Material instability-induced extreme damping in composites: A computational study

We investigate the effective viscoelastic performance of particle-reinforced composite materials whose particulate phase undergoes a material instability resulting in temporarily non-positive-definite elastic moduli. Recent experiments have shown that phase transitions in geometrically-constrained composite phases (such as in particles embedded in a stiff matrix) can lead to stable non-positive-definite elastic moduli, and they hinted at strong damping increases that can be achieved from such metastable composite phases. All previous theoretical efforts to explain such phenomena have used simplistic one-dimensional models or they were based on composite bounds and specific two-phase solids. Here, we study particle–matrix composites with periodic randomized particle dispersion. A finite element discretization is used in combination with a sophisticated nonlinear solver in order to perform the numerous calculations in a feasible amount of computing time. Our computational analysis shows that stable non-positive-definite inclusion moduli can indeed lead to extreme damping increases (i.e. greatly exceeding the intrinsic damping of each composite phase) and that such extreme damping arises from a shift in microstructural mechanisms.     

Anisotropic wave propagation and its applications to NDE of composite materials

This paper utilized anisotropic wave propagation theory to measure the elastic constants of a unidirectional fiber-reinforced composite specimen. For plane waves propagating in the composite specimen, the deviation of the propagational directions between the energy and phase velocities were measured. It is found that in such a sample, the deviations may be as large as 60 degrees. The measured energy velocities were transformed to the phase velocities of the plane waves by employing a numerical scheme. It is demonstrated that the elastic constants of a unidirectional fiber-reinforced composite can be determined by conducting ultrasonic experiments in two principal symmetry planes.     

剪切流作用下层合梁非线性振动特性研究

针对剪切流中层合梁的大变形非线性振动问题, 采用高阶剪切变形锯齿理论和冯·卡门应变描述层合梁的变形模式和几何非线性效应, 构建了大变形层合梁非线性振动有限元数值模型; 采用基于任意拉格朗日?欧拉方法的有限体积法求解不可压缩黏性流体纳维-斯托克斯方程, 结合层合梁和流体的耦合界面条件建立了剪切流作用下层合梁流固耦合非线性动力学数值模型, 采用分区并行强耦合方法对层合梁的流致非线性振动响应进行了迭代计算. 研究了不同速度分布的剪切流作用下单层梁和多层复合材料梁的振动响应特性, 并验证了本文数值建模方法的有效性. 结果表明: 剪切流作用下单层梁的振动特性与均匀流作用下的情况不同, 梁的运动轨迹受剪切流影响向下偏斜, 随着速度分布系数增加, 尾部流场中的涡结构发生改变; 刚度比对剪切流作用下层合梁的振动特性有显著影响, 随着刚度比的增加, 层合梁振动的振幅增大, 主导频率下降, 运动轨迹由‘8’字形逐渐变得不对称; 发现了不同厚度比和铺层角度情况下, 层合梁存在定点稳定模式、周期极限环振动模式和非周期振动模式三种不同的振动模式, 改变层合梁铺层角度可实现层合梁周期极限环振动模式向非周期振动模式转变.      

Numerical solution of oscillatory flow of Maxwell fluid in a rectangular straight duct

A numerical analysis is presented for the oscillatory flow of Maxwell fluid in a rectangular straight duct subjected to a simple harmonic periodic pressure gradient.The numerical solutions are obtained by a finite difference scheme method. The stability of this finite difference scheme method is discussed. The distributions of the velocity and phase difference are given numerically and graphically. The effects of the Reynolds number, relaxation time, and aspect ratio of the cross section on the oscillatory flow are investigated. The results show that when the relaxation time of the Maxwell model and the Reynolds number increase, the resonance phenomena for the distributions of the velocity and phase difference enhance.     

Nonlinear deformation of a particulate material in complex stress state

An algorithm is proposed to determine the effective deformation properties and stress-strain state of particulate composite materials with physically nonlinear components and complex stress state. The laws that govern the deformation of particulate composites are studied. A particulate composite is considered a two-component material of random structure. Its effective properties are determined by conditional averaging. The nonlinear equations that incorporate the physical nonlinearity of the components are solved by the method of successive approximations. The relationship between macrostresses and macrostrains is established. The effective deformation properties of a particulate composite as a function of the volume fractions of the components and stress state are studied __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 3, pp. 50–60, March 2006.     

