A study of influence of gravity on bulk behaviour of particulate solid

This paper examines the influence of gravity on the bulk responses of a granular solid. The loading scenarios in this study include confined compression, rod penetration into a granular medium and discharging through an orifice. Similar loading and flow conditions are likely to be encountered in the stress and deformation regimes that regoliths are subjected to in extraterrestrial exploration activities including in situ resource utilisation processes. Both spherical and non-spherical particles were studied using the discrete element method （DEM）. Whilst DEM is increasingly used to model granular solids, careful validations of the simulation outcomes are rather rare. Thus in addition to exploring the effect of gravity, this paper also compares DEM simulations with experiments under terrestrial condition to verify whether DEM can produce satisfactory predictions. The terrestrial experiments were conducted with great care and simulated closely using DEM. The key mechanical and geometrical properties for the particles were measured in laboratory tests for use in the DEM simulations. A series of DEM computations were then performed under reduced gravity to simulate these experiments under extraterrestrial environment. It was found that gravity has no noticeable effect on the force transmission in the confined compression case; the loading gradient in the rod penetration is linearly proportional to the gravity; the mass flow rate in silo discharge is proportional to square root of the gravity and the angle of repose increases with reducing gravity. These findings are in agreement with expectation and existing scientific evidence.     

Numerical simulation study on particle breakage behavior of granular materials in confined compression tests

In order to study the fragmentation law, the confined compression experiment of granular assemblies has been conducted to explore the particle breakage characteristic by DEM approach in this work. It is shown that contact and contact force during the loading process gradually transform from anisotropy to isotropy. Meanwhile, two particle failure modes caused by different contact force states are analyzed, which are single-through-crack failure and multi-short-crack failure. Considering the vertical distribution of the number of cracks and the four characteristic stress distributions (the stress related to the maximum contact force, the major principal stress, the deviatoric stress and the mean stress), it is pointed out that the stress based on the maximum contact force and the major principal stress can reflect the distribution of cracks accurately. In addition, the size effect of particle crushing indicates that small size particles are prone to break. The lateral pressure coefficient of four size particles during the loading process is analyzed to explain the reason for the size effect of particle breakage.     

Segregation of particulate solids: Experiments and DEM simulations

Segregation of granular materials is a complex phenomenon, difficult to measure quantitatively and to predict. Discrete element method (DEM) can be a useful tool to predict segregation effects and to support the industrial design. In this context, a very challenging idea is the characterization of the granular solids to provide the key parameters needed for a successful DEM simulation of segregation processes. Rolling friction, sliding friction and the coefficient of restitution are the critical parameters to be studied. These microscopic simulation parameters are calibrated by comparing the macroscopic behavior of granular matter in standard bulk experiments, which have the advantage of being highly repeatable and reliable.An experimental method is presented to characterize free surface segregation. The effects of different particle properties, particularly, shape and size, on segregation of cohesionless materials were investigated. From the experiments, particle size demonstrated a stronger effect on segregation than particle shape. Finally, the corresponding DEM simulations of the segregation experiments were presented. The parameters obtained by calibration were validated by the comparison of the modeled segregation behavior with the experimental results. Thus, calibrated DEM simulations are capable of predicting segregation effects.     

DEM speedup: Stiffness effects on behavior of bulk material

A number of techniques exist for minimizing the computational cost of discrete element simulations (DEMs). One such method is a reduction of particle stiffness, which allows for bigger time steps and therefore fewer iterations in a simulation. However, the limits and drawbacks of this approach are still unclear, and may lead to invalid results. This paper investigates the effect of a stiffness reduction on bulk behavior by examining three case studies. Two cases demonstrate that particle stiffness can be reduced without affecting the bulk material behavior, whereas the third test shows that a stiffness reduction influences the bulk behavior.     

Scale effects on strength of geomaterials, case study: Coal

Scale effects on the strength of coal are studied using a discrete element model. The key point of the model is its capability to discriminate between the “strictly sample size” effect and the “Discrete Fracture Network (DFN) density” effect on the mechanical response. Simulations of true triaxial compression tests are carried out to identify their respective roles. The possible bias due to the discretization size distribution of the discrete element model is investigated in detail by considering low-resolution configurations. The model is shown to be capable of quantitatively reproducing the dependency of the maximum strength on the size of the sample. This relationship mainly relies on the DFN density. For all given sizes, as long as the DFN density remains constant with a uniform distribution or if discontinuities are absent in the considered medium, the maximum strength of the material remains constant.     

