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Qualitative and quantitative analyses of particulate flows in rotating drums using a DEM-based approach 利用基于 DEM 的方法对旋转滚筒中的微粒流进行定性和定量分析
IF 2.8 3区 工程技术 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-04-29 DOI: 10.1007/s40571-024-00753-8
Luis Angeles, Kennia Velez, Cesar Celis

In mineral processing, ore grinding is an energy-intensive process. Tumbling mills used in grinding processes can be accounted for as rotating drums with liners. As part of an effort to evaluate ways of reducing energy consumption in such systems, therefore, particulate flows in rotating drums are studied in this work. More specifically, using a new DEM tool, which is one of the modules of a larger in-house computational package called CFLOWSS, particulate flows in rotating drums are qualitatively and quantitatively analyzed. The results from such analyses are compared with experimental ones and other numerical results obtained using a commercial DEM software. In qualitative terms, the CFLOWSS results show a relatively good agreement with experimental photographs previously taken in a laboratory. In quantitative terms, in turn, the CFLOWSS predictions show a strong correspondence with those ones made by the commercial software. For instance, the relative discrepancies of the boxplots’ medians associated with the number of contacts, power, and forces predicted by both (in-house and commercial) tools present values smaller than 8%. At a 60 RPM drum rotation velocity, indeed, the number of contacts related discrepancies reach values as low as 0.8%. Some of the contributions of this work involve (i) the development of a new DEM tool capable of realistically describing particulate flows in rotating drums, and (ii) the use of statistical treatments to quantitatively analyze DEM results. This last aspect is important because this sort of assessments provides an improved way to analyze the behavior of particulate flows.

在矿物加工中,矿石研磨是一个能源密集型过程。碾磨过程中使用的翻滚式碾磨机可以看作是带衬板的旋转滚筒。因此,作为评估降低此类系统能耗的方法的一部分,本研究对旋转滚筒中的微粒流进行了研究。更具体地说,利用一种新的 DEM 工具(这是一个名为 CFLOWSS 的大型内部计算软件包的模块之一),对旋转滚筒中的微粒流进行了定性和定量分析。分析结果与实验结果以及使用商业 DEM 软件获得的其他数值结果进行了比较。在定性方面,CFLOWSS 的结果与之前在实验室拍摄的实验照片显示出相对较好的一致性。而在定量方面,CFLOWSS 的预测结果与商业软件的预测结果非常吻合。例如,两种(内部和商业)工具预测的接触次数、功率和力的方框图中值的相对差异值均小于 8%。实际上,在滚筒转速为 60 RPM 时,与接触次数相关的差异值低至 0.8%。这项工作的一些贡献包括:(i) 开发了一种新的 DEM 工具,能够真实地描述旋转滚筒中的微粒流;(ii) 使用统计处理方法对 DEM 结果进行定量分析。最后一个方面非常重要,因为这种评估为分析颗粒流的行为提供了一种更好的方法。
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引用次数: 0
Numerical investigation on the mechanical and fracture behaviors of marble under cyclic loading and unloading true triaxial compression using discrete element method 利用离散元法对循环加载和卸载真实三轴压缩下大理石的力学和断裂行为进行数值研究
IF 3.3 3区 工程技术 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-04-26 DOI: 10.1007/s40571-024-00750-x
Yapeng Li, Qiang Zhang, Binsong Jiang

