用3D离散元实现Ⅰ/Ⅱ型拉剪混合断裂的模拟

将变形体离散元分别与弥散式旋转裂缝模型和分离式裂缝模型耦合起来,采用上述两种非线性断裂力学模型分析了混凝土、岩石等准脆性材料的Ⅰ/Ⅱ型拉剪混合模式的开裂行为,以实现从连续介质到非连续介质转化的数值模拟。基于变形体离散元方法的界面接触本构关系提出了混凝土Ⅰ/Ⅱ混合型开裂的拉剪分区开裂准则;基于缝面法向开度增大对刚度强度的逐渐折减实现了界面裂缝扩展的模拟。作为数值验证,通过单边切口非对称三点弯梁试验的数值计算与试验结果对比,表明两种断裂力学模型均能够合理预测裂缝的起裂和扩展,在混合形式的荷载条件下,裂缝通常以Ⅰ/Ⅱ型拉剪混合模式起裂,而后以Ⅰ型为控制方式稳定扩展。文末指出,基于离散单元法的分离裂缝模型能够实现系统在外载作用下破坏全过程仿真。     

考虑弹塑性本构的三维模态变形体离散元方法断裂模拟

三维模态变形体离散元(3MDEM)是针对离散块体系统在小应变、有限位移、有限转动条件下,用变形模态模拟块体变形,经过严格推导建立的一种离散元方法.该文在3MDEM平台实现对结构从弹性、到塑性再到断裂破坏的连续非连续全过程模拟.鉴于传统的接触破坏准则在塑性计算中的缺陷,该文提出基于塑性应变的接触破坏判断准则,并采用双块体...     

湿热环境对碳纳米管复合材料界面应力传递的影响

基于碳纳米管的热膨胀系数及弹性模量分别为温度变化的函数,基体的热、湿膨胀系数及弹性模量分别为温度变化和湿度变化的函数,应用连续介质力学的经典弹性壳理论及传统纤维拉拔模型,分析了湿热环境对碳纳米管复合材料界面应力传递的影响。数值计算表明,湿度、温度的效应及碳纳米管的层数等参数对界面应力的传递均有显著影响。     

基于离散宏单元的砌体结构高效非线性分析方法

砌体结构由力学性能不同的块体和砂浆构成，材料的各向异性使结构非线性行为体现出高度复杂性。砌体结构非线性分析模型主要包括分离式和整体式两种:分离式模型将块体、砂浆及二者粘结界面分开建模，可以精细化揭示砌体非线性行为和破坏形态，但非线性分析计算量大，多用于局部构件的细部分析和模拟；整体式模型将块体和砂浆假定为连续的匀质体，建模过程简单、易行，适用于整体结构的宏观分析。无论是分离式还是整体式，结构非线性计算分析中大规模刚度矩阵的实时更新与分解降低了分析效率。该文提出了一种基于整体式空间离散宏单元模型的砌体结构高效非线性分析方法，该方法采用剪切单元模拟砌体墙的斜截面剪切破坏模式，采用无厚界面单元模拟砌体墙的正截面弯曲破坏模式、正截面剪切滑移破坏模式和平面外剪扭破坏模式，进一步将剪切单元等效斜向弹簧的轴向变形和无厚界面单元上下表面的相对变形分解为线弹性和非线性两部分，并引入塑性自由度描述分离出的非线性部分，可将任意时刻的切线刚度矩阵表示为初始弹性刚度矩阵的低秩摄动形式，引入Woodbury公式进行求解，该文方法避免了大规模整体刚度矩阵的迭代更新，非线性分析的主要计算量仅集中于小规模非线性矩阵的更新与分解，显著提升了计算效率。     

高强度钢板热成形温度场数值模拟分析

高强度钢板热成形过程中,板料和模具于接触表面具有强烈的热传导现象。温度的不断变化将直接影响热成形钢板的最终成形性能和水冷模具的寿命。基于此,该文建立了板料与水冷模具间相互耦合的接触表面热传导模型,并运用传热学和一般壳体温度场有限元分析理论,构建了计算热成形过程板料和模具接触的温度分布场。通过U形件热成形数值模拟与实验结果的一致性对比,验证了建立的热传导模型的有效性。     

动力系统非连续单一叠加结构界面变形与能量损耗特性

振动与其能量通过多层叠加结构的非连续界面的传递机理和损耗特性是一项研究较少的难题,考虑其结构界面粗糙度影响的更少.通过建立"单层绝对光滑金属板一刚性平面"和"单层粗糙金属板一刚性平面"的单界面模型,采用有限元方法,对加载与卸载过程中,具有不同界面形态、不同塑性材料特性和界面摩擦的单层模型界面的接触力和变形进行计算,研究了单一界面上的接触力一变形关系,以及由塑性变形与界面摩擦引起的能量损耗特性,获得描述单一界面能量损耗与接触变形的关系表达式.为研究振动和能量在多层叠加结构的非连续粗糙多界面上的传递机理和损耗特性提供了基础.     