Oblique water entry of a wedge into waves with gravity effect

The hydrodynamic problem of a two dimensional wedge entering waves with gravity effect is analysed based on the incompressible velocity potential theory. The problem is solved through the boundary element method in the time domain. The stretched coordinate system in the spatial domain, which is based on the ratio of the Cartesian system in the physic space to the vertical distance the wedge has travelled into the water, is adopted based on the consideration that the decay of the effect of the impact away from the body is proportional to this ratio. The solution is sought for the total potential which includes both the incident and disturbed potentials, and decays towards the incident potential away from the body. A separate treatment at initial stage is used, in which the solution for the disturbed potential is sought to avoid the very large incident potential amplified by dividing the small travelled vertical distance of the wedge. The auxiliary function method is used to calculate the pressure on the body surface. Detailed results through the free surface elevation and the pressure distribution are provided to show the effect of the gravity and the wave, and their physical implications are discussed.     

A numerical study of the frontal region of gravity currents propagating on a free-slip boundary

We investigate numerically the three-dimensional flow near the head of gravity currents propagating along a free-slip boundary. The simulations show that two states are possible: a high-mixing state, where the flow departs from the analytic inviscid solution 0.5 channel heights downstream of the front location, and with characteristics similar to the ones observed for purely two-dimensional simulations; and a low-mixing state, where billows are weaker and appear further downstream. To access the high-mixing state, it is necessary to add a source of perturbation upstream of the head in the form of turbulence. At high values of the Reynolds number, the intensity of rms turbulent fluctuations necessary to switch to the high-mixing state is small (0.5% of the speed of propagation) and may explain why the low-mixing state has so far eluded experimental detection. In the low-mixing state, the flow becomes three-dimensional near the front due to centrifugal instabilities caused by the curved streamlines. This instability of the outer flow is coupled to overturning instabilities that develop within the heavy fluid in the head, and suppresses the formation of billows. This complex behavior, which feeds on the interplay of streamline curvature and stratification, should be considered a good model to understand how instabilities occur in other types of strongly nonlinear stratified flows.      

界面特性对短纤维金属基复合材料蠕变行为的影响

基于短纤维增强金属基复合材料(MMC)的单纤维三维模型(三相)，利用粘弹性有限元分析方法对影响金属基复合材料的蠕变行为的因素进行了较为系统的分析。研究中主要讨论了界面特性和纤维取向角对金属基复合材料的蠕变性能的影响。研究结果发现，界面特性诸如厚度、模量和应力指数都对纤维最大轴应力和稳定蠕变率产生影响：稳态蠕变率随界面模量的增大而逐渐减小，当高于基体模量时基本保持不变；纤维轴应力的变化与蠕变率正好相反。稳态蠕变率随界面厚度、应力指数的增加而增大；而轴应力则随之减小。同时不同的纤维取向也影响金属基复合材料蠕变时的轴应力分布和稳态蠕变率。     

Analysis of the movement behaviour of soil between subsoilers based on the discrete element method

The identification of the movement behaviour of soil in the area under the combined effect of two subsoilers (i.e., the area between two subsoilers) is one of the key issues in determining a reasonable inter-subsoiling shovel distance. The present study established a working model of subsoiling using the discrete element method (DEM). Based on this model and an indoor soil-bin experiment, the present study focused on investigating the micro-movement and macro-disturbed behaviour of soil in the area under the combined effect of two subsoilers. The results show the following. (1) The range of transverse and longitudinal disturbance of soil decreased with increasing distance between the soil and subsoiler. The range of disturbance of the soil in the shallow layer was the widest, followed by the range of disturbance of the soil in the middle layer and the range of disturbance of the soil in the deep layer. The simulated and experimental values of the mean displacement of the soil in the shallow layer (tracer blocks with a side length of 10 mm) were 34.81 mm and 34.55 mm, respectively (error: 0.75%). (2) The force on the soil particles in the deep layer was the greatest, followed by the force on the soil particles in the middle layer and the force on the soil particles in the shallow layer. The force on and the velocity of movement of the soil particles at different locations decreased with increasing distance between the soil and subsoiler. (3) The discrete element simulation could accurately simulate the disturbance process of the soil subjected to subsoiling. The sectional profiles of the disturbed soil obtained from the simulation and experiment were consistent with each other. The relative error between the simulated and experimental values of the soil looseness and the soil disturbance coefficient was 14.45% and 12.06%, respectively. Based on the DEM combined with an indoor soil-bin experiment, the present study determined the movement behaviour of the soil in the area under the combined effect of two subsoilers. The results of the present study can facilitate in-depth investigations of the subsoiling shovel–soil interaction and provide a basis for making decisions to optimise subsoiler arrangements.     