Constitutive parameters for liquid-fluidized beds

The constitutive parameters (particulate phase effective elasticity, particulate effective viscosity, added mass coefficient and drag gradient) in an unstable liquid-fluidized bed are determined as functions of voidage and slip velocity. To identify these system parameters, first, forced instability wave properties are measured in water-fluidized beds, then an optimum parameter identification method is developed to reliably determine these system parameters based on a generic instability model. The results give some insight into the internal mechanics of liquid-fluidized beds and are compared with other models when they are available.     

系统压力对含悬浮颗粒油液的影响研究

油液在运行过程中不可避免地会产生颗粒物,影响油液的正常使用,甚至出现设备故障,因而分析含悬浮颗粒油液的动态特征,掌握在不同压力变化条件下油液及颗粒物的变化规律具有重要意义。利用两相流体理论建立了含悬浮颗粒油液的悬浮流动力学模型,通过特征线法进行了数值求解,将数值结果与实验数据比较,具有较好的一致性;根据所建模型,分析了不同系统压力条件下悬浮流中各相的脉动规律。结果表明,流场中各相参数的脉动幅值随着系统压力的增加而增大;管路始端和终端各相参数的脉动时刻分别位于1/4脉动周期(T)的奇数倍和偶数倍处,管路中段各相参数的脉动时刻则位于T/8的奇数倍处;悬浮颗粒速度会受到油液速度拖曳力作用,其变化趋势与油液速度基本一致,颗粒浓度分布与油液压力的变化趋势完全相反。     

Effective elastic moduli of triply periodic particulate matrix composites with imperfect unit cells

In many problems the material may possess a periodic microstructure formed by the spatial repetition of small microstructures, or unit cells. Such a perfectly regular distribution, of course, does not exist in actual cases, although the periodic modeling can be quite useful, since it provides rigorous estimations with a priori prescribed accuracy for various material properties. Triply periodic particulate matrix composites with imperfect unit cells are analyzed in this paper. The multiparticle effective field method (MEFM) is used for the analysis of the perfect and imperfect periodic structure composites. The MEFM is originally based on the homogeneity hypothesis (H1) (see for details [Buryachenko, V.A., 2001. Multiparticle effective field and related methods in micromechanics of composite materials. Appl. Mech. Rev. 54, 1–47]) of effective field acting on the inclusions. In this way the pair interaction of different inclusions is taken directly into account by the use of analytical approximate solution. For perfect periodic structures the hypothesis (H1) is enough for estimation of effective properties. Imperfection of packing necessitates exploring some additional assumption called a closing hypothesis. The next imperfections are analyzed. (A) The probability of location of an inclusion in the center of a unit cell below one (missing inclusion). (B) Some hard inclusions are randomly replaced by the porous (modeling the complete debonding) with some probability. At first, one obtains general explicit integral representations of the effective elastic moduli and strain concentrator factors depending on three numerical solutions: for the perfect periodic structure, for the infinite periodic structure with one imperfection, and for the infinite periodic structure with two arbitrary located imperfections. The method proposed is general; it is not limited by concrete numerical scheme. No restrictions were assumed on both the concrete microstructure and inhomogeneity of stress fields in the inclusions. The inclusions of one kind are assumed to be aligned. The problem (A) is solved at the level of numerical results obtained in the framework of the hypothesis (H1). For the problem (B) the numerical results are obtained if the elastic inclusions (for example hard inclusions) are randomly replaced by another inclusion (for example by the voids modeling the complete debonding). The mentioned problems are solved by three methods. The first one is a Monte Carlo simulation exploring an analytical approximate solution for the binary interacting inclusions obtained in the framework of the hypothesis (H1). The second one is a generalization of the version of the MEFM proposed for the analysis of the perfect periodic particulate composites and based on the choice of a comparison medium coinciding with the matrix. The third method uses a decomposition of the desired solution on the solution for the perfect periodic structure and on the perturbation produced by the imperfections in the perfect periodic structure. All three methods lead to close results in the considered examples; however, the CPU times expended for the solution estimation by Monte Carlo simulation differ by a factor of 1000.     

