒破碎的演化符合最大能量耗散原理,且颗粒材料的压缩曲线可以分为弹性-破碎-拟弹性3个机制不同的阶段.      

The mesoscopic structures of dense granular materials

密集颗粒物质由大量颗粒组成的多体相互作用体系,在一定条件下,颗粒互相连接,形成相对稳定的介观尺度结构,其几何和动力学性质较大程度上决定了颗粒体系的宏观物理和力学性质,因此开展颗粒的介观结构研究具有重要的理论价值,是科学的前沿之一.自然界的堆石坝、堰塞体和碎屑流,以及工程中的高温气冷堆堆芯颗粒流和先进核裂变能系统（ADS嬗变）的颗粒散裂靶等都是典型的颗粒体系,研究颗粒体系宏观力学性质是灾害预测和调控技术的关键.本文首先介绍颗粒接触力理论和简化模型的研究进展,接着介绍介观尺度结构分析方法与测量技术,颗粒体系Jamming转变、软点和颗粒微位移测量技术等,最后列举了几个关键的科学问题.颗粒介质中很多基本力学问题的解决需要借鉴物理和数学等学科的最新成果,建立新的概念和范式,从新的角度、思路、理念去认识颗粒介质的基本问题.同时,颗粒介质的基础研究还要紧密结合工程应用领域的大量相关的核心技术,与工程领域专家共同合作,使得颗粒介质的研究有的放矢,更具生命力.     

MICROMECHANICS ANALYSIS FOR UNSATURATED GRANULAR SOILS

This paper aims at establishing an anisotropic stress expression for unsaturated pendular-state granular soils. Using the second-order fabric tensor, we formulate a micromechanics scheme of soils with statistically averaging method, and reveal that the macroscopic average stress of unsaturated granular soils in pendular-state is not isotropic. Not only is the stress from contact forces anisotropic due to the fabric, but also the capillary stress is directional dependent, which is different from the common point that the capillary stress is isotropic. The capillary stress of unsaturated pendular-state granular soils is determined by the orientation distribution of contact normals, so it is closely related to the initial and induced anisotropy of soils. Finally, DEM numerical simulations of triaxial compression tests of pendular-state soils at different degrees of saturation are used to verify the existence of above anisotropy of stresses.     

基于深度学习和细观力学的颗粒材料本构关系研究

颗粒材料的本构关系对岩土工程等众多领域至关重要. 不同于传统的唯象本构理论, 本文基于机器学习模型探索了一种细观力学理论指导下的数据驱动型颗粒材料本构关系预测方法. 根据Vogit均质化假设, 建立了小应变条件下颗粒材料应力?应变解析关系, 此关系唯一地确定了一组与颗粒材料本构行为相关的细观组构变量. 这些变量与反应颗粒材料宏观性质的主应力和主应变信息通过一系列离散元三轴压缩数值试验获得. 考虑到细观组构变量为内变量, 不能直接作为本构模型的输入. 本文基于有向图方法将颗粒材料微观结构信息隐式地包含在应力?应变的预测当中, 并采用门控循环单元(GRU)循环神经网络作为基础深度学习模型描述有向图中结点之间的映射关系. 通过将有向图从目标节点沿源节点展开, 整个应力?应变预测模型可由两个神经网络分别训练并组装而成. 将训练后的深度学习模型在全新的数据集上进行测试, 结果表明该训练策略能有效捕捉到颗粒材料在常规三轴任意加卸载, 等中主应力系数b的真三轴加载, 和等平均有效应力p的真三轴加卸载等复杂多轴加载工况下的应力?应变响应关系, 模型具有良好的内插和外推预测能力. 考虑到深度学习模型捕捉颗粒材料力学响应的能力及其开放式学习的特点, 充分结合数据驱动方法和理论本构模型可能是颗粒材料本构研究的一个重要方向.      

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.      