The deep-buried rock is subjected to true triaxial stress states and is affected by repeated disturbance loads. The discrete element method was employed to investigate the mechanical behavior and fracture mechanism of marble under true triaxial cyclic loading and unloading. The particle-based marble model with the calibrated microparameters was established based on true triaxial compression. The true triaxial cyclic loading and unloading simulations with different stress states were conducted. The increase in intermediate principal stress results in significant deformation anisotropy. The brittle–ductile transformation characteristics are presented with the increase in minimum principal stress. The crack damage stress initially increases and subsequently decreases with the increase of equivalent plastic strain under different stress states. The plastic strain increments ratios exhibit prominent nonlinear variation during the progressive failure. The rock strength presents the asymmetric distribution by the effect of intermediate principal stress, and the minimum principal stress has an enhancing effect on strength. With the increase in intermediate principal stress or the decrease in minimum principal stress, that is, the effect of high differential stress, the failure plane changes from inclined to parallel to the direction of maximum principal stress. The microcrack numbers present the S-shaped increasing trend during the progressive failure. The increasing number of microcracks parallel to the direction of intermediate principal stress and the anisotropy of microcrack tendency are subjected to high differential stress.

深埋岩石承受真实三轴应力状态,并受到反复扰动载荷的影响。采用离散元法研究了大理岩在真实三轴循环加载和卸载下的力学行为和断裂机理。在真实三轴压缩的基础上,建立了具有校准微参数的基于颗粒的大理石模型。对不同应力状态下的真实三轴循环加载和卸载进行了模拟。中间主应力的增加导致了明显的变形各向异性。随着最小主应力的增加,呈现出脆性-韧性转变特征。在不同的应力状态下,随着等效塑性应变的增加,裂纹破坏应力最初增加,随后减小。在渐进破坏过程中,塑性应变增量比呈现出显著的非线性变化。岩石强度在中间主应力的作用下呈现非对称分布,最小主应力对强度有增强作用。随着中间主应力的增大或最小主应力的减小,即在高差应力的作用下,破坏面由倾斜变为与最大主应力方向平行。在渐进破坏过程中,微裂缝数量呈 "S "形增加趋势。在高差应力作用下,平行于中间主应力方向的微裂缝数量不断增加,微裂缝趋势各向异性。
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引用次数: 0
Analysis of factors influencing micro-scale double-bubbles collapse based on molecular dynamic simulation 基于分子动力学模拟的微尺度双气泡坍缩影响因素分析
IF 3.3 3区 工程技术 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-04-26 DOI: 10.1007/s40571-024-00751-w
Xiuli Wang, Wenzhuo Guo, Guohui Zhao, Jian Wang, Yuanyuan Zhao, Wei Xu

The collapse of bubbles in hydraulic machinery has emerged as a prominent area of research. To grasp the interplay between bubbles, a model of double-bubbles is built. The bubble morphology, total pressure (P), and the center of mass displacement (Lcom) are taken as research objects, and the influence temperature (T), and bubble radius (R), bubble distance (L) on bubble collapse is summarized. Results show that the distance between the bubbles is smaller, the total collapse time is longer. However, Lcom increases when the distance is increased or decreased to some extent. Moreover, in the case of the double-bubbles model with r1 = 10 Å, as the bubbles (r2 = 7.5, 10, 12.5 Å) collapse, the released pressure gradually increases, then decrease, and the release pressure of the double-bubbles model (r1 = 10 Å, r2 = 12.5 Å) is 1.08 times that of the model (r1 = 10 Å, r2 = 15 Å). Based on the differential pressure parameters (∆P1 and ∆P2), the significance order of temperature (T), bubble distance (L), and bubble radius (r) is Lr > T. The aim of the paper is to provide technical guidance and a theoretical basis for industrial applications of techniques by enhancing the theory of cavitation.

