PREDICTIONS OF EFFECTIVE OUT-PLANE SHEAR MODULUS AND SIZE EFFECT OF HEXAGONAL HONEYCOMB

给出了预测六边形蜂窝材料等效剪切模量及其尺寸效应的圆筒扭转力学模型和扭转能量法,建立了等效面外剪切模量G₁₃相对于材料体分比ν、周向单胞数n、圆筒半径r和单胞层数参数m变化的解析表达式;同时将扭转能量法、有限元数值模拟计算和G-A经典细观力学方法进行了比较,从理论上揭示并验证了尺寸效应的存在性. 结果表明,当蜂窝体胞尺寸相对结构尺寸无穷小时,预测结果趋近于细观力学方法的结果. 此外,利用周期性蜂窝材料的结构对称特性,使用体胞子结构有限元计算模型进行等效面外剪切模量及其尺寸效应的预测,在不影响计算结果的前提下极大地提高了计算效率.     

一类多孔固体的等效偶应力动力学梁模型

一维多孔固体结构可采用等效连续介质梁模型来研究其动力学行为. 当类梁结构的高度尺寸和多孔固体单胞结构尺寸相近时,等效模型的力学行为会产生尺寸效应现象. 等效经典模型由于不包含尺度参数而无法描述尺寸相关特点,而广义连续介质力学模型则可以准确地考虑尺寸效应的影响. 基于偶应力理论,对一类单胞含有圆形孔洞的周期性多孔固体类梁结构,给出了分析其横向自由振动的等效连续介质铁木辛柯梁模型. 通过对单胞分析,在应变能等价和几何平均的意义下,定义了等效偶应力介质的材料常数. 利用已有的材料常数,推导了等效铁木辛柯梁的动力学微分方程. 将实际多孔固体结构进行完全的动力学有限元离散计算,所获得的解作为精确解以检验等效梁模型所获得的频率和振型的精度. 振型的比较借助于模态置信准则矩阵方法. 大量算例表明,等效偶应力铁木辛柯梁模型在频率和振型两方面均具有较高的计算精度. 重点研究了单胞孔径的相对大小、类梁结构高度与单胞尺寸比以及类梁结构长高比对等效梁模型精度的影响. 在此基础上,偏保守地建议了多孔固体类梁结构自振分析方法.      

圆柱夹层多孔材料的主动散热性能研究与优化设计

通过推导不同边界条件的圆柱状夹层多孔材料散热指标,研究了一种特殊结构的圆柱状夹层多孔材料主动散热问题。这种圆柱夹层材料的每一层胞体个数相同,胞体尺寸随着外径的增大而增大,从而保持每一层胞体的相对密度相同。通过计算两种不同换热边界条件下圆柱夹层多孔材料的散热性能,比较并分析了与夹层材料层数相对应的最大散热效率和最优相对密度等指标,并最终得到这些工况下的最优质量。通过分析得到,无论哪种边界条件,正六边形胞体的夹层结构散热性能优于其他构型。同时当为达到某一限定散热效率值时,正六边形胞体结构的质量最小,正六边形构型的多孔材料具有明显的综合性能优势。     

基于偶应力理论的格栅材料等效介质模型

考察了结构最小尺寸与材料特征长度量级相当的格栅材料等效性能,建议了基于偶应力理论的格栅材料等效介质模型以及确定等效模量的代表体元模型,给出了相应的位移边界条件. 在此基础上导出了正交各向异性偶应力介质的特征长度表达式和偶应力介质梁的抗弯刚度表达式,定义了偶应力影响因子\delta以表征梁的偶应力效应. 具体计算了几种典型的格栅材料的等效偶应力模量以及格栅梁在一定工况下的挠曲线,并与相应的有限元离散解进行对比,结果表明,等效结果具有较高精度,且当宏观结构的尺寸和微结构尺寸相差不大时,宏观结构表现出强烈的偶应力效应.偶应力介质的特征长度表征了偶应力效应的强弱,进而分析了格栅材料的相对密度,单胞尺寸以及几何构型对等效介质特征长度的影响.      