Local and global universal relations for first-gradient materials

Local universal relations are relations between stress and kinematic variables which hold for all materials of a particular class irrespective of specific material parameters. A method is developed for obtaining local universal relations for most first gradient materials. The currently known local universal relations for isotropic elastic materials have been extended to all isotropic first gradient materials under constant step deformation histories and have also been extended to all isotropic first gradient materials undergoing arbitrary time dependent triaxial extensions along fixed material directions. It has been shown that universal relations exist for some anisotropic materials. A set of pseudo-universal relations has been obtained for anisotropic elastic materials which can be used to decouple the material functions. These pseudo-universal relations contain some, but not all, material functions. A global universal relation has been developed for the extension and torsion of an isotropic cylindrical shaft which holds for all incompressible first gradient materials.     

A microstructural elastoplastic model for unsaturated granular materials

The homogenization technique is used to obtain an elastoplastic stress–strain relationship for dry, saturated and unsaturated granular materials. Deformation of a representative volume of material is generated by mobilizing particle contacts in all orientations. In this way, the stress–strain relationship can be derived as an average of the mobilization behavior of these local contact planes. The local behavior is assumed to follow a Hertz–Mindlin’s elastic law and a Mohr–Coulomb’s plastic law. For the non-saturated state, capillary forces at the grain contacts are added to the contact forces created by an external load. They are calculated as a function of the degree of saturation, depending on the grain size distribution and on the void ratio of the granular assembly. Numerical simulations show that the model is capable of reproducing the major trends of a partially saturated granular assembly under various stress and water content conditions. The model predictions are compared to experimental results on saturated and unsaturated samples of silty sands under undrained triaxial loading condition. This comparison shows that the model is able to account for the influence of capillary forces on the stress–strain response of the granular materials and therefore, to reproduce the overall mechanical behavior of unsaturated granular materials.     

非均匀颗粒材料的类固-液相变行为及本构方程

以非均匀颗粒介质为研究对象，采用三维离散元方法对其在不同密集度和剪切速率下的动 力过程进行了数值模拟，分析了其在由瞬时接触的快速流动向持续接触的准静态流动的转变 过程及其行为特点. 通过对不同材料性质下相变过渡区内颗粒材料的宏观应力、接触时间数、 配位数、团聚颗粒数量、有效摩擦系数等参量的计算，更加全面地描述了非均匀颗粒材料在 类固-液相变过程中的基本特征. 基于以上数值计算结果，建立了一个适用于颗粒材料 类固态、类液态以及其相变过程的本构方程，并通过剪切室实验结果验证了它的合理性.     

散料在料仓内流动特性的实验研究

用振动筛测量多种散料的筛分尺寸，测量散料的容积密度、安息角，用应变直剪仪进行散料内摩擦角、壁面摩擦角的测量，分析了散料颗料的形状、尺寸对散料的安息角、内摩擦角、壁面摩擦角的影响。用示踪法进行了圆筒内散料重力场中颗粒流线和等时线的试验，以及出口直径与流量的关系、筒仓内散料高度对流量的影响的试验，流量与筒仓内散料高度关系的试验。分析了散料各物性参数对散料流动性的影响，为散料存贮和运输设备的结构设计提供实验依据。     

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.     

Stress and fabric in granular material

It has been well recognized that, due to anisotropic packing structure of granular material, the true stress in a specimen is different from the applied stress. However, very few research efforts have been focused on quantifying the relationship between the true stress and applied stress. In this paper, we derive an explicit relationship among applied stress tensor, material-fabric tensor, and force-fabric tensor; and we propose a relationship between the true stress tensor and the applied stress tensor. The validity of this derived relationship is examined by using the discrete element simulation results for granular material under biaxial and triaxial loading conditions.     