二三维连续介质分析中的等效弹簧元

该文给出了一类将二维和三维连续介质等效成弹簧元体系进行分析的研究思路,并将二维和三维的等效弹簧单元应用于容器结构与内部连续介质相互作用的静力与动力分析中。首先,该文给出了基于刚度等效原理的二维与三维等效弹簧元理论。其次,利用二维等效弹簧元模型作为基本单元分析了连续介质对容器壁的压力分布规律,并利用三维等效弹簧元模型分析了容器壁与内部连续介质共同响应的动力特性。数值算例表明:与常用的连续介质有限元模型相比,等效弹簧元模型的计算效率和精度更高。在容器结构与内部连续介质共同响应动力分析中,等效弹簧元体系与工程中常用的附加质量法相比,不光有更高的计算效率,而且能更正确地反映内部连续介质刚度对共同响应动力特性的影响。等效弹簧元在工程应用分析中具有良好的适应性。     

液体调速离合器中摩擦副热效应分析

液体粘性调速离合器是利用多个摩擦圆盘间的油膜剪切力来传递动力，并通过改变油膜厚度实行无级调速。由于近来工程中广泛采用聚α-稀烃型、聚酯型等合成油作润滑剂，液体粘性调速离合器在调速范围内，其摩擦副往往工作在流体润滑、混合润滑、边界润滑直到直接接触的工况。基于这些特点，笔者采用了幂律型非牛顿流体模型、Patir-Cheng的平均流量模型、GT两粗糙平面接触模型、计入油膜的惯性影响、平均能量方程、热传导方程，建立了热效应研究模型，推导了相应的计算方程式，并在流体润滑、流体混合润滑状态下，进行了数值计算与分析     

基于参变量变分原理的三维Cosserat体模型弹塑性分析与应变局部化模拟

基于参变量变分原理,该文发展了三维Cosserat连续体模型弹塑性有限元分析的二次规划算法。由于Cosserat连续体模型的本构方程中存在材料内尺度参数,该模型可以解决经典连续介质理论在分析应变软化问题时病态的有限元网格依赖性问题。数值结果表明所发展的三维Cosserat连续介质弹塑性有限元模型可以有效的模拟应变局部化现象并且该算法具有很好的数值稳定性,同时获得的数值结果具有良好的非网格依赖性。     

混合润滑状态下粗糙界面法向接触刚度计算模型与特性研究

机械装备系统的静态特性和动力学特性取决于系统接触界面法向接触刚度。基于粗糙表面形貌的Greenwood-Williamson统计模型描述与液体润滑界面的油膜共振模型和弹簧模型,推导了机械结构混合润滑粗糙界面固体接触刚度和液体润滑介质接触刚度,并实现粗糙微凸体固体接触刚度与液体润滑介质接触刚度的耦合,提出了一种混合润滑状态下粗糙界面法向接触刚度的计算模型,分析了接触界面形貌参数、润滑介质和接触基体材料属性对界面法向接触刚度的影响规律。结果表明:润滑介质的声阻抗是影响液体接触刚度的主要因素,声阻抗增大时,液体接触刚度减小;接触基体材料的表面形貌和弹性模量是影响固体接触刚度的主要因素,界面粗糙度和弹性模量增大时,固体接触刚度增大。混合润滑粗糙界面接触刚度计算模型的提出,为机械结构润滑接触界面的刚度计算、性能预测与优化提供理论和实验参考。     

Variational inequality‐based framework of discontinuous deformation analysis

For modeling discrete particle‐block systems, a new framework of discontinuous deformation analysis is established on the basis of finite‐dimensional variational inequality. The presented method takes into account the contacts, the rolling resistance, and the tensile resistance of cemented interface among particles and blocks using the corresponding variational or quasivariational inequalities. The new formulation avoids using the artificial springs that are usually indispensable in many conventional methods dealing with similar discrete problems and conveniently integrates the rigid circle particles, the nonrigid ring particles, and the arbitrary shape blocks into a uniform framework. The proposed discontinuous deformation analysis approach is further coupled with the finite element method using a node‐based composite contact matrix and several simple transformation matrices to solve practical problems. A particle/block‐based composite contact matrix is constructed to further broaden the application of the proposed method. The accuracy, robustness, and capability of the presented method are demonstrated with examples.     