考虑内部胞元能量等效的代表体元法

具有周期性胞元的超轻质材料在制造和应用过程中,不可避免地会出现基体材料、微结构拓扑和尺寸的随机性变化.此时,评价材料的等效弹性性能需要借助基于均匀化方法(周期性边界条件)或代表体元法(周期性边界条件,均匀应力或均匀应变边界条件等)的蒙特卡洛模拟.该文首先通过算例分析和比较了不同边界条件下的数值结果,讨论了结果的尺度效应和对胞元选取的依赖性.为了提高和改善Dirichlet边界条件下的计算效率和结果,提出了一种考虑内部胞元能量等效的代表体元法.该方法能够有效削弱边界条件和胞元选取的影响,从而实现了采用较小的代表体元得到更好的结果.数值算例验证了方法在预测确定性材料和随机性材料等效模量时的有效性.     

周期性蜂窝材料微极等效模型及其微观应力的一种快速算法

将周期性蜂窝材料等效为具有非局部本构的微极连续介质,以解释实验中出现的尺度效应和边界层效应.在评论相关的多种不同方法(能量法、体积平均的均匀化法等)之后,提出了一种基于位移连续和单胞力平衡的推导微极等效本构参数的新方法.以正方形单胞制成的结构为例,在不同的结构与单胞尺寸比下,考虑承受集中点载荷、均布轴力和均布剪力三种载荷工况,比较了离散完全计算、经典连续介质等效和不同微极连续体等效本构的计算结果,建议了较好的微极本构参数值.数值模拟表明,集中点载荷和剪切载荷作用时,在加载点附近和边界部分,微极等效可以显著提高计算精度.最后,给出了一种映射算法,可以根据微极等效连续体分析的结果,快速计算出对应微观单胞构件的应力,以开有圆孔的方板应力集中为例,验证并考察了所提快速算法的有效性和计算精度.     

剪切和扭转工况下微纳米薄壁蜂窝的等效剪切模量计算

分别针对剪切和扭转两种工况给出了微纳米薄壁蜂窝等效剪切模量的解析计算方法.该方法综合考虑了由面板对芯层的约束导致的高度效应和当蜂窝胞壁厚度进入微纳米量级时引起的尺度效应.首先对蜂窝各胞壁选取了可反映面板约束以及受力状态的三角级数位移场,然后在本构关系中引入修正偶应力理论以描述尺度效应,最后应用能量均匀化方法求得蜂窝的等效剪切模量.以典型六边形蜂窝为例,给出了完整的计算过程和结果.与文献中的等效剪切模量结果进行对比,讨论了不同工况下等效剪切模量随芯层高度和胞壁厚度的变化趋势,以及高度效应和尺度效应之间的相互影响.     

松质骨弹性模量计算的均匀化方法

对松质骨建立了六种单胞微观结构模型，采用均匀化方法和有限元方法计算松质骨的宏观等效弹性模量。给出了六种单胞模型的松质骨弹性模量与材料密度(体分比）的关系，与实验数据进行了对比，分析了不同微观结构模型在不同骨骼中的应用。结果表明，本文方法及六种单胞模型可以对松质骨微观结构和材料性能进行有效的模拟计算。同时本文又着重对松质骨的宏观等效弹性模量与体分比的指数关系进行了探讨。     

基于二维不同尺寸旋转刚性单元的负泊松比研究

负泊松比材料(也称拉胀材料)是一种具有特殊力学性能的新型功能材料,有着良好的应用前景.对于该类材料的变形机理研究,基于旋转刚性单元模型,提出一类新型多尺寸刚性矩形单元组合模型.该模型中不同尺寸的刚性矩形单元通过旋转铰链方式连接,在材料受单向外力作用下展现出宏观的负泊松比效应.在模型中通过对周期循环胞体的分析,得到了材料的泊松比随刚体单元之间夹角θ变化的解析表达式.结果表明,该模型的泊松比在夹角θ趋近90°时取极值,通过调整刚性单元的几何尺寸可以改变模型的泊松比的大小.这些结果对二维多胞拉胀材料的微结构设计具有参考价值.     