Automated fringe pattern analysis for moiré interferometry

The theory of an automated fringe-pattern analysis using temporal phase stepping method for moiré interferometry is presented. The automated method provides a fast and accurate strain measurement for moiré interferometry. Measurements on a tapered composite specimen with a dropped ply are shown to highlight the capability of this technique to obtain the strain distribution, particularly around the region with a dropped ply.     

爆速对爆炸焊接铝/不锈钢复合管界面及结合性能的影响

通过在粉状乳化炸药中添加不同比例的密度调节剂,配制了爆速范围为1 450~2 550 m/s的低爆速炸药;采用该爆速炸药进行了铝/不锈钢复合管爆炸焊接实验,结合最小碰撞速度理论,对实验结果及其界面微观结构和结合强度进行了测试和分析,确定该复合管爆炸焊接的合适爆速约为1 950~2 150 m/s,其结合质量能够满足后续加工要求;同时发现界面由介于直线与波形之间的波状形态组成,且呈现不太规则的扁平波状结合,经分析,炸药爆速、复合管的爆炸焊接环境和爆炸产物飞散条件对界面结合波形及熔化层厚度有很大影响。     

高尺寸稳定性铝基复合材料研究新进展

本文在讨论材料尺寸稳定性基本原理的基础上，对几种铝基复合材料的尺寸稳定性特性进行了综合分析对比，表明：亚微米铝基复合材料具有很高的尺寸稳定性性能，符合组织稳定、相稳定、应力稳定、晶粒细化等基本要求，是目前惯性器件较理想的选材。     

Numerical Study of the Effect of Periodic Velocity Excitation on Aerodynamic Characteristics of an Oscillating Circular Cylinder

A finite element method based on ALE formulation has been adopted in order to examine the effect of periodic velocity excitation on the aerodynamic characteristics of an oscillating circular cylinder. Periodic excitation, which was placed on the cylinder surface, stimulated the separated shear layers around the cylinder, and numerical results showed that some excitation can reduce negative damping, which is caused by unsteady lift force, and thereby stabilize the aerodynamics of the cylinder. Furthermore, the change of lift phase caused by periodic excitation seems to be important in stabilizing the aerodynamics of the cylinder. The simulation also confirmed that periodic excitation can suppress the vortex-induced vibration of the cylinder.     

Buckling analysis of fibers in composite materials by wave propagation analogy

The analogy between the governing equations for the analysis of buckling in elastic structures and the elastodynamic equations of motion for wave propagation is presented. By employing this analogy, the exact and approximate buckling stresses of periodic layered materials and continuous fiber composites, respectively, are established. This is performed by utilizing micromechanically based dispersion relations for elastic wave propagating in the composite materials, which provide for a given wave length the corresponding phase velocity. By a specific change of variables in these dispersion relations, the corresponding buckling stresses can be determined. Results are presented and compared with solutions based on the mechanics of materials approach as well as with the well known Rosen’s fiber buckling predictions.     

Semi-analytical method for computing effective properties in elastic composite under imperfect contact

A parallel fiber-reinforced periodic elastic composite is considered with transversely iso-tropic constituents. Fibers with circular cross section are distributed with the same periodicity along the two perpendicular directions to the fiber orientation, i.e., the periodic cell of the composite is square. The composite exhibits imperfect contact, in particular, spring type at the interface between the fiber and matrix is modeled. Effective properties of this composite for in-plane and anti-plane local problems are calculated by means of a semi-analytic method, i.e. the differential equations that described the local problems obtained by asymptotic homogenization method are solved using the finite element method. Numerical computations are implemented and comparisons with exact solutions are presented.     