Proper orthogonal decomposition‐based reduced basis element thermal modeling of integrated circuits

Various reduced basis element methods are compared for performing transient thermal simulations of integrated circuits. The reduced basis element method is a type of reduced order modeling that takes advantage of repeated geometrical features. It uses a reduced set of basis functions to approximate the solution of a PDE on subdomains (blocks); then these blocks are coupled together to perform a simulation on an entire domain. As the simulations are transient, a proper orthogonal decomposition basis is used, and the proper orthogonal decomposition eigenvalues from each block are used to derive error bounds for the entire simulation. These bounds are used to examine choices of block decompositions for a simplified integrated circuit structure. A decomposition that uses a single block for each transistor device is compared with a decomposition that uses one block for multiple devices. It was found that larger blocks are more computationally efficient; however, the advantage decreases if the devices within a block receive independent signals. Continuous and discontinuous methods of coupling the blocks were also compared. The coupling methods lend themselves to different solution approaches such as static condensation (continuous coupling) and block‐based inversion (discontinuous). Static condensation yielded the best convergence rate, accuracy, and operation count. Copyright © 2017 John Wiley & Sons, Ltd.     

局部约束结构振动的模态研究

制动盘/摩擦块系统的制动过程属于局部接触振动问题。摩擦块局部接触(约束)会对系统模态及固有频率造成影响,进而影响制动噪声的产生。将刹车盘简化为一维循环梁结构,并建立了在摩擦块作用下的运动方程。首先计算无接触时梁自由振动的模态(参考模态)。然后用线性弹簧代替局部接触,列写出连续条件并计算模态,得到所谓局部非连续基函数。将局部非连续基函数与参考模态进行正交化处理后,作为参考模态的补充,用于计算系统响应。与差分法结果比较表明,与传统模态方法相比,局部非连续基函数法更为准确。研究发现局部接触会抑制循环结构振动的对称性,导致正弦或余弦模态消失,以及刚度非线性和摩擦作用,会使振动是波动型的。该工作为基于局部非连续基函数法研究摩擦结构不稳定振动机理打下了基础。     

Bounds on the effective thermal conductivity of composites with imperfect interface

A new model is developed to bound the effective thermal conductivity of composites with thermal contact resistance between spherical inclusions and matrix. To construct the trial temperature and heat flux fields which satisfy the necessary interface conditions, the transition layer for each spherical inclusion is introduced. For the upper bound, the trial temperature field needs to satisfy the thermal contact resistance conditions between spherical inclusions and transition layers and the continuous interface conditions between transition layers and remnant matrix. For the lower bound, the trial heat flux field needs to satisfy the continuous interface conditions between different regions. It should be pointed out that the continuous interface conditions mentioned above are absolutely necessary for the application of variational principles, and the thermal contact resistance conditions between spherical inclusions and transition layers are suggested by the author. According to the principles of minimum potential energy and minimum complementary energy, the bounds of the effective thermal conductivity of composites with imperfect interfaces are rigorously derived. The effects of the size and distribution of spherical inclusions on the bounds of the effective thermal conductivity of composites are analyzed. It should be shown that the present method is simple and does not need to calculate the complex integrals of multi-point correlation functions. Meanwhile, the present method provides an entirely different way to bound the effective thermal conductivity of composites with imperfect interface, which can be developed to obtain a series of bounds by taking different trial temperature and heat flux fields. In addition, the present upper and lower bounds are finite when the thermal conductivity of spherical inclusions tends to ∞ and 0, respectively.     

考虑接触刚度的燃气轮机拉杆转子动力特性研究

基于弹塑性理论对具有粗糙表面的长方微元体进行有限元接触分析,根据受力和变形关系得到了不同载荷作用下的法向和切向界面接触刚度。将微元体界面接触刚度与宏观结构应力分析结果相结合,给出了考虑接触刚度的组合结构动力特性研究方法,分析了压气段轮盘接触刚度对某重型燃气轮机拉杆转子固有振动频率的影响。结果表明,界面接触刚度导致转子固有频率降低,随着接触刚度的增加,其对固有频率的影响逐渐减小。接触刚度对转子各阶固有频率的影响不同,法向刚度对第一阶弯曲频率影响较大,切向刚度对第二阶弯曲频率影响较大。     

高温接触热阻的有限元模拟方法

基于多点接触理论建立了高温接触热阻的计算模型及其有限元格式,模型的基本尺寸取自表面粗糙度测量时的特征尺寸,该模型能有效模拟界面粗糙度、界面压力、界面温度和间隙填料热导率等参数对界面接触热阻的影响,同时也考虑了高温环境下材料热导率随温度变化的特点以及通过界面间隙的辐射换热效应。在此基础上,针对影响接触热阻的若干主要参数进行了研究。数值算例表明:该文所建立的有限元计算模型及其计算方法不仅能有效地模拟不同条件下高温接触热阻的变化规律,也为进行高温接触热阻研究提供了一种新途径。     

