DEM Modeling of Particle Breakage in Silica Sands under One-Dimensional Compression

A Discrete Element Method(DEM) model is developed to study the particle breakage effect on the one-dimensional compression behavior of silica sands. The ‘maximum tensile stress' breakage criterion considering multiple contacts is adopted to simulate the crushing of circular particles in the DEM. The model is compared with published experimental results. Comparison between the compression curves obtained from the numerical and experimental results shows that the proposed method is very effective in studying the compression behavior of silica sands considering particle breakage. The evolution of compression curves at different stress levels is extensively studied using contact force distribution, variation of contact number and particle size distribution curve with loading. It is found that particle breakage has great impact on compression behavior of sand, particularly after the yield stress is reached and particle breakage starts.The crushing probability of particles is found to be macroscopically affected by stress level and particle size distribution curve, and microscopically related to the evolutions of contact force and coordination number. Once the soil becomes well-graded and the average coordination number is greater than 4 in two-dimension, the crushing probability of parent particles can reduce by up to5/6. It is found that the average contact force does not always increase with loading, but increases to a peak value then decreases once the soil becomes more well-graded. It is found through the loading rate sensitivity analysis that the compression behavior of sand samples in the DEM is also affected by the loading rate. Higher yield stresses are obtained at higher loading rates.     

Influence of specimen-reconstituting method on the undrained response of loose granular soil under static loading

This paper describes the results of an experimental study on the undrained shear behaviour of loose sand collected from the location close to the epicenter of the recent Chlef (Algeria) Earthquake (October 10,1980).The study focuses on the effects of the mode of the soil deposition on the liquefaction resistance of the Chlef sand.For this purpose,the results of undrained monotonic triaxial compression tests performed on samples with initial density of 0.29 under initial confining pressures ranged from 50 kPa to 200 kPa are presented.The specimens were prepared by two depositional methods namely dry funnel pluviation and wet deposition.It was found that there was a marked difference in the undrained behaviour of sand in terms of maximal deviatoric stress,peak strength,residual strength and excess pore water pressure,even though the density and stress conditions were identical.The conclusion was that the soil fabric was responsible for this result.The results indicated also that at low confining pressures,the specimens reconstituted by the wet deposition method exhibited complete static liquefaction (zero effective confining pressure and zero stress difference).     

Micromechanics of breakage in sharp-edge particles using combined DEM and FEM

By combining DEM （Discrete Element Method） and FEM （Finite Element Method）, a model is established to simulate the breakage of twodimensional sharp-edge particles, in which the simulated particles are assumed to have no cracks. Particles can, however, crush during different stages of the numerical analysis, if stress-based breakage criteria are fulfilled inside the particles. With this model, it is possible to study the influence of particle breakage on macro- and micro-mechanical behavior of simulated angular materials. Two series of tests, with and without breakable particles, are simulated under different confining pressures based on conditions of biaxial tests. The results, presented in terms of micromechanical behavior for different confining pressures, are compared with macroparameters. The influence of particle breakage on microstructure of sharp-edge materials is discussed and the related confining pressure effects are investigated. Breakage of particles in rockfill materials are shown to reduce the anisotropy coefficients of the samples and therefore their strength and dilation behaviors.     

Effect of sample size on the response of DEM samples with a realistic grading

This paper shows that for DEM simulations of triaxial tests using samples with a grading that is repre- sentative of a real soil, the sample size significantly influences the observed material response. Four DEM samples with identical initial states were produced： three cylindrical samples bounded by rigid wails and one bounded by a cubical periodic cell, When subjected to triaxial loading, the samples with rigid boundaries were more dilative, stiffer and reached a higher peak stress ratio than the sample enclosed by periodic boundaries. For the rigid-wall samples, dilatancy increased and stiffness decreased with increasing sample size, The periodic sample was effectively homogeneous, The void ratio increased and the contact density decreased close to the rigid walls, This heterogeneity reduced with increasing sample size. The positions of the critical state lines （CSLs） of the overall response in e-log p＇ space were sensitive to the sample size, although no difference was observed between their slopes. The critical states of the interior regions of the rigid-wall-bounded samples approached that of the homogeneous periodic sample with increasing sample size. The ultimate strength of the material at the critical state is independent of sample size.     

