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.     

颗粒破碎的微观力学模拟

基于颗粒尺度建立了考虑颗粒破碎过程中能量耗散的微观力学模型。为了模拟颗粒体的破碎过程和侧向应力的影响,把胶结在一起的三个等粒径的颗粒体当作颗粒破碎体。基于颗粒破碎准则和热力学原理,考虑了颗粒破碎过程中颗粒接触点之间的塑性滑移和颗粒转动以及侧向应力作用,通过颗粒破碎体内部颗粒之间的接触破碎来模拟颗粒体的破碎。计算结果表明:本文所提出的微观力学模型可以模拟胶结在一起的大颗粒的破碎过程;颗粒之间的微观力学参数对颗粒破碎过程中的力、塑性滑移、颗粒的转动角有不同程度的影响;力-位移关系曲线在破碎前是线性的,而颗粒破碎时竖向力迅速降低到较小值,并伴有颗粒的转动。     

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.      

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.     

基于三维细观力学模型的开孔泡沫弹性性能预测

泡沫材料的宏观力学性能主要取决于基体材料的力学特性及其微细观结构特征,基于细观力学模型的分析方法是泡沫材料力学性能研究的重要途径。文中基于Matlab语言和Abaqus软件构建了描述中等孔隙率开孔弹性泡沫材料微结构特征的三维随机分布球形泡孔模型,并采用有限元方法对弹性泡沫压缩变形进行了模拟,并计算给出了不同孔隙率弹性泡沫材料弹性模量、剪切模量、体积模量以及泊松比的分布,建立了相应的唯象表达式。与理论模型及测试结果的比较表明,本文基于三维随机泡孔模型模拟结果构建的唯象表达式能够对弹性泡沫材料的弹性力学性能给出很好的预测。     

基于细观方向平均模型的颗粒材料宏观Cosserat连续体本构关系

提出了基于细观微-方向模型（Micro—Directional Model）的宏观Cosserat连续体本构关系。在细观尺度上考虑颗粒旋转自由度及接触力矩,微结构的影响通过接触分布函数体现。给出均质各向同性Cosserat连续体模型弹性常数的细观参数表达式,并建议了二维情况下内尺度参数的细观力学表达式。对颗粒材料宏观行...     

颗粒土的亚塑性-塑性本构模拟

颗粒土在低应力区与高应力区的力学响应有较大的差别.低应力区的材料响应具有很强的密度依赖性,而在高应力区,则有显著的颗粒破碎效应.论文基于颗粒土压缩变形特性,将与颗粒破碎引起的土体压缩性的显著增大当作材料的塑性屈服,采用一个塑性势来描述.以亚塑性模型作为基础模型,描述低应力区的力学响应.两者结合建立了一个亚塑性-塑性本构模型框架,用于描述颗粒土在较宽广应力范围内的应力应变关系.     

基于微形态模型的颗粒材料中波的频散现象研究

基于颗粒材料冲击与波动响应特性的调控波传播行为的超材料设计受到广泛关注,设计这类材料需要对颗粒材料的波传播机制及调控机理有深入认识. 波在颗粒材料中传播的频散现象及频率带隙等行为与材料的非均匀性密切相关,通常讨论频散现象是基于弹性理论框架建立微结构连续体或高阶梯度连续体等广义连续体模型来进行. 本研究基于细观力学给出了一个颗粒材料的微形态连续体模型. 在该模型中,考虑了颗粒的平动和转动,且颗粒间的相对运动分解为两部分:即宏观平均运动和细观真实运动. 基于此分解,提出了一个完备的变形模式,得到了对应于不同应变及颗粒间运动的宏细观本构关系. 结合宏观变形能的细观变形能求和表达式,获得了基于细观量表示的宏观本构模量. 应用所建议模型考察了波在弹性颗粒介质的传播行为,给出了不同形式的波的频散曲线,结果显示此模型具有预测频率带隙的能力.      

