Investigation of vacancy defects effects on the buckling behavior of SWCNTs via a structural mechanics approach

In this paper, the influence of various vacancy defects on the critical buckling loads and strains in carbon nanotubes under axial compression is investigated via a new structural model in ABAQUS software. The necessity of desirable conditions and expensive tests for experimental methods, in addition to the time expenditure required for atomic simulations, are the motivation for this work, which, in addition to yielding accurate results, avoids the obstacles of the previous methods. In fact, this model is a combination of other structural models designed to eliminate the deficiencies inherent in individual approaches. Because the present model is constructed in the CAE space of ABAQUS, there is no need to program for different loading and boundary conditions. A nonlinear connector is considered for modeling of stretching and torsional interactions, and a nonlinear spring is used for modeling of the angle variation interactions. A Morse potential is employed for stretching and bending potentials, and a periodic type of bond torsion is used for torsion interactions. The effect of different types of vacancy defects at various locations on the critical buckling loads and strains is studied for zigzag and armchair nanotubes with various aspect ratios (Length/Diameter). Comparison of our results with those of buckling of shells with cutouts indicates that vacancy defects in the carbon nanotubes can most likely be modeled as cutouts of the shells. Finally, results of the present structural model are compared with those from molecular dynamics (MD) simulation and show good agreement between our model and the MD model.     

Dynamic buckling of discrete structural systems under combined step and static loads

The dynamic instability of discrete, elastic, multiple degree of freedom (d.o.f.) systems under a combination of static and step loads is studied. Conservative, autonomous and holonomic systems are considered, in which the associated static response is a bifurcation under one load parameter, and a limit point under the second parameter. A review of different criteria and algorithms obtained from them for the computation of dynamic buckling loads is first presented, followed by a procedure derived from previous investigations on one d.o.f. systems. The different procedures are applied to a two d.o.f. problem under axial and lateral load, with quadratic and cubic non-linearities. The response in time shows that the system oscillates about the static equilibrium position before dynamic buckling is reached, with the kinetic energy tending to zero as assumed in the static (energy) procedures of stability.     

Fatigue crack growth of cable steel wires in a suspension bridge: Multiscaling and mesoscopic fracture mechanics

Intrinsically, fatigue failure problem is a typical multiscale problem because a fatigue failure process deals with the fatigue crack growth from microscale to macroscale that passes two different scales. Both the microscopic and macroscopic effects in geometry and material property would affect the fatigue behaviors of structural components. Classical continuum mechanics has inability to treat such a multiscale problem since it excludes the scale effect from the beginning by introducing the continuity and homogeneity assumptions which blot out the discontinuity and inhomogeneity of materials at the microscopic scale. The main obstacle here is the link between the microscopic and macroscopic scale. It has to divide a continuous fatigue process into two parts which are analyzed respectively by different approaches. The first is so called as the fatigue crack initiation period and the second as the fatigue crack propagation period. Now the problem can be solved by application of the mesoscopic fracture mechanics theories developed in the recent years which focus on the link between different scales such as nano-, micro- and macro-scale.On the physical background of the problem, a restraining stress zone that can describe the material damaging process from micro to macro is then introduced and a macro/micro dual scale edge crack model is thus established. The expression of the macro/micro dual scale strain energy density factor is obtained which serves as a governing quantity for the fatigue crack growth. A multiscaling formulation for the fatigue crack growth is systematically developed. This is a main contribution to the fundamental theories for fatigue problem in this work. There prevail three basic parameters μ^∗, σ^∗ and d^∗ in the proposed approach. They can take both the microscopic and macroscopic factors in geometry and material property into account. Note that μ^∗, σ^∗ and d^∗ stand respectively for the ratio of microscopic to macroscopic shear modulus, the ratio of restraining stress to applied stress and the ratio of microvoid size ahead of crack tip to the characteristic length of material microstructure.To illustrate the proposed multiscale approach, Hangzhou Jiangdong Bridge is selected to perform the numerical computations. The bridge locates at Hangzhou, the capital of Zhejiang Province of China. It is a self-anchored suspension bridge on the Qiantang River. The cables are made of 109 parallel steel wires in the diameter of 7 mm. Cable forces are calculated by finite element method in the service period with and without traffic load. Two parameters α and β are introduced to account for the additional tightening and loosening effects of cables in two different ways. The fatigue crack growth rate coefficient C₀ is determined from the fatigue experimental result. It can be concluded from numerical results that the size of initial microscopic defects is a dominant factor for the fatigue life of steel wires. In general, the tightening effect of cables would decrease the fatigue life while the loosening effect would impede the fatigue crack growth. However, the result can be reversed in some particular conditions. Moreover, the different evolution modes of three basic parameters μ^∗, σ^∗ and d^∗ actually have the different influences on the fatigue crack growth behavior of steel wires. Finally the methodology developed in this work can apply to all cracking-induced failure problems of polycrystal materials, not only fatigue, but also creep rupture and cracking under both static and dynamic load and so on.     