Effect of particle polydispersity on micromechanical properties and energy dissipation in granular mixtures

A series of numerical tests was conducted to study the micromechanical properties and energy dissipation in polydisperse assemblies of spherical particles subjected to uniaxial compression. In general, distributed particle size assemblies with standard deviations ranging from 0% to 80% of the particle mean diameter were examined. The microscale analyses included the trace of the fabric tensor, magnitude and orien- tation of the contact forces, trace of stress, number of contacts and degree of mobilization of friction in contacts between particles. In polydisperse samples, the average coordination numbers were lower than in monodisperse assemblies, and the mobilization of friction was higher than in monodisperse assemblies due to the non-uniform spatial rearrangement of spheres in the samples and the smaller displacements of the particles. The effect of particle size heterogeneity on both the energy density and energy dissipation in systems was also investigated.     

Micromechanical investigation of granular ratcheting using a discrete model of polygonal particles

We use a two-dimensional model of polygonal particles to investigate granular ratcheting. Ratcheting is a long-term response of granular materials under cyclic loading, where the same amount of permanent deformation is accumulated after each cycle. We report on ratcheting for low frequencies and extremely small loading amplitudes. The evolution of the sub-network of sliding contacts allows us to understand the micromechanics of ratcheting. We show that the contact network evolves almost periodically under cyclic loading as the sub-network of the sliding contacts reaches different stages of anisotropy in each cycle. Sliding contacts lead to a monotonic accumulation of permanent deformation per cycle in each particle. The distribution of these deformations appears to be correlated in form of vortices inside the granular assembly.     

Effects of polydispersity on the micro–macro behavior of granular assemblies under different deformation paths

The micromechanical and macromechanical behavior of idealized granular assemblies, made by linearly elastic, frictionless, polydisperse spheres, are studied in a periodic, triaxial box geometry, using the discrete element method. Emphasis is put on the effect of polydispersity under purely isotropic loading and unloading, deviatoric(volume conserving), and uniaxial compression paths.We show that scaled pressure, coordination number and fraction of rattlers behave in a very similar fashion as functions of volume fraction, irrespective of the deformation path applied. Interestingly, they show a systematic dependence on the deformation mode and polydispersity via the respective jamming volume fraction. This confirms that the concept of a single jamming point has to be rephrased to a range of variable jamming points, dependent on microstructure and history of the sample, making the jamming volume fraction a state-variable.This behavior is confirmed when a simplified constitutive model involving structural anisotropy is calibrated using the purely isotropic and deviatoric simulations. The basic model parameters are found to depend on the polydispersity of the sample through the different jamming volume fractions. The predictive power of the calibrated model is checked by comparison with an independent test, namely uniaxial compression. The important features of the uniaxial experiment are captured and a qualitative prediction for the evolution of stress and fabric is shown involving a "softening" regime in both stress and fabric – stronger for the latter – that was not prescribed into the model a priori.     

FAILURE MODE AND CONSTITUTIVE MODEL OF PLAIN HIGH-STRENGTH HIGH-PERFORMANCE CONCRETE UNDER BIAXIAL COMPRESSION AFTER EXPOSURE TO HIGH TEMPERATURES

An orthotropic constitutive relationship with temperature parameters for plain highstrength high-performance concrete （HSHPC） under biaxial compression is developed. It is based on the experiments performed for characterizing the strength and deformation behavior at two strength levels of HSHPC at 7 different stress ratios including a=σs ： σ3=0.00：-1,-0.20：-1,-0.30 ： -1,-0.40：-1,-0.50：-1,-0.75：-1,-1.00：-1, after the exposure to normal and high temperatures of 20, 200, 300, 400, 500 and 600℃, and using a large static-dynamic true triaxial machine. The biaxial tests were performed on 100 mm×100 mm×100 mm cubic specimens, and friction-reducing pads were used consisting of three layers of plastic membrane with glycerine in-between for the compressive loading plane. Based on the experimental results, failure modes of HSHPC specimens were described. The principal static compressive strengths, strains at the peak stress and stress-strain curves were measured; and the influence of the temperature and stress ratios on them was also analyzed. The experimental results showed that the uniaxial compressive strength of plain HSHPC after exposure to high temperatures does not decrease dramatically with the increase of temperature. The ratio of the biaxial to its uniaxial compressive strength depends on the stress ratios and brittleness-stiffness of HSHPC after exposure to different temperature levels. Comparison of the stress-strain results obtained from the theoretical model and the experimental data indicates good agreement.     

