Influence of heterogeneity on rock strength and stiffness using discrete element method and parallel bond model

The particulate discrete element method(DEM) can be employed to capture the response of rock,provided that appropriate bonding models are used to cement the particles to each other.Simulations of laboratory tests are important to establish the extent to which those models can capture realistic rock behaviors.Hitherto the focus in such comparison studies has either been on homogeneous specimens or use of two-dimensional(2D) models.In situ rock formations are often heterogeneous,thus exploring the ability of this type of models to capture heterogeneous material behavior is important to facilitate their use in design analysis.In situ stress states are basically three-dimensional(3D),and therefore it is important to develop 3D models for this purpose.This paper revisits an earlier experimental study on heterogeneous specimens,of which the relative proportions of weaker material(siltstone) and stronger,harder material(sandstone) were varied in a controlled manner.Using a 3D DEM model with the parallel bond model,virtual heterogeneous specimens were created.The overall responses in terms of variations in strength and stiffness with different percentages of weaker material(siltstone) were shown to agree with the experimental observations.There was also a good qualitative agreement in the failure patterns observed in the experiments and the simulations,suggesting that the DEM data enabled analysis of the initiation of localizations and micro fractures in the specimens.

Kekulé-based Valence Bond Model. I. The Ground-state Properties of Conjugated π-Systems

The Kekulé-based valence bond (VB) method, in which the VB model is solved using covalent Kekulé structures as basis functions, is justified in the present work. This method is demonstrated to provide satisfactory descriptions for resonance energies and bond lengths of benzenoid hydrocarbons, being in good agreement with SCF-MO and experimental results. In addition, an alternative way of discussing characters of localized substructures within a polycyclic benzenoid system is suggested based upon such simplified VB calculations. Finally, the symmetries of VB ground states for nonalternant conjugated systems are also illustrated to be obtainable through these calculations, presenting very useful information for understanding the chemical behaviors of some nonalternant conjugated molecules.

Kekulé-based Valence Bond Model. II. Diels-Alder Reactivity of Polycyclic Aromatic Hydrocarbons

The Kekulé-based valence bond (VB) method was employed to study the ground state properties of 52 polycyclic aromatic hydrocarbons. The reactivity indices defined upon our VB calculations were demonstrated to be capable of quantitatively interpreting the second order rate constants of the Diels-Alder reactions. The qualitative trends of the reactivities of many homologous series can be also explained based on the local aromaticity index defined in this work.

Theoretical Model of Transformation Superlastic Diffusion Bonding for Eutectoid Steel

Based on current theories of diffusion and creep cavity closure at high temperature, a theoretical analysis of phase transformation diffusion bonding for T8/T8 eutectoid steel is carried out. The diffusion bonding is mainly described as two-stage process: Ⅰ The interfacial cavity with shape change from diamond to cylinder.Ⅱ The radius of the cylindrical cavity are reduced and eliminated gradually. A new theoretical model is established for the process of transformation superplastic diffusion bonding (TSDB) on the basis of a theoretical model for isothermal superplastic diffusion. The model can predict the bonding quality which is affected by technological parameters, such as limit cycling temperature, the compressive stress, the numbers of thermal cycles and temperature cycling through the phase transformation in the thermal cycling and so on. Results show that the maximum temperature, the compressive stress, the numbers of thermal cycles and the rate of temperature changing speed in the thermal cycling have an important influence on TSDB process. Meanwhile, reasonable technological parameters chosen from theoretical analysis is in good agreement with those obtained from experimental results.

DEM investigation of weathered rocks using a novel bond contact model

The distinct element method（DEM） incorporated with a novel bond contact model was applied in this paper to shed light on the microscopic physical origin of macroscopic behaviors of weathered rock, and to achieve the changing laws of microscopic parameters from observed decaying properties of rocks during weathering. The changing laws of macroscopic mechanical properties of typical rocks were summarized based on the existing research achievements. Parametric simulations were then conducted to analyze the relationships between macroscopic and microscopic parameters, and to derive the changing laws of microscopic parameters for the DEM model. Equipped with the microscopic weathering laws, a series of DEM simulations of basic laboratory tests on weathered rock samples was performed in comparison with analytical solutions. The results reveal that the relationships between macroscopic and microscopic parameters of rocks against the weathering period can be successfully attained by parametric simulations. In addition, weathering has a significant impact on both stressestrain relationship and failure pattern of rocks.