液压机械中气泡的崩溃已成为一个突出的研究领域。为了掌握气泡之间的相互作用,本文建立了双气泡模型。以气泡形态、总压(P)和质心位移(Lcom)为研究对象,总结了温度(T)和气泡半径(R)、气泡间距(L)对气泡溃散的影响。结果表明,气泡间距越小,总坍塌时间越长。然而,当距离在一定程度上增大或减小时,Lcom 会增大。此外,在 r1 = 10 Å 的双气泡模型中,随着气泡(r2 = 7.5、10、12.5 Å)的坍塌,释放压力逐渐增大,然后减小,双气泡模型(r1 = 10 Å,r2 = 12.5 Å)的释放压力是模型(r1 = 10 Å,r2 = 15 Å)的 1.08 倍。根据压差参数(ΔP1 和 ΔP2),温度(T)、气泡距离(L)和气泡半径(r)的重要性顺序为 L≈r > T。本文旨在通过强化空化理论,为工业应用技术提供技术指导和理论依据。
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引用次数: 0
Calibration of particle interactions for discrete element modeling of powder flow 校准粉末流动离散元素模型中的颗粒相互作用
IF 2.8 3区 工程技术 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-04-24 DOI: 10.1007/s40571-024-00739-6
Mike Fazzino, Ummay Habiba, Lukasz Kuna, Serge Nakhmanson, Rainer J. Hebert

An ASTM B213 standard Hall Flowmeter Funnel experiment was conducted for Ti 6–4 powder particles and simulated utilizing a discrete element method approach implemented in the LIGGGHTS package. Particle interactions were described with a modified simplified Johnson–Kendall–Roberts theory that includes adhesion as a function of the particle surface free energy. Experimental data for the powder particle size distribution were used as input for the simulations. Adjustable parameters, such as cohesion energy density, coefficient of restitution and dynamic friction, were tuned to match the general shape of the experimentally obtained particle pile. Geometrical properties of the simulated powder pile, including its diameter, height and inside/outside slope angles, were computed and compared with the experimental results where available. Local particle size distributions for different areas within the pile (top vs. bottom) were obtained, indicating the dominance of larger particles at the top of the pile, akin to the Brazil nut effect.

对钛 6-4 粉末颗粒进行了 ASTM B213 标准霍尔流量计漏斗实验,并利用 LIGGGHTS 软件包中的离散元素法进行了模拟。颗粒间的相互作用是用修正的简化约翰逊-肯德尔-罗伯茨理论来描述的,其中包括作为颗粒表面自由能函数的附着力。粉末粒度分布的实验数据被用作模拟的输入。对内聚能密度、恢复系数和动态摩擦力等可调参数进行了调整,以符合实验所得颗粒堆积的一般形状。计算了模拟粉末堆的几何特性,包括其直径、高度和内/外倾斜角,并将其与实验结果(如有)进行了比较。获得了粉末堆内不同区域(顶部与底部)的局部粒度分布,表明较大的颗粒主要位于粉末堆顶部,类似于巴西坚果效应。
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引用次数: 0
The mechanism of crack propagation under dynamic loading stress at different rates 不同速率动态加载应力下的裂纹扩展机理
IF 3.3 3区 工程技术 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-04-19 DOI: 10.1007/s40571-024-00748-5
Zhongshun Chen, Yong Yuan, Zhenghan Qin, Wenmiao Wang, Heng Li

The generation and propagation of cracks are influenced by dynamic loading stresses induced by different fracturing methods. In order to investigate the influence of dynamic loading stress rate on the crack propagation and crack distribution characteristics, theoretical analysis and numerical simulation were used to study the crack propagation mechanism and distribution state of the rock, and zoning standards for different loading stresses were proposed. The form of fracture around the borehole is determined by the peak value of dynamic loading stress and the dynamic strength of the rock, while the number of rock fractures is influenced by the propagation rate of dynamic loading stress and the dynamic path of unloading wave propagation. Under high-stress and rapid dynamic loading, the rock around the borehole undergoes dynamic compression failure. For moderate dynamic loading, the rock mass experiences initial fracture due to tensile stress, leading to the generation of multiple radial cracks through the combined action of shock and unloading waves. Under quasi-static loading, the rock mass undergoes tensile failure under tensile stress and is effectively unloaded. Based on the peak value of dynamic loading and loading time, different fracture modes are divided into crushing fracture zone, multiple fracture zone, and single fracture zone. The relationship between the characteristics of rock fragments and loading stress was determined, and the fractal method was used to describe the distribution characteristics of cracks. The effects of loading rate and rock fragmentation were finally discussed, providing guidance for the selection and utilization of different fracturing methods.