多体非连续变形系统的计算力学模型及其应用

针对由不同特性物体所组成的多体系统,探讨了能够涵盖各种变形状态和运动形式的广义有限单元模式及其插值函数形式。对于多体接触问题,发展了能够合理描述界面特性的接触力元模型,即采用某种应力插值函数将界面上的相互作用力由接触对上的接触应力来表达,并将接触对上的接触应力当作需满足界面上屈服准则与流动法则等状态控制条件的参变量,将其作为约束条件加入系统控制方程。根据非连续变形系统的分区参变量最小势能变分原理,联立变分驻值条件与参变量的状态控制条件建立了多体系统非连续变形计算力学分析的基本控制方程,将问题最终归结为一个含有自由变量和等式约束条件的线性互补问题,对此发展了数值解法,并进行了多个算例的数值分析。计算结果表明该模型不仅能够对多体系统进行静、动力耦合分析,而且还能够模拟多体系统的变形与应力及接触界面上的接触应力和相对运动等复杂的非线性过程。     

Ultrasonic wave scattering from rough,imperfect interfaces. Part I. Stochastic interface models

A theoretical model for ultrasonic wave scattering by geometrically irregular and imperfectly bonded interfaces is presented. In Part I, the normal stiffness of interfaces formed by the partial contact of solids with rough surfaces is estimated for two models of contacting surfaces with random roughness in one dimension only. The first model considers nonconforming surfaces with a single-scale of roughness, while double-scale roughness characterizes the surfaces of the second model, which are conforming at the large scale and nonconforming at the smaller scale. The surfaces' profiles are described by Gaussian probability and spectral densities. The surfaces at each contact are modeled by two cylinders under a compressive load and the normal stiffness per unit area of the interface is evaluated by averaging the stiffness of all the contacts, assuming they do not interact with each other. It is shown that the smaller the roughness, the softer the interface; the larger the autocorrelation length, the softer the interface; and the smaller the initial aperture, the stiffer the interface. Furthermore, interfaces described by the second model appear much stiffer than those described by the first model. The interface characterizations and normal stiffness models developed in Part I will be used in Part II to study the scattering of ultrasonic plane waves by such an interface.     

Pullout resistance of straight NiTi shape memory alloy fibers in cement mortar after cold drawing and heat treatment

In our study, we found cold drawing to be an effective method for enhancing the pullout resistance of NiTi shape memory alloy (SMA) fibers in concrete. The pullout resistance was observed to be dependent on the contact pressure and friction coefficient at the interface between the fibers and the mortar matrix. The drawing process increased the stiffness and yield stress of the fibers and consequently increased the contact pressure at the interface between the fibers and the mortar matrix. Moreover, heat treatment of the fibers after cold drawing was found to noticeably recover the fiber diameter, thereby significantly enhancing the pullout resistance. The enhancement of the interfacial bond strength by heat treatment verified the crack-closing capabilities of SMA-fiber-reinforced cement composites.     

Nonlinear wave scattering at the flexible interface of a granular dimer chain

Uncompressed granular dimer chains composed of repetitive pairs of heavy-light spherical, linearly elastic beads exhibit interesting intrinsic responses. The dynamics of these highly discontinuous nonlinear media is governed by the mass ratio scaling the mass disparity of each heavy-light pair of beads. In particular, it has been theoretically and experimentally shown that they support countable infinities of anti-resonances at a discrete set of mass ratios leading to solitary pulses propagating through the dimers with no attenuation or distortion. Conversely, they support countable infinities of resonances at a different discrete set of mass ratios, leading to substantial and rapid attenuation of propagating pulses due to energy scattering from low-to-high frequencies and wavenumbers by means of radiating traveling waves. In this work we computationally study nonlinear scattering of impeding pulses at the interface of an impulsively excited dimer chain with a dispersive elastic boundary, namely, a finite linear string resting on an elastic foundation. We develop a computational algorithm which, through iteration and interpolation at successive time steps, accurately computes (and ensures convergence of) the highly discontinuous contact forces and displacements at the flexible interface of the granular medium. This enables accurate computation of wave transmission, reflection, localization or multi-scale nonlinear scattering at the flexible interface for varying mass ratios of the dimer and the interface parameters. We show that, depending on the mass ratio of the dimer and the stiffness of the elastic foundation, the nonlinear scattering at the flexible interface may lead to significant reduction of the maximum contact force at the interface, and, thus, drastically affect the transmitted and reflected energy at the flexible boundary. In fact, an inverse relation between the stiffness of the elastic foundation and the residual energy transferred from the dimer chain to the flexible boundary is found. Moreover, for sufficiently small mass ratios of the dimer chain transient breathers are realized close to the interface in the form of localized “fast” oscillations of light granules of the dimer that entrap shock energy and then release in a slow time scale back to the chain and the flexible boundary. This work paves the way for studying highly discontinuous and nonlinear scattering phenomena at interfaces of granular media with flexible continua.