含有随机夹杂非均匀体的有效弹性模量

在对含有随机夹杂的非均匀体求有效弹性模量时,一般多根据Eshelby的等效夹杂法,但由于该方法没有充分考虑非均匀体内部的微结构,所以其理论具有一定的局限性。本文认为Kunin的微结构理论与Eshelby的等效夹杂法相比更具一般性,因而本文采用了文[9]中一些合理的思想,摒弃了其中不合理的假设,并且建立了一种新的理论模型.最后,本文针对球夹杂的情况给出了非均匀体有效弹性模量依赖于夹杂体积份数的关系,并将该结果与文[10]中的结果进行了比较.     

含正交排列夹杂和缺陷材料的等效弹性模量和损伤

研究含正交排列夹杂和缺陷材料的等效弹性模量和损伤,推导了以Eshelby－Mori－Tanaka方法求解多相各向异性复合材料等效弹性模量的简便计算公式,针对含三相正交椭球状夹杂的正交各向异性材料,得到了由细观参量（夹杂的形状、方位和体积分数）表示的等效弹性模量的解析表达式．在此基础上,提出了一个宏细观结合的正交各向异性损伤模型,从而建立了以细观量为参量的含损伤材料的应力应变关系．最后,对影响材料损伤的细观结构参数进行了分析．     

三维编织复合材料剪切性能分析

根据三维四向编织复合材料的结构特点，提出了刚度合成法预测编织复合材料剪切弹性模量，比较了整体编织试件和裁剪所得试件理论剪切性能差别，分析了三维编织T300／QY9512复合材料的剪切性能随试件沿宽度和厚度两个方向内部单胞数目的变化规律。结果表明，三维编织复合材料剪切弹性模量是与试件尺寸相关的，只有当试件尺寸较大、沿宽度和厚度两个方向内部单胞数目较多时，试件尺寸的影响可以忽略。当沿宽度方向单胞数目较大时，整体编织试件和裁剪所得试件的剪切模量相近。本文还得到了在复合材料板的纤维体积含量不变的情况下，剪切模量随编织角的变化规律。     

混杂短纤维增强复合材料弹性模量预测

在现代工程结构中，纤维增强复合材料具有较高的刚度重量比、优异的耐久性和设计灵活性等优点，因此得到了广泛应用．本文结合细观力学中的Mori-Tanaka方法和Halpin-Tsai方法推导了混杂碳纤维和玻璃纤维增强复合材料有效弹性模量的解析表达式．通过引入参数λ，提出了计算随机方向混合纤维增强复合材料弹性模量的新模型，分析了纤维长径比和体积分数对复合材料弹性模量的影响．结果表明，复合材料的弹性性能对纤维长径比和体积分数非常敏感．根据提出的理论，混杂纤维增强复合材料的弹性模量处于单一纤维（纯碳纤维或纯玻璃纤维）增强复合材料弹性模量之间．对于单一纤维增强复合材料，采用Halpin-Tsai方法计算的复合材料弹性模量高于Mori-Tanaka方法计算结果．     

功能梯度界面相对周期分布纤维增强复合材料反平面剪切的影响

基于复变函数理论和边界配点法,探索了功能梯度界面相在周期均匀分布纤维增强复合材料反平面剪切问题中所起的作用。由于纤维在复合材料基体中的周期分布是均匀的,将其简化成含一功能梯度界面相夹杂的方形单胞。采用分层均匀化方法,将功能梯度界面相离散成K层界面层。当K足够大时,每个界面层可视为匀质材料,同时计算得到的复合材料宏观性能趋于定值。根据单胞内的基体、界面相和夹杂的几何外形特点,分别给出复势函数的级数形式,这些复势函数在各组分的相邻界面应满足连续性条件,在单胞的外边界应满足周期性边界条件和远场加载条件,从而确定复势函数中的待定系数,进而根据平均场理论确定复合材料有效模量。主要探讨了夹杂体积分数、各组分模量、功能梯度界面相的模量渐变形式等因素对纤维增强复合材料性能的影响。结果表明：不管基体模量相对于夹杂模量是大还是小,都有对应的界面相模量渐变形式可使夹杂周围的等效应力集中系数减小;另外还发现仅当夹杂模量较大时,功能梯度界面相模量的变化方式对复合材料有效模量产生不可忽视的影响。     