Fracture of granular materials composed of arbitrary grain shapes: A new cohesive interaction model

Discrete Element Methods (DEM) are a useful tool to model the fracture of cohesive granular materials. For this kind of application, simple particle shapes (discs in 2D, spheres in 3D) are usually employed. However, dealing with more general particle shapes allows to account for the natural heterogeneity of grains inside real materials. We present a discrete model allowing to mimic cohesion between contacting or non-contacting particles whatever their shape in 2D and 3D. The cohesive interactions are made of cohesion points placed on interacting particles, with the aim of representing a cohesive phase lying between the grains. Contact situations are solved according to unilateral contact and Coulomb friction laws. In order to test the developed model, 2D uniaxial compression simulations are performed. Numerical results show the ability of the model to mimic the macroscopic behavior of an aggregate grain subject to axial compression, as well as fracture initiation and propagation. A study of the influence of model and sample parameters provides important information on the ability of the model to reproduce various behaviors.     

Evolution of functional connectivity in contact and force chain networks: Feature vectors,k-cores and minimal cycles

We analyze the rheological response, i.e., fabric and contact force evolution, of dense granular materials from a complex networks perspective. The strain evolution of three classes of subnetworks, i.e., k-cores, minimal cycles and force chain networks, elucidates the breakdown of functional connectivity and structure in the lead up to and during failure. Feature vectors and dynamics occurring in such networks in three different biaxially compressed two-dimensional samples reveal some common aspects which are suggestive of an intrinsic structural hierarchy in granular networks – while differences shed light on the influence of confining pressure and interparticle rolling resistance on the evolution of these networks both at the mesoscopic as well as macroscopic levels.     

Automatic extraction method of force chain information and its application in the flow photoelastic experiment of granular matter

The force chain is the core of the multi-scale analysis of granular matter. Accurately extracting the force chain information among particles is of great significance to the study of particle mechanics and geological hazards caused by particle flow. However, in the photoelastic experiment, the precise identification of the branching points of force chains has not been effectively realized. Therefore, this study proposes an automatic extraction method of force chain key information. First, based on the Hough transform and the Euclidean distance, a particle geometric information identification model is established and geometric information such as particle circle center coordinates, radius, contact point location, and contact angle is extracted. Then, a particle contact force information identification model is established following the color gradient mean square method. The model realizes the rapid calibration and extraction of a large number of particle media contact force information. Next, combined with the force chain composition criterion and its quasilinear feature, an automatic extraction method of force chain information is established, which solves the problem of the accurate identification of the force chain branch points. Finally, in the photoelastic experiment of ore drawing from a single drawpoint, the automatic extraction method of force chain information is verified. The results show that the macroscopic distribution of force chains during ore drawing from a single drawpoint is left–right symmetrical. Strong force chains are mostly located on the two sides of the model but in small numbers and they mainly develop vertically. Additionally, the ends are mostly in a combination of Y and inverted Y shapes, while the middle is mostly quasilinear. Weak force chains are abundant and mostly distributed in the middle of the model, and develop in different directions. The proposed extraction method accurately extracts the force chain network from the photoelastic experiment images and dynamically characterizes the force chains of granular matter, which has significant advantages in particle geometry information extraction, force chain branch point discrimination, force chain retrieval, and force chain distribution and its azimuthal characterization. The results provide a scientific basis for studying the macroscopic and microscopic mechanical parameters of granular matter.     