BIAXIAL LOADING OF NEO-CLASSICAL LIQUID CRYSTAL ELASTOMERS:CONSTITUTIVE RELATIONS AND SOFT BEHAVIOR

The thermo-order-mechanical behaviors of liquid crystal elastomers(LCEs) under biaxial loading are studied in this paper.Inverse method for nonlinear elastic problems is utilized by imposing biaxial stretching to thin rectangular samples.Neo-classical elastic energy is used together with the Landau-de Gennes nematic free energy.Under plane stress assumptions,the constitutive equations are derived.Due to the possible reorientations of the liquid crystal molecules induced by the imposed biaxial loading,the in-plane nonlinear stress-strain relations can have different expressions depending on which loading axis will have the largest effective principal strain.And the free energy is a multi-well non-convex potential function.As shown by some typical loading paths,the LCE samples will exhibit an anisotropic nonlinear elastic behavior,as long as the loading has not induced a reorientation of the liquid crystal molecules.When this did occur,jumps of stresses could take place for dead loadings due to the losing of stability.     

FINITE ELEMENT ANALYSIS OF CARDIAC MYOCYTE DEBONDING AND REORIENTATION DURING CYCLIC SUBSTRATE STRETCH EXPERIMENTS

The substrate stretch experiment, which is carried out on several kinds of adherent cells, is usually used to catch the physiological variation and morphological response to cyclic substrate deformation. In this paper, stretch loading was exerted on cardiac myocytes cultured on silica substrates using a custom-made substrate stretch device. The effect of stretch on the alignment orientation of cardiac myocytes was studied through morphocytological statistics. Under cyclic stretch stimulus, the long axes of cardiac myocytes oriented perpendicularly to the stretch direction for continuous stretch acting. However, the mechanism underlying these behaviors is not well understood from such in vitro tests. Finite element （FE） model was developed in the analysis to investigate these behaviors. Xu-Needleman formulation was used to define the interaction behavior for contact surfaces between cell and substrate. The role of cell viscoelasticity nature is studied in adherent cell debonding with the substrate and aligning perpendicular to the stretch direction during long time cyclic stretch stimulation. There were four different strain magnitudes considered in the simulation to find out the cell debonding affected by the cyclic strains. The potential role of cyclic strain frequency in regulating cell debonding and alignment was also studied using FE analysis.     

Micro-scale behavior of granular materials during cyclic loading

This study presents the micro-scale behavior of granular materials under biaxial cyclic loading for different confining pressures using the two-dimensional (2D) discrete element method (DEM). Initially, 8450 ovals were generated in a rectangular frame without any overlap. Four dense samples having confining pressures of 15, 25, 50, and 100 kPa were prepared from the initially generated sparse sample. Numerical simulations were performed under biaxial cyclic loading using these isotropically compressed dense samples. The numerical results depict stress–strain–dilatancy behavior that was similar to that observed in experimental studies. The relationship between the stress ratio and dilatancy rate is almost independent of confining pressures during loading but significantly dependent on the confining pressures during unloading. The evolution of the coordination number, effective coordination number and slip coordination number depends on both the confining pressures and cyclic loading. The cyclic loading significantly affects the microtopology of the granular assembly. The contact fabric and the fabric-related anisotropy are reported, as well. A strong correlation between the stress ratio and the fabric related to contact normals is observed during cyclic loading, irrespective of confining pressures.     