裂缝的产生和扩展受不同压裂方法引起的动态加载应力的影响。为了研究动加载应力速率对裂缝扩展和裂缝分布特征的影响,采用理论分析和数值模拟的方法研究了岩石的裂缝扩展机理和分布状态,提出了不同加载应力的分区标准。钻孔周围的断裂形式由动加载应力的峰值和岩石的动强度决定,而岩石断裂的数量则受动加载应力的传播速度和卸荷波传播的动态路径影响。在高应力和快速动荷载作用下,钻孔周围的岩石会发生动压缩破坏。在中度动荷载下,岩体因拉伸应力而发生初始断裂,在冲击波和卸荷波的共同作用下产生多条径向裂缝。在准静态加载下,岩体在拉应力作用下发生拉伸破坏,并有效卸载。根据动荷载的峰值和加载时间,不同的断裂模式可分为破碎断裂带、多重断裂带和单一断裂带。确定了岩石碎块特征与加载应力之间的关系,并采用分形法描述了裂缝的分布特征。最后讨论了加载速率和岩石破碎的影响,为选择和使用不同的压裂方法提供了指导。
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引用次数: 0
Semi-empirical model for abrasive particle velocity prediction in abrasive waterjet based on momentum transfer efficiency 基于动量传递效率的加砂水刀加砂颗粒速度预测半经验模型
IF 3.3 3区 工程技术 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-04-16 DOI: 10.1007/s40571-024-00747-6
Hyun-Joong Hwang, Yohan Cha, Seok-Jun Kang, Gye-Chun Cho

Abrasive waterjet (AWJ) is a technology that removes a target material with an abrasive accelerated by ultra-high-pressure water. Recently, its application for rock excavations in civil and geotechnical engineering has increased. AWJ excavation performance is affected by the abrasive velocity formed by momentum transfer during mixing and acceleration. The abrasive velocity varies owing to changes in the abrasive flow rate, focusing tube diameter, and focusing tube length. In this study, the momentum transfer efficiency (MTE) according to the abrasive flow rate and focusing tube geometry was investigated by a numerical analysis to better understand the multiphase flow inside the AWJ system. The MTE was defined based on the theoretical relationship between the abrasive velocity ratio and focusing tube factor, and evaluated through the empirical relationship between the water stiffness and focusing tube length. The optimal abrasive flow rate for generating efficient MTE was approximately 15 g/s, which enabled economical and effective acceleration of abrasive particles. Accordingly, a prediction model based on the derived MTE was developed for the final abrasive velocity generated at the tip of the focusing tube. Using the prediction model, it is possible to evaluate the comprehensive relationship between various AWJ parameters. Based on the prediction model, the abrasive–water flow ratio to generate the optimal abrasive velocity was 0.83. The developed prediction model provides guidelines for selecting the optimal focusing tube geometry and applying an economical abrasive flow rate when designing an AWJ system.

加砂水刀(AWJ)是一种利用超高压水加速磨料去除目标材料的技术。最近,它在土木工程和岩土工程岩石开挖中的应用有所增加。AWJ 的挖掘性能受混合和加速过程中动量传递所形成的磨料速度的影响。磨料速度随磨料流速、聚焦管直径和聚焦管长度的变化而变化。本研究通过数值分析研究了磨料流速和聚焦管几何形状所决定的动量传递效率(MTE),以更好地了解 AWJ 系统内部的多相流。MTE 基于磨料流速比和聚焦管系数之间的理论关系进行定义,并通过水硬度和聚焦管长度之间的经验关系进行评估。产生高效 MTE 的最佳磨料流速约为 15 克/秒,这使得磨料颗粒的加速既经济又有效。因此,根据推导出的 MTE,为聚焦管顶端产生的最终磨料速度建立了一个预测模型。利用该预测模型,可以评估各种 AWJ 参数之间的综合关系。根据预测模型,产生最佳磨料速度的磨料-水流量比为 0.83。所开发的预测模型为设计 AWJ 系统时选择最佳聚焦管几何形状和应用经济的磨料流速提供了指导。
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引用次数: 0
Micro-mechanical analysis of residual stresses in cohesive-frictional particulate materials under moving surface loads 移动表面载荷下内聚摩擦颗粒材料残余应力的微观力学分析
IF 3.3 3区 工程技术 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-04-15 DOI: 10.1007/s40571-024-00740-z
Wei Cai, Ping Xu, Runhua Zhang