基于渐进均匀化的平纹编织复合材料低速冲击多尺度方法

针对平纹编织复合材料低速冲击响应和损伤问题,提出了一种多尺度分析方法. 首先, 建立微观尺度单胞模型,引入周期性边界条件,采用最大主应力失效准则和直接刚度退化模型表征纤维丝和基体的损伤起始与演化,预测了纤维束的弹性性能和强度性能. 其次,将这些性能参数代入介观尺度单胞模型,基于Hashin和Hou的混合失效准则以及连续介质损伤模型对介观尺度单胞进行6种边界条件下的渐进损伤模拟.然后采用渐进均匀化方法,以介观尺度单胞为媒介预测了0$^\circ$和90$^\circ$子胞的性能参数,并建立平纹编织复合材料的子胞模型,进而扩展成为材料的宏观尺度低速冲击模型. 在此基础上,研究了平纹编织复合材料低速冲击下的力学响应与损伤特征.结果表明:宏观冲击仿真和试验吻合较好, 验证了多尺度方法的正确性;最大接触力、材料吸能和分层面积均随冲击能量的增大而增大,分层损伤轮廓逐渐从椭圆形向圆形转化;基体拉伸和压缩损伤的长轴方向分别与子胞材料主方向正交和一致,损伤面积前者远大于后者.      

纳米夹杂复合材料的有效反平面剪切模量研究

基于Gurtin-Murdoch表面/界面理论模型,利用复变函数方法,获得了考虑夹杂界面应力时夹杂/基体/等效介质模型的全场精确解,发展了能够预测纳米夹杂复合材料有效反平面剪切模量的广义自洽方法,给出了复合材料有效反平面剪切模量的封闭形式解。数值结果显示：当夹杂尺寸在纳米量级时,复合材料的有效反平面剪切模量具有尺度相关性,随着夹杂尺寸的增大,本文结果趋近于经典弹性理论的预测值;夹杂尺寸对于有效反平面剪切模量(本文结果)的影响范围要小于其对有效体积模量与剪切模量(各向同性材料)的影响范围;有效反平面剪切模量受夹杂的界面性能和夹杂刚度影响显著。     

Vibration analysis of periodic cellular solids based on an effective couple-stress continuum model

Cellular solids are usually treated as homogeneous continuums with effective properties. Nevertheless, these mechanical properties depend strongly on the ratio of the specimen size to the cell size. These size effects may be accounted for according to preliminary static analysis of effective continuums based on couple-stress theory. In this paper an effective dynamic continuum model, based on couple-stress theory, is proposed to analyze the behavior of free vibrations of periodic cellular solids. In this continuum model, the effective mechanical constants of the effective continuum are deduced by an equivalent energy method. The cellular solid structure is then replaced with the equivalent couple-stress continuum with same overall dimension and shape. Moreover, the finite element formulation of the couple-stress continuum for the generalized eigenvalue analysis is developed to implement the free vibration analysis. The eigenfrequencies of the effective continuum are then obtained via the shear beam theory or the finite element method. A conventional finite element analysis by discretizing each cell of the cellular solids is also carried out to serve as an exact solution. Several structural cases are calculated to demonstrate the accuracy and effectiveness of the proposed continuum model. Good agreement on structural eigenfrequencies between the effective continuum solutions and the exact solutions shows that the proposed continuum model can accurately simulate the dynamic behavior of the cellular solids.     