Investigation on behavior of crack penetration/deflection at interfaces in intelligent coating system

Based on the three-phase model, the propagation behavior of a matrix crack in an intelligent coating system is investigated by an energy criterion. The effect of the elastic mismatch parameters and the thickness of the interface layer on the ratio of the energy release rate for infinitesimal deflected and penetrated crack is evaluated with the finite element method. The results show that the ratio of the energy release rates strongly depends on the elastic mismatch α1between the substrate and the driving layer.It also strongly depends on the elastic mismatch α2between the driving layer and the sensing layer for a thinner driving layer when a primary crack reaches an interface between the substrate and the driving layer. Moreover, with the increase in the thickness of the driving layer, the dependence on α2gradually decreases. The experimental observation on aluminum alloys monitored with intelligent coating shows that the established model can better explain the behavior of matrix crack penetration and can be used in optimization design of intelligent coating.     

A micro-investigation on water bridge effects for unsaturated granular materials with constant water content by discrete element method

The most common state of surface soil is unsaturated. Changes in water content will substantially impact its strength, leading to geological and engineering catastrophes. This paper used LIGGGHTS software to simulate the water bridge effect of unsaturated granular materials with constant water content and verify the rationality of the simplification of the stress-force-fabric (SFF) relationship. The results showed that the capillary force was not isotropic, which was different from the previous study, thus it cannot be overlooked in the simplification of the SFF relationship. Moreover, the influence of water content on the macroscopic mechanical behavior of unsaturated granular materials was interpreted through the evolutions of coordination number, interparticle force, fabric and force anisotropy, and other microscopic parameters. Compared to the literature, we found that different water bridge models would not change the characteristics of the solid skeleton.     

Numerical investigation of the influence of shear band localization on the resonant behavior in the VHCF regime

The monitored resonant behavior of fatigue specimens of metastable austenitic stainless steel (AISI304) is correlated with its damage accumulation in the very high cycle fatigue (VHCF) regime. The resonant behavior is studied experimentally and shows a distinct transient characteristic. Microscopic examinations indicate that during VHCF a localized plastic deformation in shear bands arises on the specimen surface. Hence, this work focuses on the effect of damage accumulation in shear bands on the resonant behavior of AISI304 in the VHCF regime. A microstructural simulation model is proposed that takes into account specific mechanisms in shear bands proven by experimental results. The simulation model is solved numerically using the two-dimensional boundary element method and the resonant behavior is characterized by evaluating the force-displacement hysteresis loop. Simulation of shear bands agrees well with microscopic examinations and plastic deformation in shear bands influences the transient characteristic of the resonant behavior.     

Forces acting on water droplets falling in oil under the influence of an electric field: numerical predictions versus experimental observations

The combination of an electric field and a moderate turbulent flow is a promising technique for separating stable water–oil emulsions. Field-induced charges on the water droplets will cause adjacent droplets to align with the field and attract each other. The present work describes the forces that influence the kinematics of droplets falling in oil when exposed to an electric field. Mathematical models for these forces are presented and discussed with respect to a possible implementation in a multi-droplet Lagrangian framework. The droplet motion is mainly due to buoyancy, drag, film-drainage, and dipole–dipole forces. Attention is paid to internal circulations, non-ideal dipoles, and the effects of surface tension gradients.Experiments are performed to observe the behavior of a droplet falling onto a stationary one. The droplet is exposed to an electric field parallel to the direction of the droplet motion. The behavior of two falling water droplets exposed to an electric field perpendicular to the direction of their motion is also investigated until droplet coalescence. The droplet motion is recorded with a high-speed CMOS camera. The optical observations are compared with the results from numerical simulations where the governing equations for the droplet motion are solved by the RK45 (Runge Kutta) Fehlberg method with step-size control and low tolerances. Results, using different models, are compared and discussed in detail. A framework is otlined to describe the kinematics of both a falling rigid spherical particle and a fluid droplet under the influence of an electric field.     