This study focuses on the build-up of residual stresses of cohesive-frictional materials under moving surface loads, and corresponding micromechanisms are studied in particle scales using discrete element methods. The numerical procedure is validated with macroscopic residual stresses obtained by experimental tests and finite element methods. It is found that residual stresses are dominated by normal contact and normal bond forces, and strong force chains make a leading contribution to build-ups of residual stresses. A further study indicates that the increase of averaged interparticle forces is a critical factor to growths of residual stresses, which is generally accompanied with decreased proportions of contacts carrying small forces. Simultaneously, the averaged magnitude of interparticle forces belonging to single orientations generally grows with developments of residual stresses, and for resultant forces it distributes almost isotropically. Nevertheless, because of gradual developments of residual stresses, macroscopic stress fields should be anisotropic, which is subsequently validated to be dominated by the fabric anisotropy.

本研究的重点是内聚摩擦材料在移动表面载荷作用下残余应力的积累,并采用离散元方法研究了颗粒尺度上的相应微观机制。通过实验测试和有限元方法获得的宏观残余应力验证了数值程序。研究发现,残余应力主要受法向接触力和法向结合力的影响,强力链对残余应力的形成起主导作用。进一步的研究表明,颗粒间平均作用力的增加是残余应力增长的关键因素,通常伴随着小作用力接触比例的下降。同时,属于单一方向的颗粒间力的平均值通常会随着残余应力的发展而增加,对于结果力来说,其分布几乎是各向同性的。然而,由于残余应力的逐渐发展,宏观应力场应该是各向异性的,这一点随后被证实是由织物的各向异性所主导的。
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引用次数: 0
Thermosolutal convection of NEPCM inside a curved rectangular annulus: hybrid ISPH method and machine learning 弯曲矩形环内 NEPCM 的热固性对流:ISPH 混合法和机器学习
IF 3.3 3区 工程技术 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-04-15 DOI: 10.1007/s40571-024-00744-9
Abdelraheem M. Aly, Sang-Wook Lee, Nghia Nguyen Ho, Zehba Raizah

In this work, the incompressible smoothed particle hydrodynamics (ISPH) method is utilized to simulate thermosolutal convection in a novel annulus barred by NEPCMs. The novel annulus is formed between a horizontal curved rectangle connected to a vertical rectangle containing a vertical ellipse. It is the first attempt to investigate the heat and mass transmission of NEPCM in such a unique annulus. NEPCM’s sophisticated designs of closed domains during heat/mass transfer can be applied in energy savings, electrical device cooling, and solar cell cooling. The ISPH method solved the fractional time derivative of governing partial differential equations. The artificial neural network (ANN) is integrated with the ISPH results to predict the average Nusselt (overline{{text{Nu}} }) and Sherwood numbers (overline{{text{Sh}} }). The scales of physical parameters are Hartmann number (Ha = 0–80), buoyancy ratio parameter (N = − 10–20), Dufour/Soret numbers (Du = 0–0.4 & Sr = 0–0.8), Rayleigh number (Ra=103–105), fractional time derivative (α = 0.85–1), nanoparticle parameter (φ = 0–0.15), and fusion temperature (θf = 0.05–0.95). The main findings showed the importance of buoyancy ratio and Rayleigh number in enhancing the buoyancy-driven convection which accelerates the velocity field and strengths the isotherms and isoconcentration. The velocity field decreases according to an enhancement in Hartmann number and nanoparticle parameter. The exact agreement of the ANN model prediction values with the goal values demonstrates that the created ANN model can predict the (overline{{text{Nu}} }) and (overline{{text{Sh}} }) values properly. The complicity of a closed domain by carving the horizontal rectangle and inserting the ellipse inside a vertical rectangle can be utilized into cooling equipment, solar cells, and heat exchangers.