基于界面层模型的双周期纳米夹杂复合材料反平面问题研究

利用复变函数方法并结合双准周期Riemann边值问题理论，获得了含双周期分布非均匀相（夹杂/界面层）的复合材料在远场均匀反平面应力下弹性场的全场解答．该解答可用于对纳米夹杂复合材料的应力进行分析，结合平均场理论也用于预测纳米夹杂复合材料的有效性能．计算结果表明：当夹杂尺度在纳米量级时，应力和有效反平面剪切模量具有明显的尺度依赖性，并且随着夹杂尺寸的增加，趋近于不考虑界面效应时的结果；界面层厚度和性能对应力和有效反平面剪切模量明显变化时所对应的夹杂尺度范围和趋近于无界面效应结果的快慢有显著影响；当界面厚度足够薄时，界面层模型可用于模拟零厚度界面情况．     

EXACT SOLUTION FOR ORTHOTROPIC MATERIALS WEAKENED BY DOUBLY PERIODIC CRACKS OF UNEQUAL SIZE UNDER ANTIPLANE SHEAR

Orthotropic materials weakened by a doubly periodic array of cracks under far-field antiplane shear are investigated, where the fundamental cell contains four cracks of unequal size. By applying the mapping technique, the elliptical function theory and the theory of analytical function boundary value problems, a closed form solution of the whole-field stress is obtained. The exact formulae for the stress intensity factor at the crack tip and the effective antiplane shear modulus of the cracked orthotropic material are derived. A comparison with the finite element method shows the efficiency and accuracy of the present method. Several illustrative examples are provided, and an interesting phenomenon is observed, that is, the stress intensity factor and the dimensionless effective modulus are independent of the material property for a doubly periodic cracked isotropic material, but depend strongly on the material property for the doubly periodic cracked orthotropic material. Such a phenomenon for antiplane problems is similar to that for in-plane problems. The present solution can provide benchmark results for other numerical and approximate methods.     

Dynamic effective property of fibrous piezoelectric composites with spring- or membrane-type imperfect interfaces

The present paper studies the dynamic effective property of piezoelectric composites embedded with cylindrical piezoelectric fibers under anti-plane harmonic electro-elastic waves. By using the dynamic generalized self-consistent method (DGSM) of electro-elastic coupling wave, the problem of randomly distributed cylindrical fibers in a piezoelectric medium can be analyzed in terms of a representative volume element with a coated fiber embedded in an equivalent effective medium. The interfaces between the fibers and the matrix are assumed to be imperfect which are here modeled as spring- or membrane-type interfaces. Through wave function expansion method and an iterative method, the effective piezoelectrically stiffened shear modulus and the effective wave number are obtained. Examples are conducted to verify the present solutions and to illustrate the dependence of the effective piezoelectrically stiffened shear modulus on the wave number (frequency) as well as the interface properties. The special size effect related to interfacial imperfection is also discussed.     

Bimodal model of slurry viscosity with application to coal-slurries. Part 1. Theory and experiment

The rheological behavior of stable slurries is shown to be characterized by a bimodal model that represents a slurry as made up of a coarse fraction and a colloidal size fine fraction. According to the model, the two fractions behave independently of each other, and the non-Newtonian behavior of the viscosity is solely caused by the colloidal fraction, while the coarse fraction increases the viscosity level through hydrodynamic interactions. Data from experiments run with colloidal coal particles of about 2–3 µm average size dispersed in water show the viscosity of these colloidal suspensions to exhibit a highly shearrate-dependent behavior and, in the high shear limit, to match very closely the viscosity of suspensions of uniform size rigid spheres although the coal volume fraction must be determined semi-empirically. Different amounts of coarse coal particles are added to the colloidal suspension and the viscosity of the truly bimodal slurries measured as a function of shear rate. In agreement with the bimodal model, the measured shear viscosities show the coarse fraction to behave independently of the colloidal fraction and its contribution to the viscosity rise to be independent of the shear rate. It is shown that the shear rate exerted on the colloidal fraction is higher than that applied by the viscometer as a result of hydrodynamic interactions between the coarse particles, and that it is this effective higher shear rate which is necessary to apply in the correlations. For determining the coal volume fraction a relatively simple and quite accurate measurement technique is developed for determining the density and void fraction of coarse porous particles; the technique directly relates volume fraction to mass fraction.     