均匀受压矩形管的屈曲后板组效应研究

本文根据势能驻值原理,建立了均匀受压矩形管的大挠度弹性屈曲理论,用于分析屈曲后相邻板件间的相互约束作用,即屈曲后板组效应。该方法通过引入拉格朗日乘子,使系统总势能取驻值的同时,形函数能满足一系列基本的,但非完备的边界条件;在此基础上采用增量法将非线性方程组线性化,从而确定给定荷载下矩形管的受力状态及变形。由于系统总势能是以解析式的形式给出,且仅需取有限的级数项就可达到满意的精度,故该半解析法具有计算效率高的特点。目前许多国家的钢结构设计规范中,在计算受压板件的有效宽度时,常采用板组约束系数来考虑板组效应。由于有效宽度法本身考虑了板的屈曲后强度,而约束系数多数却是建立在小挠度弹性屈曲理论上的,故有必要分析板件的屈曲后板组效应。本文详细讨论了矩形管的屈曲后板组效应,并与小挠度理论给出的计算结果进行比较,得出了均匀受压矩形管屈曲后板组效应减弱的结论。     

几何精确NURBS有限元中边界条件施加方式对精度影响的三维计算分析

非均匀有理B样条(NURBS)有限元法把计算机辅助几何设计(CAGD)中的NURBS几何构形方法与有限元方法有机结合起来,有效消除了有限元离散模型的几何误差,提高了计算精度。但是由于NURBS基函数不是插值函数,直接在控制节点上施加位移边界条件会引起较大误差。本文详细讨论了NURBS基函数的插值特性,在NURBS有限元分析中采用罚函数法施加位移边界条件,提高了收敛率和计算精度。结合典型三维弹性力学问题,对两种施加位移边界条件的方法进行了对比和分析。计算结果表明,直接施加位移边界条件会导致收敛率和精度的明显降低,而基于罚函数法的NURBS有限元分析则能达到最优收敛率,并具有更高的精度。     

A numerical study on the deformation and fracture modes of steel projectiles during Taylor bar impact tests

A heterogeneous material model based on macro-mechanical observations is proposed for simulation of fracture in steel projectiles during impact. A previous experimental study on the deformation and fracture of steel projectiles during Taylor bar impact tests resulted in a variety of failure modes. The accompanying material investigation showed that the materials used in the impact tests were heterogeneous on scales ranging from microstructure as investigated with SEM to variation in fracture strains from tensile tests. A normal distribution is employed to achieve a heterogeneous numerical model with respect to the fracture properties. The proposed material model is calibrated based on the tensile tests, and then used to independently simulate the Taylor bar impact tests. A preliminary investigation showed that the simulations are sensitive to assumptions regarding the anvil behaviour and friction properties. A flexible anvil and a yield-limited friction law are shown to be necessary to correctly reproduce the experimental behaviour. The proposed model is then shown to be capable of correctly reproducing all fracture modes but one, and also predict critical impact velocities for projectile fracture with reasonable accuracy. Fragmentation at velocities above the critical velocity is not well reproduced due to excessive element erosion. Measures to make the element erosion process more physical are proposed and discussed with their respective drawbacks. The use of a simple fracture criterion in combination with an element erosion technique accentuates the effect of distributing the fracture parameter.     

A numerical study on flow through the spiral casing of a hydraulic turbine

Flow through the spiral casing of a hydraulic turbine was analyzed. Reynolds averaged Navier–Stokes equations were solved using a finite element method. The physical domain was divided into a number of hexahedral elements which are isoparametrically mapped onto standard cubic elements. Numerical integration for the unsteady momentum equation is performed over such hexahedral elements to obtain a provisional velocity field. Compliance with the mass conservation equation and determination of the pressure correction are accomplished through an iterative procedure. The velocity distribution inside the spiral casing corroborates the results available in literature. The static pressure at the midplane generally decreases from the outside wall towards the exit of the spiral casing. © 1998 John Wiley & Sons, Ltd.     

A micro mechanical study on failure initiation of dual phase steels under tension using single crystal plasticity model

Both experimental and numerical methods were employed to investigate the mechanism of failure in dual phase steels. The tensile test was interrupted in different steps to capture the mechanism of void initiation and void growth during material failure. The results can be considered as a first report for the commercial DP800 steel. Numerical simulations, which were carried out using the real micro-structure, are able to predict the void initiation in the material. In addition, through the numerical simulation a new understanding of the deformation localization was gained. Deformation localization, which causes severely deformed regions in the material, is most probably the main source of rupture in the final stages of the failure. In the SEM micrographs of the material after failure some voids are observable which can validate the results obtained by the simulation.