在这项研究中,利用不可压缩平滑粒子流体力学 (ISPH) 方法模拟了由 NEPCM 遮挡的新型环形空间中的热固性对流。这种新型环形结构是在一个水平弯曲矩形与一个包含垂直椭圆的垂直矩形之间形成的。这是首次尝试研究 NEPCM 在这种独特环形结构中的热量和质量传输。NEPCM 在传热/传质过程中对封闭域的精密设计可用于节能、电气设备冷却和太阳能电池冷却。ISPH 方法求解了支配偏微分方程的分数时间导数。人工神经网络(ANN)与 ISPH 结果相结合,预测了平均努塞尔特数(Nusselt)和舍伍德数(Sherwood)。物理参数的尺度为哈特曼数(Ha = 0-80)、浮力比参数(N = - 10-20)、杜弗/索雷特数(Du = 0-0.4 & Sr = 0-0.8)、瑞利数(Ra=103-105)、分数时间导数(α = 0.85-1)、纳米粒子参数(φ = 0-0.15)和聚变温度(θf = 0.05-0.95)。主要研究结果表明,浮力比和瑞利数在增强浮力驱动对流方面具有重要作用,浮力驱动对流加速了速度场,增强了等温线和等浓度。速度场随着哈特曼数和纳米粒子参数的增加而减小。ANN 模型的预测值与目标值完全一致,这表明所创建的 ANN 模型可以正确预测 (overline{{text{Nu}} }) 和 (overline{{text{Sh}} }) 值。通过雕刻水平矩形和在垂直矩形内插入椭圆来实现闭合域的复杂性,可用于冷却设备、太阳能电池和热交换器。
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引用次数: 0
Numerical investigation of collision characteristics of non-spherical particles on ductile surfaces under normal impact 韧性表面上的非球形颗粒在正常冲击下的碰撞特性的数值研究
IF 3.3 3区 工程技术 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-04-10 DOI: 10.1007/s40571-024-00746-7
Rahul Tarodiya, Avi Levy

The particle–wall collision behavior plays a crucial role in determining particle motion during the simulation of multiphase flow processes. The coefficient of restitution (COR) is generally used to characterize the particle–wall collisional behavior. Correct consideration of COR is essential for obtaining accurate results in numerical simulations. In the present work, the COR during the normal impact of a rigid prolate ellipsoidal particle on the target wall is investigated using the finite element method. The loss in kinetic energy of the particles after impact is used to analyze the COR. The simulations are conducted with a particle of sphericity 1, 0.9, 0.8, 0.7, and 0.5 impacted at different orientation angles (angle between particle major axis to the horizontal plane) in the range 0°–90°. The effect of particle sphericity, particle orientation before impact, impact velocity, and target surface material on COR is determined. Further, an understanding is established on the deviation in COR for the impact of non-spherical particles as compared to the COR for the impact of spherical particles. The insights gained from this study are valuable for accurately predicting the motion of non-spherical particles in multiphase processes using the discrete element method.