Effective elastic shear stiffness of a periodic fibrous composite with non-uniform imperfect contact between the matrix and the fibers

In this contribution, effective elastic moduli are obtained by means of the asymptotic homogenization method, for oblique two-phase fibrous periodic composites with non-uniform imperfect contact conditions at the interface. This work is an extension of previous reported results, where only the perfect contact for elastic or piezoelectric composites under imperfect spring model was considered. The constituents of the composites exhibit transversely isotropic properties. A doubly periodic parallelogram array of cylindrical inclusions under longitudinal shear is considered. The behavior of the shear elastic coefficient for different geometry arrays related to the angle of the cell is studied. As validation of the present method, some numerical examples and comparisons with theoretical results verified that the present model is efficient for the analysis of composites with presence of imperfect interface and parallelogram cell. The effect of the non uniform imperfection on the shear effective property is observed. The present method can provide benchmark results for other numerical and approximate methods.     

基于修正压力场理论的再生混凝土梁抗剪承载力计算方法研究

基于修正压力场理论分析有腹筋再生混凝土梁的剪切破坏机理,建立了更接近有腹筋再生混凝土梁实际受力的抗剪模型,并通过考虑再生骨料有效粒径和受箍筋作用下的裂缝宽度与构件裂缝处应力的联系,分析了再生骨料咬合力对梁斜截面抗剪性能的影响,提出了再生混凝土梁极限抗剪承载力的计算方法。此外,本文将理论结果与课题组自制的6根再生混凝土梁的抗剪承载力试验结果进行了对比,理论值与试验值吻合较好,验证了本文方法的有效性,从而为设计人员提供了一种预测再生混凝土梁极限抗剪承载力的计算方法。     

An experimental investigation into the dimension-sensitive viscosity of polymer containing lubricant oils in microchannels

In many lubrication processes, lubricating oils containing polymer additives are subject to high shear rate through very small clearance channels. While the influence of shear rate on the performance of these lubricants has been well examined, very little is known about the effects of channel size. In this study a specially designed microchannel viscometer has been used to experimentally characterize the influence of channel height on the effective viscosity of oil lubricants with two different polymer additives (a radial hydrogenated styrene–isoprene copolymer and an A–B–A block ethylene–propylene copolymer) commenly used as viscosity index (VI) modifiers. The mass concentration of the polymer solutions ranged from 0.5% to 1.5% in this study. The viscosity was measured over a range of shear rates in steel slit microchannels with heights of 4.5, 7 and 11.5 μm, respectively. For all solutions a significant viscosity dependence on channel size was observed. In the higher shear rate range the smaller channels exhibited a lower viscosity while in the lower shear rate range all solutions exhibited a significant increase in viscosity. Generally, this observed increase in viscosity is more dramatic in the smaller channels. Possible causes of these behaviors were discussed in this paper.     

Particle size and boundary geometry effects on the bulk friction coefficient of sheared granular materials in the inertial regime

Glass beads of varying diameters (d=2,3,4$d=2,3,4$, and 5 mm) are used to measure the ratio of shear-to-normal stress, or bulk friction coefficient, generated inside an annular shear cell at high shearing rates. The effects of the particle size, the solids concentration, and the shear rate are explored. It is found that (1) for a given particle size, the magnitude of the bulk friction coefficient decreases with increasing solids concentration, (2) for a given solids concentration, the bulk friction coefficient decreases with increasing particle size, and (3) the bulk friction coefficient is independent of the shear rate except for cases with low solids concentration, where it decreases with increasing shear rate. The boundary geometry is found to affect bulk friction only for dilute (low solids concentration) flows involving small particles.