Reducing the anisotropy of a Brazilian disc generated in a bonded-particle model

The Brazilian test is a widely used method for determining the tensile strength of rocks and for calibrating parameters in bondedparticle models（BPMs）. In previous studies, the Brazilian disc has typically been trimmed from a compacted rectangular specimen. The present study shows that different tensile strength values are obtained depending on the compressive loading direction. Several measures are proposed to reduce the anisotropy of the disc. The results reveal that the anisotropy of the disc is significantly influenced by the compactibility of the specimen from which it is trimmed. A new method is proposed in which the Brazilian disc is directly generated with a particle boundary, effectively reducing the anisotropy. The stiffness（particle and bond） and strength（bond） of the boundary are set at less than and greater than those of the disc assembly, respectively,which significantly decreases the stress concentration at the boundary contacts and prevents breakage of the boundary particle bonds. This leads to a significant reduction in the anisotropy of the disc and the discreteness of the tensile strength. This method is more suitable for carrying out a realistic Brazilian test for homogeneous rock-like material in the BPM.

Critical behaviours and magnetic properties of three-dimensional bond and anisotropy dilution Blume-Capel model in the presence of an applied field

This paper studies the critical behaviours and magnetic properties of three-dimensional bond and anisotropy dilution Blume-Capel model （BCM） in the presence of an applied field within the effective field theory. The trajectory of tricritical point, reentrant transitions and degenerate patterns of anisotropy are obtained both for the bond and the anisotropy dilutions. The global phase diagrams demonstrate unusually reentrant phenomena. The temperature dependences of magnetization curves undergo remarkable spin glass behaviour at low temperatures, and transform from ferromagnetism to paramagnetism at high temperature in applied fields. Temperature dependence of magnetic susceptibility curve is in qualitative agreement with experimental result.

A novel diffusion model considering curvature radius at the bonding interface in a titanium/steel explosive clad plate

This article introduces an element diffusion behavior model for a titanium/steel explosive clad plate characterized by a typical curved interface during the heat-treatment process. A series of heat-treatment experiments were conducted in the temperature range from 750℃ to 950℃, and the effects of heat-treatment parameters on the microstructural evolution and diffusion behavior were investigated by optical microscopy, scanning electron microscopy, X-ray diffraction analysis, and electron-probe microanalysis. Carbon atoms within the steel matrix were observed to diffuse toward the titanium matrix and to aggregate at the bonding interface at 850℃ or lower; in contrast, when the temperature exceeded 850℃, the mutual diffusion of Ti and Fe occurred, along with the diffusion of C atoms, resulting in the for- marion of Ti-Fe intermetallics （Fe2Ti/FeTi）. The diffusion distances of C, Ti, and Fe atoms increased with increasing heating temperature and/or holding time. On the basis of this diffusion behavior, a novel diffusion model was proposed. This model considers the effects of various factors, including the curvature radius of the curved interface, the diffusion coefficient, the heating temperature, and the holding rime. The experimental results show good agreement with the calculated values. The proposed model could clearly provide a general prediction of the elements＇ diffusion at both straight and curved interfaces.

A MULTISCALE MECHANICAL MODEL FOR MATERIALS BASED ON VIRTUAL INTERNAL BOND THEORY

Only two macroscopic parameters are needed to describe the mechanical properties of linear elastic solids, i.e. the Poisson＇s ratio and Young＇s modulus. Correspondingly, there should be two microscopic parameters to determine the mechanical properties of material if the macroscopic mechanical properties of linear elastic solids are derived from the microscopic level. Enlightened by this idea, a multiscale mechanical model for material, the virtual multi-dimensional internal bonds （VMIB） model, is proposed by incorporating a shear bond into the virtual internal bond （VIB） model. By this modification, the VMIB model associates the macro mechanical properties of material with the microscopic mechanical properties of discrete structure and the corresponding relationship between micro and macro parameters is derived. The tensor quality of the energy density function, which contains coordinate vector, is mathematically proved. From the point of view of VMIB, the macroscopic nonlinear behaviors of material could be attributed to the evolution of virtual bond distribution density induced by the imposed deformation. With this theoretical hypothesis, as an application example, a uniaxial compressive failure of brittle material is simulated. Good agreement between the experimental results and the simulated ones is found.