基于深度强化学习算法的颗粒材料应力?应变关系数据驱动模拟研究

颗粒材料的宏观力学行为受颗粒组分等材料参数, 孔隙率、配位数等状态参数的影响, 同时又具备复杂的加载路径和加载历史相关性, 建立包含多个内变量以及各变量间相互关联的颗粒材料本构模型是一个重要的科学难题. 不同于传统的基于屈服面、流动法则和硬化函数框架下的唯象本构模型, 本文基于颗粒物质力学的研究基础, 以颗粒材料平均孔隙率、细观组构参数和弹性刚度参数作为内变量, 结合深度学习方法建立以有向图表征的数据本构模型. 有向图中以不同的链接网络表示不同的内变量信息流动方向, 各个内变量间的映射关系采用循环神经网络来建立, 将各个神经网络相互组合, 形成包含不同内变量且具有不同预测能力的本构模型. 该本构模型的建立过程等价于在众多可能的内变量链接关系空间中寻找最能描述实际材料宏观应力应变行为的优化问题. 因此, 可将有向图本构模型的建立过程看作“马尔可夫决策过程”, 采用深度强化学习算法构建有向图的内变量链接组合优化过程, 具体采用AlphaGo Zero算法自动寻找最优的颗粒材料数据驱动本构模型建模路径. 研究结果表明, 采用有向图和深度强化学习算法可建立起完全依靠“数据驱动”的颗粒材料应力?应变关系. 此外, 本方法提供了一种将不同理论模型从数据角度统一起来, 且基于人工智能算法发展更优模型的研究思路, 可为相似问题的研究提供借鉴.      

分数维空间中的损伤力学研究初探

结合损伤力学和分形几何理论，给出分数维空间中分形损伤变量定义ω（ｄ，ζ）及其解析表达式．指出欧氏空间损伤变量ω０实际是分数维空间分形损伤变量ω（ｄ，ζ）当维数取Ｅｕｃｌｉｄｅａｎ维数时的一种特例，将欧氏空间损伤变量定义推广到分数维空间，建立起一种兼顾反映损伤细观结构效应和宏观损伤力学分析需要的损伤定义与描述方法．在此基础上，推导了材料损伤演化律和损伤本构关系的分形表达形式．作为例证，文中分析了单调压缩载荷下混凝土损伤及演化行为．实验对比分析表明：分形损伤模型较好地反映了混凝土实际损伤力学行为．     

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.      

Evolution of mesoscopic granular clusters in comminution systems: a structural mechanics model of grain breakage and force chain buckling

A major scientific challenge in establishing a micromechanics theory for complex materials is the characterisation and modelling of emergent mesoscopic phenomena. This study demonstrates the key elements of a structural mechanics approach to the modelling of mesoscopic dissipative phenomena in comminution systems where grain breakage and force chain buckling coexist. Given the many degrees of freedom in these systems, there are multitude of possible configurations and configurational transitions accessible even for a small particle cluster (e.g. a particle and its immediate neighbours). Here, we develop a model of the evolution of a 6-particle cluster undergoing breakage and force chain buckling, in sequence. The analysis lays bare the intricate connections between the contact topology, the relative kinematics arising from the interactions of particles at the bonded versus non-bonded contacts, and the collective dynamics of these interactions as the cluster is monotonically compressed under confinement. The stress-displacement response profiles at the cluster scale exhibit qualitatively similar properties to those seen in macroscopic assemblies under confined compression. A parametric analysis is undertaken to explore the effects of grain-scale resistances to breakage and buckling with respect to the overall force-displacement behaviour of the granular cluster. The study casts light on open problems for future research into the micromechanics of emergent cluster behaviour germane to comminution systems.     