颗粒柱塌落中的尺寸效应和瞬态流变性研究

颗粒材料是自然界和工程中广泛存在和普遍应用的材料,泥石流、滑坡和混凝土等均可视为颗粒材料。颗粒材料研究有助于更好地控制相关自然灾害或利用其某些特性。对颗粒材料柱体的塌落动力学研究不仅可以方便理解颗粒材料在瞬态流动时的流变性,还可以引申到泥石流等岩土材料的运动与堆积形态。本文利用扩展多面体离散单元法对颗粒堆积柱的塌落进行了细致的研究,探索高宽比、摩擦系数以及颗粒柱相对尺寸等对柱体塌落的影响。对颗粒集合进行分网并分析每个网格内的应力与应变率之间的关系,讨论其瞬态本构关系。相关研究对于深入理解颗粒材料重力流的动力学性质以及颗粒集合体的堆积形态具有重要意义。     

STRUCTURE AND THERMODYNAMICS OF GRANULAR MATERIALS

颗粒介质由大量离散的粗颗粒聚集而成,如自然界中的粗砂和碎屑堆积体等. 在工程实践中,人们依据经验和实验数据建立了许多模型,虽然可以满意地描述某些力学现象,但是对颗粒介质力学性质全貌的认识以及颗粒介质物理本质的理解仍远远不够. 颗粒介质长程无序、短程有序的结构和复杂的能量转化过程,注定了其独特的力学性质. 该文综述了颗粒介质结构探测和表征技术、热力学理论和固态-流态转变方面的新进展,特别介绍了清华大学近5 年来开展的颗粒介质结构模型化方法和双颗粒温度热力学理论. 最后,提出了开展结构分析-热力学理论的联合研究思路,以期更加深入认识颗粒介质的力学特性,探究颗粒介质的热力学根源,改善现有唯象研究现状.     

考虑破碎影响的颗粒材料亚塑性模型及应变局部化模拟

在基于2ndP-K应力率的亚塑性模型基础上,通过引入一个能够考虑颗粒破碎影响的孔隙比-平均压力临界状态方程,形成了一个能够模拟颗粒破碎影响的颗粒材料亚塑性模型,数值算例考查了颗粒破碎对应变局部化模式及位移-承载曲线的影响,结果表明,所建议模型具有模拟破碎对颗粒材料应变局部影响的良好性能。     

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.     

颗粒流动力学及其离散模型评述

颗粒流是由众多颗粒组成的具有内在相互作用的非经典介质流动. 自然界常见颗粒流都是密集流, 颗粒间接触形成力链, 诸多力链相互交接构成支撑整个颗粒流重量和外载荷的网络, 其局部构型及强度在外载荷下演化, 是颗粒流摩擦特性和接触应力的来源.本文介绍球形颗粒间无粘连作用时的Hertz法向接触理论和Mindlin-Deresiewicz切向接触理论. Campbell依据是否生成较为稳定的力链把颗粒流分为弹性流和惯性流两大类, 其中弹性-准静态流和惯性-碰撞流分别对应准静态流和快速流, 作为两种极端流动情况通常处理成连续体, 分别采用摩擦塑性模型和动理论予以描述, 但是表征接触力链的颗粒弹性参数并不出现这两个模型和理论框架中, 如何进一步考虑颗粒弹性参数将非常困难. 目前离散动力学方法逐渐成为复现其复杂颗粒流动现象、提取实验不可能获得的内部流动信息进而综合起来探索颗粒流问题的一种有效工具, 其真实性强于连续介质理论的描述. 软球模型对颗粒间接触力简化处理, 忽略了切向接触力对法向接触力及其加载历史的依赖, 带来了法向和切向刚度系数如何标度等更艰难的物理问题, 但由于计算强度小而广泛应用于工程问题中. 硬球模型不考虑颗粒接触变形, 因而不能描述颗粒流内在接触应变等物理机理, 仅适用于快速颗粒流, 这不仅仅是由于两体碰撞的限制. 因此基于颗粒接触力学的离散颗粒动力学模型是崭新的模型,适用于准静态流到快速流整个颗粒流态的模拟, 可以细致考虑接触形变及接触力的细节,建立更为合理的颗粒流本构关系, 进而有力的促进颗粒流这一非经典介质流动的研究.      

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.