在模拟多相流过程中,颗粒与壁面的碰撞行为对确定颗粒运动起着至关重要的作用。恢复系数 (COR) 通常用于描述颗粒与壁面的碰撞行为。正确地考虑 COR 对于在数值模拟中获得准确的结果至关重要。在本研究中,使用有限元方法研究了刚性椭圆形颗粒对目标壁面的法向冲击过程中的 COR。粒子撞击后的动能损失用于分析 COR。模拟以球度为 1、0.9、0.8、0.7 和 0.5 的粒子在 0°-90°范围内的不同方位角(粒子主轴与水平面的夹角)进行撞击。确定了颗粒球度、颗粒撞击前的方向、撞击速度和目标表面材料对 COR 的影响。此外,还了解了非球形颗粒撞击 COR 与球形颗粒撞击 COR 的偏差。本研究获得的见解对于使用离散元素法准确预测多相过程中非球形颗粒的运动非常有价值。
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引用次数: 0
3D DEM-based particle-scale analysis of drained and undrained triaxial behaviors of granular materials 基于三维 DEM 的颗粒尺度分析颗粒材料的排水和非排水三轴行为
IF 3.3 3区 工程技术 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-04-05 DOI: 10.1007/s40571-024-00743-w
Lei Jin, Jingjing Li, Yang Ye, Yu Wang

Some numerical simulations of drained and undrained triaxial tests on granular materials with different initial densities are carried out with the three-dimensional discrete element method. An in-depth particle-scale analysis is performed quantitatively to illustrate the physical mechanism of the shear mechanical behaviors, with a special attention paid to the characteristics of quasi-steady state and critical state. The simulation results show that the initial density and shear drainage condition both have significant effects on the evolution of stress–strain, coordination number, fabric anisotropy factor, force chains and clusters. The chained grains ratio and the mean length of force chains in the specimens are constantly adjusted to bear and transfer the changing external loads. The transitions between small clusters and large clusters are also continually taking place in varying degrees, correlating to volumetric contraction or dilation. For the loose undrained triaxial specimen presenting quasi-steady state during shearing, the coordination number decreases obviously to nearly 4 and then increases again; the chained grains ratio decreases after a slight increase in the initial loading stage, and then begin to increase again after a period of lower value of around 0.285; the volume ratio of small, submedium and medium clusters all first decreases and then increase gradually, meanwhile volume ratio of large clusters increases sharply to as much as 0.28 and then decreases gradually. The macroscopic critical state of granular materials is a comprehensively external manifestation when the microscopic coordination number and mesoscopic force chains and clusters all evolute to a dynamic equilibrium. At the critical state, the deviator stress, void ratio, coordination number, fabric anisotropy factor, and the volume ratio of small clusters and large clusters all manifest a respectively unique linear relationship with the mean effective stress.

采用三维离散元方法对不同初始密度的颗粒材料的排水和不排水三轴试验进行了数值模拟。对颗粒尺度进行了深入的定量分析,以说明剪切力学行为的物理机制,并特别关注准稳态和临界状态的特征。模拟结果表明,初始密度和剪切排水条件对应力应变、配位数、织物各向异性因子、力链和团簇的演变均有显著影响。试样中的链粒比和力链平均长度不断调整,以承受和传递不断变化的外部载荷。小团簇和大团簇之间也不断发生不同程度的转变,这与体积收缩或扩张有关。对于在剪切过程中呈现准稳态的松散不排水三轴试样,配位数明显降低到接近 4 后又重新升高;链状晶粒比在加载初期略有升高后降低,经过一段时间降低到 0.285 左右后又开始升高;小晶簇、亚中晶簇和中晶簇的体积比均先降低后逐渐升高,而大晶簇的体积比则急剧升高到 0.28 左右后又逐渐降低。颗粒材料的宏观临界状态是微观配位数和中观力链、力簇都演化到动态平衡的综合外在表现。在临界状态下,偏差应力、空隙率、配位数、织物各向异性因子、小团体积比和大团体积比都分别与平均有效应力呈独特的线性关系。
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引用次数: 0
期刊
Computational Particle Mechanics
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