Incorporating the effects of fabric in the dilatant double shearing model for planar deformation of granular materials

The objective of this paper is to incorporate the effects of fabric and its evolution into the Dilatant Double Shearing Model [Mehrabadi, M.M., Cowin, S.C., 1978. Initial planar deformation of dilatant granular materials. J. Mech. Phys. Solids 26, 269–284] for granular materials in order to capture the anisotropic behavior and the complex response of granular materials in cyclic shear loading. An important consequence of considering the fabric is that one can have unequal shearing rates along the two slip directions. This property leads to the non-coaxiality of the principal axes of stress and strain rate, which is more appropriate for a material that exhibits initial and induced anisotropy. In addition, we employ a fabric-dependent elasticity tensor with orthotropic symmetry. The model developed in this paper also predicts one of the experimentally observed characteristics of granular materials: the gradual concentration of the contact normals towards the maximum principal stress direction.We implement the constitutive equations into ABAQUS/Explicit by writing a user material subroutine in order to predict the strength anisotropy of granular materials in a plane strain biaxial compression test and investigate the mechanical behavior of granular materials under the cyclic shear loading conditions. The predictions from this model show good quantitative agreement with the experiments of [Park, C.S., 1990. Anisotropy in deformation and strength properties of sands in plane strain compression, Masters Thesis, University of Tokyo; Park, C.S., Tatsuoka, F., 1994. Anisotropic strength and deformation of sands in plane strain compression. In: XIII ICSMFE, New Delhi, India; Okada, N., 1992. Energy dissipation in inelastic flow of cohesionless granular media. Ph.D. Thesis, University of California, San Diego].     

Exploring the undrained cyclic behavior of methane-hydrate-bearing sediments using CFD–DEM

Based on the mechanical experimental results of methane hydrate (MH), a bond contact model considering the rate-dependency of MH is proposed. A CFD–DEM scheme considering fluid compressibility is used to simulate a series of undrained cyclic shear tests of numerical methane-hydrate-bearing sediment (MHBS) samples. The dynamic behavior, including stress–strain relationship, dynamic shear modulus, and damping ratio, is investigated. In addition, the force chains, contact fabric and averaged pure rotation rate (APR) are examined to investigate the relationships between micromechanical variables and macromechanical responses in the DEM MH samples. The effects of temperature, confining pressure and MH saturation are also analyzed. Due to the micro-structural strengthening by the MH bonds, no obvious change in microscopic quantities is observed, and the samples remain at the elastic stage under the applied low-shear stress level. When confining pressure and MH saturation increase, the dynamic elastic modulus increases, while the damping ratio decreases. An increasing temperature (leading to weakening of MH bonds) can lower the dynamic elastic modulus, but has almost no impact on the damping ratio. On the contrary, an increasing cyclic shear stress level lowers the damping ratio, but has almost no effect on the dynamic elastic modulus.     

DEM investigation of strain behaviour and force chain evolution of gravel–sand mixtures subjected to cyclic loading

The strain characteristic and load transmission of mixed granular matter are different from those of homogeneous granular matter. Cyclic loading renders the mechanical behaviours of mixed granular matter more complex. To investigate the dynamic responses of gravel–sand mixtures, the discrete element method (DEM) was used to simulate the cyclic loading of gravel–sand mixtures with low fines contents. Macroscopically, the evolution of the axial strain and volumetric strain was investigated. Mesoscopically, the coordination number and contact force anisotropy were studied, and the evolution of strong and weak contacts was explored from two dimensions of loading time and local space. The simulation results show that increasing fines content can accelerate the development of the axial strain and volumetric strain but has little effect on the evolution of contact forces. Strong contacts tend to develop along the loading boundary, presenting the spatial difference. Weak contacts are firstly controlled by confining pressure and then controlled by axial stress, while strong contacts are mainly controlled by axial stress throughout the whole cyclic loading. Once compression failure occurs, the release of axial stress causes the reduction of strong contact proportion in all local regions. These findings are helpful to understand the dynamic responses of gravel–sand mixtures, especially in deformation behaviours and the Spatio-temporal evolution of contact forces.     