A hybrid force model to estimate the dynamics of curved legs in granular material

Robot locomotion on rigid terrain or in fluids has been studied to a large extent. The locomotion dynamics on or within soft substrates such as granular material (GM) has not been fully investigated. This paper proposes a hybrid force model to simulate and evaluate the locomotion performance of a legged terrestrial robot in GM. The model incorporates an improved Resistive Force Theory (RFT) model and a failure-based model. The improved RFT model integrates the force components of individual leg elements over the curved leg portion submerged in GM at any moment during a full period of leg rotation. The failure-based model is applied in a bar drag model to yield the normal and the lateral forces of the individual RFT elements as functions of the locomotion depth and speed. The hybrid model is verified by the coincidence between the theoretical predictions and the experimental results. The hybrid model is used to analyze the effects of angular velocity and leg shape with high precision and can guide the design of the legs with any profiles. Our study reveals that the interactions between locomotor and substrate are determined by the locomotor structural characteristics, the nature of the substrate, and the control strategy.     

Temporal correlation of force and position in granular materials

We investigate the quasi-static mechanical response of dense granular materials under biaxial compressions by using discrete element simulation. The internal force network and its evolution are observed for different strains. Our results show that correlation of force and position appropriately characterize the bulk response and volumetric strain.     

Multi-scale kinetic description of granular clusters: invariance,balance, and temperature

We discuss a multi-scale continuum representation of bodies made of several mass particles flowing independently each other. From an invariance procedure and a nonstandard balance of inertial actions, we derive the balance equations introduced in earlier work directly in pointwise form, essentially on the basis of physical plausibility. In this way, we analyze their foundations. Then, we propose a Boltzmann-type equation for the distribution of kinetic energies within control volumes in space and indicate how such a distribution allows us to propose a definition of (granular) temperature along processes far from equilibrium.     

Numerical studies of transportation of granular material by a pin-point blast using models of the mechanics of continuous and granular media

Mathematical models for numerical studies of transportation of a mass of loose granular material during occurrence of a series of deep gas-dynamic ejections are developed using methods of the mechanics of continuous and granular media. Features of the kinematics and dynamics of development of this phenomenon are analyzed. Results of a numerical experiment and recommendations on use of the models in studies of specific transportation regimes are given. Mozhaisk Military Space-Engineering Academy, St. Petersburg 197082. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 1, pp. 3–14, January–February, 1998.     

Modeling of the lag in the mechanics of a chain of links

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 27, No. 5, pp. 110–118, May, 1991.     

从动力学角度看力系等效与简化

力系等效与简化本质上是动力学问题,但在理论力学教学和教材中习惯于放在刚体静力学部分,并且通常仅限于研究作用在刚体上的力系.本文从动力学角度研究作用在一般质点系上的力系,将刚体作为质点系的特例,用多种简洁的途径得到理论力学中关于力系等效、力系简化的全部结论.自1996年起在清华大学面向工科院系开设的理论力学课程中进行了教学实践,取得了很好的效果.     