用管轴流速确定动脉中血液振荡流的速度剖面

本文通过求解圆管内血液振荡流的基本方程，求得圆管内血液流的速度与压力梯度之间的关系式，文章提出一种利用管轴外流速计算管内压力梯度，进而确定血液振荡流动速度分布的方法，该方法用于检测活体血管内血液振荡流的速度剖面，具有操作简单，精度较高的优点，最后，以人体颈动脉为例，讨论血液周期振荡流的速度分布特征，发现在任意时刻，除了邻近管壁速度迅速降为零之外，沿管截面速度分布相当均匀，呈现出与定常流不同的速度分布特征。     

Computer aided photoelasticity by an optimum phase stepping method

In this paper an automated photoelastic method based on the phase stepping technique is described. It provides full-field maps of the isoclinic parameter and the relative retardation. The technique is based on processing six images of a photoelastic specimen acquired using plane and circularly polarized light. The number of acquisitions and the type of polariscope used in this approach have been chosen with the aim at reducing the influence of quarter wave plate errors and obtaining raw photoelastic data in a periodic form suitable for easy applications of automatic unwrapping routines.     

Design of three dimensional isotropic microstructures for maximized stiffness and conductivity

The level-set method of topology optimization is used to design isotropic two-phase periodic multifunctional composites in three dimensions. One phase is stiff and insulating whereas the other is conductive and mechanically compliant. The optimization objective is to maximize a linear combination of the effective bulk modulus and conductivity of the composite. Composites with the Schwartz primitive and diamond minimal surfaces as the phase interface have been shown to have maximal bulk modulus and conductivity. Since these composites are not elastically isotropic their stiffness under uniaxial loading varies with the direction of the load. An isotropic composite is presented with similar conductivity which is at least 23% stiffer under uniaxial loading than the Schwartz structures when loaded uniaxially along their weakest direction. Other new near-optimal isotropic composites are presented, proving the capablities of the level-set method for microstructure design.     

Micro–macro analysis of shape memory alloy composites

The aim of the paper is to develop a micro–macro approach for the analysis of the mechanical behavior of composites obtained embedding long fibers of Shape Memory Alloys (SMA) into an elastic matrix. In order to determine the overall constitutive response of the SMA composites, two homogenization techniques are proposed: one is based on the self-consistent method while the other on the analysis of a periodic composite. The overall response of the SMA composites is strongly influenced by the pseudo-elastic and shape memory effects occurring in the SMA material. In particular, it is assumed that the phase transformations in the SMA are governed by the wire temperature and by the average stress tensor acting in the fiber. A possible prestrain of the fibers is taken into account in the model.Numerical applications are developed in order to analyze the thermo-mechanical behavior of the SMA composite. The results obtained by the proposed procedures are compared with the ones determined through a micromechanical analysis of a periodic composite performed using suitable finite elements.Then, in order to study the macromechanical response of structural elements made of SMA composites, a three-dimensional finite element is developed implementing at each Gauss point the overall constitutive laws of the SMA composite obtained by the proposed homogenization procedures. Some numerical applications are developed in order to assess the efficiency of the proposed micro–macro model.     

一种滞弹簧耗能的新型离散元滚动阻力模型研究

颗粒间滚动阻力对颗粒体系的稳定性起着重要作用. 在传统的离散元法中, 滚动阻力模型通常由转动弹簧、转动黏壶和摩擦元件表达, 颗粒滚动动能由黏滞力(矩)和摩擦力做功耗散. 由于黏滞力(矩)与滚动速度相关, 临近静止状态的颗粒滚动速度变小, 动能耗散减弱, 传统的离散元模拟得到颗粒由滚动到静止耗费的时间比试验观测的结果要长. 为解决这一问题, 基于摩擦学理论分析了滚动阻力产生的材料滞弹性机理, 将其引入离散元滚动阻力模型, 提出了一种速度无关型动能耗散的滞弹簧, 给出了滞弹簧的弹性恢复力计算公式, 建立了一种新型的离散元滞弹性滚动阻力模型(HDEM). 为验证新型滚动阻力模型的正确性, 通过一个光学物理试验对单个圆形颗粒试件的自由滚动过程进行了测量, 将测量数据与新型的滞弹型离散元模型和传统离散元模型计算结果进行了对比. 结果显示, 基于滞弹性滚动阻力模型HDEM计算结果与试验数据吻合程度更高, 而且模拟得到的颗粒摆动频率更符合试验现象.