循环荷载下硅藻土应变和孔压特性

针对嵊州硅藻土的高结构性及地基应力场的复杂多变，应用GDS 动三轴仪进行不同围压和不同循环应力比下的不排水循环加载试验，分析应力-应变滞回曲线演化、应变累积特性、回弹特性及孔压特性．研究表明：循环应力比及围压对原状硅藻土应变和孔压的发展规律影响明显，随着循环应力比的增加，滞回曲线由线性状态转变为非线性状态，且逐渐向x 轴倾斜，累计应变和回弹应变都随着循环应力比的增加而略微增加，但总应变基本小于2 %；残余孔压比随循环应力比增大而增大，范围为0.1~0.5．并且存在一个临界循环应力比，其值随有效围压的增大而减小，范围为0.8~2.2，当循环应力比大于该值时，试样内部产生一个破裂面迅速发生破坏．在相同循环应力比下，试样的应变随着有效围压的增大而增大．     

Structural stability and jamming of self-organized cluster conformations in dense granular materials

We examine emergent, self-organized particle cluster conformations in quasistatically deforming dense granular materials from the perspective of structural stability. A structural mechanics approach is employed, first, to devise a new stability measure for such conformations in equilibrium and, second, to use this measure to explore the evolving stability of jammed states of specific cluster conformations, i.e. particles forming force chains and minimal contact cycles. Knowledge gained on (a) the spatial and temporal evolution of stability of individual jammed conformations and (b) their relative stability levels, offer valuable clues on the rheology and, in particular, self-assembly of granular materials. This study is undertaken using data from assemblies of nonuniformly sized circular particles undergoing 2D deformation in two biaxial compression tests: a discrete element simulation of monotonic loading under constant confining pressure, and cyclic loading of a photoelastic disk assembly under constant volume. Our results suggest that the process of self-assembly in these systems is realized at multiple length scales, and that jammed force chains and minimal cycles form the basic building blocks of this process. In particular, 3-cycles are stabilizing agents that act as granular trusses to the load-bearing force chain columns. This co-evolutionary synergy between force chains and 3-cycles proved common to the different materials under different loading conditions. Indeed, the remarkable similarities in the evolution of stability, prevalence and persistence of minimal cycles and force chains in these systems suggest that these structures and their co-evolution together form a generic feature of dense granular systems under quasistatic loading.     

饱和砂土的循环边界面本构模

饱和砂土在循环加卸载过程中，土体发生显著的组构变化和塑性变形的累积。试验现象分析表明，循环过程中，砂土的首次与再循环塑性模量既有区别又有联系。因此，论文引入考虑组构变化的剪胀内变量，并提出循环塑性模量的关系式，真实描述上述两种现象；进而基于已有本构模型的基础上，建立饱和砂土的循环边界面本构模型。最后，将饱和砂土的模型预测结果与三轴试验结果进行验证对比，得到较好地吻合，这表明该模型能够合理反映饱和砂土循环加卸载的变形行为。     

基于细观拓扑结构演化的颗粒材料剪胀性分析

剪胀性是包括岩土材料在内的摩擦性颗粒材料的重要特征之一,其形成机制与颗粒体系内部拓扑结构的演化有关.基于颗粒体系细观数据,可对颗粒体系内部的拓扑结构特征及演化进行分析,进而建立拓扑演化与宏观剪胀变形之间的联系.采用离散单元法,根据密实、中密和松散摩擦性颗粒材料双轴试验的宏微观数据,从拓扑参量演化及接触网络拓扑变化所引起...     

An elasto-plastic model for granular materials with microstructural consideration

In this paper, we have extended the granular mechanics approach to derive an elasto-plastic stress–strain relationship. The deformation of a representative volume of the material is generated by mobilizing particle contacts in all orientations. Thus, 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. Essential features such as continuous displacement field, inter-particle stiffness, and fabric tensor are discussed. The predictions of the derived stress–strain model are compared to experimental results for sand under both drained and undrained triaxial loading conditions. The comparisons demonstrate the ability of this model to reproduce accurately the overall mechanical behavior of granular media and to account for the influence of key parameters such as void ratio and mean stress. A part of this paper is devoted to the study of anisotropic specimens loaded in different directions, which shows the model capability of considering the influence of inherent anisotropy on the stress–strain response under a drained triaxial loading condition.     

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.