Breakage mechanics—Part II: Modelling granular materials

The compression of granular materials has been traditionally modelled with the limitations of classical elasto-plasticity. The energy was implicitly assumed to dissipate from the frictional interaction of particles. However, the fact that brittle granular materials crush suggests that energy must also be dissipated from the fracturing of the grains, as in fracture mechanics. The concept of breakage as a thermomechanical internal variable was introduced in Part I [Einav, I., 2006. Breakage mechanics—Part I: theory. J. Mech. Phys. Solids 00,000-000] to describe the fracturing mechanisms. The theory allows to treat ideal theoretical materials that undergo dissipation purely from breakage with no other mechanism allowed for the energy consumption. However, as accounted for in elasto-plasticity, dissipation must also occur from the frictional rearrangement of grains. The combination of the two dissipative mechanisms of breakage and plasticity must therefore be investigated, as we do in this paper. Those two mechanisms are generally coupled, in the sense that one inevitably appears when the other develops. Plastic dissipation emerges as a by-product of breakage dissipation because after grains crush, local rearrangement must occur. This scenario may be termed an ‘active breakage mechanism’, and typifies compression deformations. In shear the plastic dissipation is dominant but breakage appears inevitably from grains abrasion. This scenario may be called a ‘passive breakage mechanism’. Based on the coupling assumption, models are developed for granular materials. In particular, we show that in compression isotropic hardening of sands may appear without involving plastic strains, i.e., independent of frictional dissipation. This interpretation of hardening is different from the one used in classical critical state soil mechanics. However, frictional dissipation leads to plastic straining that are necessary for the models to be predictive in unloading.     

Relationship between single and bulk mechanical properties for zeolite ZSM5 spray-dried particles

In this work typical mechanical properties for a catalyst support material, ZSM5 （a spray-dried granular zeolite）, have been measured in order to relate the bulk behaviour of the powder material to the single particle mechanical properties. Particle shape and size distribution of the powders, determined by laser diffraction and scanning electron microscopy （SEM）, confirmed the spherical shape of the spray-dried particles. The excellent flowability of the material was assessed by typical methods such as the Hausner ratio and the Cart index, This was confirmed by bulk measurements of the particle-particle internal friction parameter and flow function using a Schulze shear cell, which also illustrated the low compressibility of the material. Single particle compression was used to characterize single particle mechanical properties such as reduced elastic modulus and strength from Hertz contact mechanics theory. Comparison with surface properties obtained from nanoindentation suggests heterogeneity, the surface being harder than the core. In order to evaluate the relationship between single particle mechanical properties and bulk compression behaviour, uniaxial confined compression was carried out. It was determined that the Adams model was suitable for describing the bulk compression and furthermore that the Adams model parameter, apparent strength of single particles, was in good agreement with the single particle strength determined from single particle compression test.     

Modelling long-term deformation of granular soils incorporating the concept of fractional calculus

Many constitutive models exist to characterise the cyclic behaviour of granular soils but can only simulate deformations for very limited cycles. Fractional derivatives have been regarded as one potential instrument for modelling memory-dependent phenomena. In this paper, the physical connection between the fractional derivative order and the fractal dimension of granular soils is investigated in detail.Then a modified elasto-plastic constitutive model is proposed for evaluating the long-term deformation of granular soils under cyclic loading by incorporating the concept of factional calculus. To describe the flow direction of granular soils under cyclic loading, a cyclic flow potential considering particle breakage is used. Test results of several types of granular soils are used to validate the model performance.     

岩石爆破分形损伤模型研究

在Ｋｕｓ和Ｔｈｏｒｎｅ等人研究基础上，利用分形理论及应用成果提出了一种新的岩石爆破损伤模型。新模型将岩体中各种结构弱面视为初始损伤，并将其分形维数作为岩石性质的主要参量，用损伤能量耗散率及与分形维数的关系表征爆破过程中的岩石损伤演化规律，从而弥补了现有模型未考虑初始损伤影响和将损伤演化归结为体积应变函数的不足。还通过模拟试验等手段验证了新模型的如上观点。     