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。     

颗粒增强橡胶细观力学性能二维数值模拟

在细观层次上建立了具有随机分布形态的代表性体积单元,通过细观力学有限元方法对炭黑颗粒填充橡胶复合材料的宏观力学性能进行了研究。采用二维平面应变模型进行单轴压缩模拟仿真,通过施加周期边界条件保证了代表性体积单元变形场的协调性。重点研究讨论了颗粒的随机分布形态和粒径大小、刚度、体积分数对复合材料宏观应力-应变关系曲线和有效弹性模量的影响。结果表明:炭黑颗粒的填充显著提升了橡胶材料的刚度,在炭黑含量Vf=0.2513时,复合材料的有效弹性模量值高于橡胶初始模量值的2倍;复合材料的有效弹性模量随颗粒所占体积分数的增加而增大。     

智能复合材料的热力学特性

由形状记忆合金丝或颗粒增强的智能复合材料具有特殊的力学性能，本文从理论上预测了智能复合材料的热力学特性。利用Ｅｓｈｅｌｂｙ的等效夹杂原理与Ｍｏｒｉ－Ｔａｎａｋａ的平均场理论导出了本构列式和相变条件，揭示了形状记忆合金在弹性介质约束下的相变机理与过程。     

含界面相Voronoi单元的等效弹性常数的计算

采用含界面相Voronoi单元有限元法,根据广义胡克定律,计算了在给定边界条件下,颗粒增强复合材料的等效弹性常数。建立了含多个随机分布的椭圆形夹杂及界面相的VCFEM模型,分析了夹杂体分比,界面相厚度和界面相弹性模量等因素对颗粒增强复合材料等效弹性常数的影响,并利用普通有限元方法对比验证。结果表明,当界面相弹性模量小于基体与夹杂时,材料的等效弹性模量会随着界面相厚度的增大而减小,随着夹杂体分比的增大而减小,并且界面过薄时,材料的等效弹性模量会随着夹杂体分比的增大而增大;当界面相弹性模量大于基体或夹杂时,材料的等效弹性模量会随着夹杂体分比和界面相厚度的增大而增大。而界面相的厚度和弹性模量对材料的等效泊松比的影响较小,材料的等效泊松比主要受夹杂体分比的影响,与其呈反比关系。     

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．     

Prediction of the overall moduli of a cylindrical short-fiber reinforced composite

With respect to obtaining the effective elastic moduli of the composite, the present theory differs from both Eshelby's equivalent inclusion method and Hill's self-consistent one, both of which only consider the mechanical properties of the matrix and inclusions (fibers). In fact, the inclusion-inclusion interaction is more pronounced when the volume fraction of inclusions of the composite increases. Hence, in this paper the effective elastic moduli of the composite are derived by taking into account the shapes, sizes and distribution of inclusions, and the interactions between inclusions. In addition, it is more convincing to assume short-fibers as cylindrical inclusions as in the present paper than as ellipsoidal ones as in others^[7,8]. Finally, numerical results are given.     

Asymptotic determination of effective elastic properties of composite materials with fibrous square-shaped inclusions

We propose an asymptotic approach for evaluating effective elastic properties of two-components periodic composite materials with fibrous inclusions. We start with a nontrivial expansion of the input elastic boundary value problem by ratios of elastic constants. This allows to simplify the governing equations to forms analogous to the transport problem. Then we apply an asymptotic homogenization method, coming from the original problem on a multi-connected domain to a so called cell problem, defined on a characterizing unit cell of the composite. If the inclusions' volume fraction tends to zero, the cell problem is solved by means of a boundary perturbation approach. When on the contrary the inclusions tend to touch each other we use an asymptotic expansion by non-dimensional distance between two neighbouring inclusions. Finally, the obtained “limiting” solutions are matched via two-point Padé approximants. As the results, we derive uniform analytical representations for effective elastic properties. Also local distributions of physical fields may be calculated. In some partial cases the proposed approach gives a possibility to establish a direct analogy between evaluations of effective elastic moduli and transport coefficients. As illustrative examples we consider transversally-orthotropic composite materials with fibres of square cross section and with square checkerboard structure. The obtained results are in good agreement with data of other authors.     