Integration of three-dimensional continuum model and two-dimensional bonded block model for studying the damage process in a granite pillar at the Creighton Mine,Sudbury,Canada

Bonded blockmodel(BBM)has shownpotential in replicating rockmass behavior aswell as the rockesupport interactionmechanism,but their practical application is limited totwo dimensions due to the high associated computational demand.To allow for the use of BBM in simulating three-dimensional(3D)problems,this study proposes an integrated 3D continuumetwo-dimensional(2D)discontinuum approach,in context of rock pillars.A cross-section of a granite pillar was simulated using a BBM with a load path from a calibrated mine-scale FLAC^(3D)model.Pillar support as employed in the mine was also incorporated in different stages during the simulation.Themodel was calibrated by varying the input parameters until the displacements at six locations within the pillarmatchedthosemeasuredby amulti-point borehole extensometer(MPBX)inthe field.The calibratedmodel was subsequently used to understand how the support and load path influenced the damage evolution in the pillar.The shear component of the load pathwas found to have amajor effect on the severity and extent of the damaged regions.When the support density was increased in the model,the lateral displacements along the pillar walls were significantly suppressed in a somewhat unpredictable manner.Thiswas explained by the interaction between the supports and the damaged regions at the corners,which ultimately modified the stresses along the pillar periphery.The amount of displacement reduction obtained by increasing the support density illustrates the potential of BBMto be used as a support design tool.

Universal critical properties of the Eulerian bond-cubic model

We investigate the Eulerian bond-cubic model on the square lattice by means of Monte Carlo simulations, using an efficient cluster algorithm and a finite-size scaling analysis. The critical points and four critical exponents of the model are determined for several values of n. Two of the exponents are fractal dimensions, which are obtained numerically for the first time. Our results are consistent with the Coulomb gas predictions for the critical O（n） branch for n 〈 2 and the results obtained by previous transfer matrix calculations. For n = 2, we find that the thermal exponent, the magnetic exponent and the fractal dimension of the largest critical Eulerian bond component are different from those of the critical 0（2） loop model. These results confirm that the cubic anisotropy is marginal at n = 2 but irrelevant for n〈2.

Structural bonding-breakage constitutive model for natural unsaturated clayey soils

The natural clayey soils are usually structural and unsaturated,which makes their mechanical properties quite different from the remolded saturated soils.A structural constitutive model is proposed to simulate the bonding-breakage micro-mechanism.In this model,the unsaturated soil element is divided into a cementation element and a friction element according to the binary medium theory,and the stress-strain coordination for these two elements is obtained. The cementation element is regarded as elastic,whereas the friction element is regarded as elastoplastic which can be described with the Gallipoli＇s model.The theoretical formulation is verified with the comparative experiments of isotropic compressions on the saturated and unsaturated structural soils.Parametric analyses of the effects of damage variables on the model predictions are further carried out,which show that breakage deformation of natural clayey soils increases with the rising amount of initial defects.

Investigation of Highly Designable Dented Structures in HP Model with Hydrogen Bond Energy

Some highly designable protein structures have dented on the surface of their native structures, and are not full compactly folded. According to hydrophobic-polar （HP） model the most designable structures are full compactly folded. To investigate the designability of the dented structures, we introduce the hydrogen bond energy in the secondary structures by using the secondary-structure-favored HP model proposed by Ou-yang etc. The result shows that the average designability increases with the strength of the hydrogen bond. The designabilities of the structures with same dented shape increase exponentially with the number of secondary structure sites. The dented structures can have the highest designabilities for a certain value of hydrogen bond energy density.

Spectroscopic Characterization, Molecular Modeling and DFT/TD-DFT/PCM Calculations of Novel Hydrogen-Bonded Charge Transfer Complex between Chloranilic Acid and 2-Amino-4,6-Dimethylpyridine

A charge transfer hydrogen bonded complex between the electron donor (proton acceptor) 2-amino-4,6-dimethylpyridine with the electron acceptor (proton donor) chloranilic acid has been synthesized and studied experimentally and theoretically. The stability constant recorded high values indicating the high stability of the formed complex. In chloroform, ethanol, methanol and acetonitrile were found the stoichiometric ratio 1:1. The solid complex was prepared and characterized by different spectroscopy techniques. FTIR, 1H and 13C NMR studies supported the presence of proton and charge transfers in the formed complex. Complemented with experimental results, molecular modelling using the density functional theory (DFT) calculations was carried out in the gas, chloroform and methanol phases where the existence of charge and hydrogen transfers. Finally, a good consistency between experimental and theoretical calculations was found confirming that the applied basis set is the suitable one for the system under investigation.