Measurement techniques of grain motion and inter-grain structures in dense granular materials

颗粒材料由大量粗颗粒堆积形成, 是复杂的多体相互作用体系, 呈现出颗粒尺度的结构不均匀和动力学不均匀性的基本特征, 这决定了颗粒材料具有很多独特的宏观性质. 借鉴学科历史的发展途径, 基于统计力学, 从颗粒结构和动力学开始建立颗粒材料体系的宏观连续介质力学理论框架是必然途径.但是, 颗粒材料的基本特征决定了从基本理论到实验手段上, 表征与建立颗粒材料结构与性能的相关性都极其困难.这是由于现有测试分析手段所描述的颗粒系统组织结构过于简单化, 缺乏对颗粒结构和动力学的真正认识, 从而制约了颗粒物质研究的发展.因此, 开展颗粒体系结构和动力学性质的测量, 是理解和认识颗粒材料重要物理和力学问题的基础和依据.笔者来自不同的科研院所, 近十年来开展了颗粒体系结构和动力学性质的测量研究, 主要集中于以下两个方向: (1)数字图像测速法、散斑能见度光谱法和X射线- CT等非侵入式测量技术在颗粒运动方面的应用; (2)体积响应谱、力学谱(有效质量和内耗等)和声速测量技术等直接或间接测量颗粒接触力和颗粒结构技术.本文综述了这些实验手段的基本原理及其特点、取得的主要成果, 以及国际最新进展和困难. 最后是对全文的总结, 结合笔者开展测量的经验和教训, 提出了自己的看法, 并试图展望颗粒材料测量技术研究的前景.     

密集颗粒体系的颗粒运动及结构测量技术

颗粒材料由大量粗颗粒堆积形成, 是复杂的多体相互作用体系, 呈现出颗粒尺度的结构不均匀和动力学不均匀性的基本特征, 这决定了颗粒材料具有很多独特的宏观性质. 借鉴学科历史的发展途径, 基于统计力学, 从颗粒结构和动力学开始建立颗粒材料体系的宏观连续介质力学理论框架是必然途径.但是, 颗粒材料的基本特征决定了从基本理论到实验手段上, 表征与建立颗粒材料结构与性能的相关性都极其困难.这是由于现有测试分析手段所描述的颗粒系统组织结构过于简单化, 缺乏对颗粒结构和动力学的真正认识, 从而制约了颗粒物质研究的发展.因此, 开展颗粒体系结构和动力学性质的测量, 是理解和认识颗粒材料重要物理和力学问题的基础和依据.笔者来自不同的科研院所, 近十年来开展了颗粒体系结构和动力学性质的测量研究, 主要集中于以下两个方向: (1)数字图像测速法、散斑能见度光谱法和X射线- CT等非侵入式测量技术在颗粒运动方面的应用; (2)体积响应谱、力学谱(有效质量和内耗等)和声速测量技术等直接或间接测量颗粒接触力和颗粒结构技术.本文综述了这些实验手段的基本原理及其特点、取得的主要成果, 以及国际最新进展和困难. 最后是对全文的总结, 结合笔者开展测量的经验和教训, 提出了自己的看法, 并试图展望颗粒材料测量技术研究的前景.      

Occurrence of gradual resonance in a finite-length granular chain driven by harmonic vibration

This study presents numerical simulations of the resonance of a finite-length granular chain of dissipative grains driven by a harmonically vibrated tube. Multiple gradual resonant modes, namely non-resonance mode, partial-resonance mode, and complete-resonance mode, are identified. With a fixed vibration frequency, increasing vibration acceleration leads to a one-one-one increase in the number of grains participating in resonance, which is equal to the number of grain-wall collisions in a vibration period. Compared with the characteristic time of the grain–grain and the grain–wall collisions, the time of free flight plays a dominant role in grain motion. This situation results in the occurrence of large opening separation gaps between the grains and independent grain–grain and grain–wall collisions. A general master equation that describes the dependence of the system energy on the length of the granular chain and the number of grain–wall collisions is established, and it is in good agreement with the simulation results. We observe a gradual step-jump increase in system energy when the vibration acceleration is continuously increased, which is dedicated to an individual energy injection. The phase diagrams in the spaces of packing density and vibration acceleration, chain length and vibration acceleration show that shorter granular chain and larger packing density favor the occurrence of complete-resonance mode.