Statistics of particle interactions in dense granular material under uniaxial compression

Stress evolution in a dense granular material is closely related to interactions of contacting particles. We investigate statistics related to particle interactions and the relationship between the averaged local relative motion and the macroscopic motion. The validity of the Voigt and Reuss assumptions is examined, and extensions to these assumptions are proposed. Effects of history in the dense granular material are investigated. Statistical samples used in this paper are obtained using three-dimensional numerical simulations of dense granular media under uniaxial cyclical compression. The results show that stresses arise mostly from normal forces between particles, and direct contributions from frictional tangential forces between particles are small. Tangential friction, however, significantly increases the particle contact time, and thus reduces the rate of contact breakage. The contact breakage rate is demonstrated to be a stress relaxation rate. Therefore, stress increases significantly with friction between particles as a result of prolonged relaxation time.     

Dilation and breakage dissipation of granular soils subjected to monotonic loading

Dilation and breakage energy dissipation of four different granular soils are investigated by using an energy balance equation. Due to particle breakage, the dilation curve does not necessarily pass through the origin of coordinates. Breakage energy dissipation is found to increase significantly at the initial loading stage and then gradually become sta-bilised. The incremental dissipation ratio between breakage energy and plastic work exhibits almost independence of the confining pressure. Accordingly, a plastic flow rule consid-ering the effect of particle breakage is suggested. The critical state friction angle is found to be a combination of the basic friction between particles and the friction contributed by par-ticle breakage.     

准脆性材料抗压强度能量平衡尺寸效应模型

针对现有尺寸效应模型难以体现准脆性材料完整的抗压强度尺寸效应变化规律及其内在机理, 本文通过分析准脆性材料单轴压缩破坏过程中能量输入、储存、整体和局部能量耗散, 建立体现整体和局部损伤的力学模型及描述上述能量演化过程的双线性名义和真实应力应变曲线, 在此基础上确定了名义应力最大时输入能量、储存弹性能、整体和局部能量耗散的表达式, 最后基于能量平衡原理建立抗压强度尺寸效应模型. 抗压强度能量平衡尺寸效应模型能完整体现名义抗压强度尺寸效应, 即随试样尺寸增大, 名义抗压强度在试样尺寸小于等于局部损伤区尺寸时为真实强度, 然后逐渐减小, 最终当试样尺寸趋于无穷大时趋于弹性极限强度; 抗压强度能量平衡尺寸效应模型也能同时体现高径比和试样直径对名义强度的影响, 其包含的参数具有明确的物理意义, 可以反映真实强度、弹性极限强度、名义损伤模量非线性、局部损伤区大小和方向对准脆性材料名义抗压强度尺寸效应的影响; 通过把抗压强度能量平衡尺寸效应模型和现有尺寸效应模型应用于预测各种材料尺寸效应试验和数值模拟数据, 结果表明: 抗压强度能量平衡尺寸效应模型能很好描述试验和数值模拟尺寸效应的非线性变化规律及内在机理, 和现有尺寸效应模型相比, 其总体平均误差最小, 且小于5%.      

颗粒物质的分形特征与其物理力学性质的关系探讨

从颗粒流的一般本构方程出发,利用室内大型相对密度仪和直接剪切仪,针对粒径分形分布对孔隙率和内摩擦角的影响进行了实验研究。结果表明,在相同实体密度、弹性恢复系数和几何平均中值粒径条件下,随粒径分维数的增大,孔隙率增大,而内摩擦角、颗粒浓度、剪切应力系数与正应力系数均减小。进而分析了粒径分形特性对颗粒流动行为的影响,得出粒径分维数小的颗粒系统剪切应力大,系统的流动性能差,鲁棒性强;反之,分维数大的颗粒系统剪切应力小,系统的流动性能好,敏感性强。对系统组构的分形特征影响系统颗粒物质崩塌流动行为的机制进行了初步探索,为颗粒流系统的研究提供了新思路。