A Study on Modifying the Calculation Model of Valid Opening Size of Heat-bonded Nonwoven Fabrics

It has been found that there are marked errors in the value of valid opening size of heat-bonded nonwoven fabrics between theoretical calculations and engineering measurements. A new modified theoretical model is advanced in this paper. The equivalent diameter of the pore of a fibre web is used to calculate the valid opening size instead of the maximum diameter of inscribed circle used, because the fibres in practical fibre webs are flexible elastomers with definite diameters and the pore of fibre web may produce deformation in screening teat and engineering usage. The results show that the theoretical calculations coincide well with the engineering measurements. This method offers a theoretical basis for computer simulation to the performance of filters of heatbonded nonwoven fabrics.

基于Bond Graph的风力发电机建模

简单介绍了Bond Graph的状态变量、标准元件和建模方法等基本概念。基于Bond Graph能深入描述系统内部变化过程,对复杂系统物理模型研究更具优势,将其引入电力系统,在笼型三相异步风力发电机数学模型的基础上,提出基于Bond Graph理论的风力发电机建模与仿真,重点研究分析了发电机abc-αβ0坐标变换的Bond Graph模型,以及描述发电机定子和转子之间电磁联系的惯性场、电量与机械量转换关系以及描述发电机机械转矩的Bond Graph模型,在此基础上得出完整的风力发电机模型,并利用20-Sim软件进行了仿真,仿真结果验证了该模型的正确性。

STUDIES ON THERMODYNAMICAL PROPERTIES OF RANDOM-BOND ISING MODEL IN A TRANSVERSE FIELD WITH CEA AND DPIR

A effective approximate scheme which is combined by cluster with the discrelized path-integral representation (DPIR) is used in the study on the random-bond Ising model in a transverse field (RTIM). The critical thermodynamical properties, such as the critical temperature, the critical transverse field, the average magnetization ,the susceptibility and the special heat atc.. are calculated, And some results have been improved.

基于bond-graphs的机电系统建模和仿真

研究了多领域机电系统的键合图建模方法,在此基础上采用20-sim软件包对直流电机伺服系统进行建模和仿真,设计了LQG控制器。建模和仿真过程表明,键合图法建模简练、实用,是一种理想的多领域机电系统图形建模方法,其参数与物理组件直接相关,可广泛应用于多领域机电系统的建模和仿真。

多体动力学的键合图表达及其在Modelica中的实现

给出了多体动力学第一类拉格朗日方程的键合图表达,并采用键合图的Modelica库在Dymola中对示例进行了建模和仿真,结果表明,多体动力学拉格朗日方程的键合图表示是非常简单的,清晰地表明了拉格朗日乘子的物理含义,可将其容易地扩展到柔性多体动力学领域,是一种非常合适的多体动力学表达方法。

基于离散元的包膜肥料Bonding模型参数标定

包膜肥料是在粒状水溶性肥料表面涂覆半透水性或不透水性物质,养分通过包膜的微孔、缝隙慢慢释放出来,节肥增效作用显著。包膜肥料的养分释放特性与包膜层材料、结构紧密相关,目前常用的排肥器在排施肥料过程中会对肥料颗粒造成不同程度的机械损伤,导致包膜层破坏。为设计适用于包膜肥料无损排施的排肥器,同时缩短研发周期,采用离散元软件中的Bonding模型建立肥料颗粒仿真模型。为提高仿真精度,需对Bonding模型进行参数标定。首先通过单轴压缩试验得到包膜肥料颗粒的实际极限破碎位移和极限破碎载荷,在离散元软件中以此为目标依次通过PlacketBurman试验、Steepest ascent试验和BoxBehnken试验确定最优的Bonding模型参数组合。最优条件下单轴压缩试验表明,极限破碎位移和极限破碎载荷与实际值的相对误差分别为0.222%、0.554%。借助外槽轮排肥器验证所得标定参数组合的可靠性,以肥料颗粒破碎率为指标,得到实际与仿真中肥料颗粒破碎率相对误差不大于11.40%,满足施肥机械设计参数优化需求,可为研究包膜肥料颗粒机械破碎机理、优化设计无损排施的新型排肥器提供参考。