Linear rheology of compressible soft nanocomposites

The influences of interfacial tension and compressibility to the linear viscoelastic properties of nanocomposite and nanoporous materials are considered theoretically. The effective bulk and shear moduli of the systems are calculated within the generalized composite sphere model which takes into account the effect of interfacial tension. It is found that frequency dependence of the effective dynamic shear and bulk moduli of nanocomposites with the compressible elastic matrix and viscous inclusions may be represented in terms of the Zener model comprising of the viscoelastic Kelvin element in series with the elastic spring. The relations of the Zener model parameters with the material characteristics are revealed. The physical interpretation of the frequency behavior of the dynamic shear and bulk moduli against the interfacial tension, component compressibility, viscosity, and inclusion volume fraction is discussed. Victor G. Oshmyan deceased.     

Differential schemes for the elastic characterisation of dispersions of randomly oriented ellipsoids

The paper deals with the elastic characterisation of dispersions of randomly oriented ellipsoids: we start from the theory of strongly diluted mixtures and successively we generalise it with a differential scheme. The micro-mechanical averaging inside the composite material is carried out by means of explicit results which allows us to obtain closed-form expressions for the macroscopic or equivalent elastic moduli of the overall composite materials. This micromechanical technique has been explicitely developed for describing embeddings of randomly oriented not spherical objects. In particular, this study has been applied to characterise media with different shapes of the inclusions (spheres, cylinders and planar inhomogeneities) and for special media involved in the mixture definition (voids or rigid particles): an accurate analysis of all these cases has been studied yielding a set of relations describing several composite materials of great technological interest. The differential effective medium scheme (developed for generally shaped ellipsoids) extends such results to higher values of the volume fraction of the inhomogeneities embedded in the mixture. For instance, the analytical study of the differential scheme for porous materials (with ellipsoidal zero stiffness voids) reveals a universal behaviour of the effective Poisson ratio for high values of the porosity. This means that Poisson ratio at high porosity assumes characteristic values depending only on the shape of the inclusions and not on the elastic response of the matrix.     

Differential geometrical method in elastic composite with imperfect interfaces

I.IntroductionWhethertheinterfacesofcompositematerialsareperfectornotwillaffectitsmacromechanicaloreffectivepropertiesimportantly.Butsofar,almostallofthestudiesontheeffectivepropertiesofcompositematerialsarebasedontheassumptionthattheinterfacesareperfectl"2].Infact,thisisnotappropriateforallinterfaces[31.Thusthestudiesonmechanicalpropertyofcompositematerialswithimperfaceintert'acehavebeenconsideredrecentlyinsomeliteratures.Hashin16]hasextendedtheelasticextremumprinciplesofminimumpotentialandm…     

Stress intensity factors for ring-shaped crack surrounded by spherical inclusions

Interaction of a ring-shaped crack with inhomogeneities such as inclusions is analyzed for the resulting three-dimensional stress field. Considered for the composite solid with a given volume fraction of inclusions are the two cases of (a) spherical voids and (b) spherical inclusions with elastic moduli different from the matrix. A ring-shaped crack is initiated at the equator of one of the voids or inclusions. A three-phase model is used to examine the interaction between the crack and surrounding inhomogeneities. Finite element method is then applied to calculate the stress intensity factor for different configurations. The effects of volume fraction of inhomogeneities, relative size of crack to inclusions, and material constants on crack behavior are discussed.     

On effective moduli of inhomogeneous media characterized by several small parameters

Composites and porous media of elongated structure, as well as materials with pores or inclusions having the shape of parallelepipeds or channels of rectangular cross-section, are considered under certain conditions on the inclusion-to-matrix modulus ratio and the volume fraction of inclusions (pores). The effective moduli are calculated by the method of mathematical homogenization theory. Numerical results on the dependence of the effective moduli on the prolateness of the structure, the shape of the inclusions (pores), the inclusion-to-matrix modulus ratio, and the volume fraction of inclusions (pores) are given. The effective moduli computed according to the algorithm of mathematical homogenization theory are compared with those given by the explicit approximate formulas earlier developed by the authors.     

Simple algebraic approximations for the effective elastic moduli of cubic arrays of spheres

Recently, Cohen and Bergman (Phys. Rev. B 68 (2003a) 24104) applied the method of elastostatic resonances to the three-dimensional problem of nonoverlapping spherical isotropic inclusions arranged in a cubic array in order to calculate the effective elastic moduli. The leading order in this systematic perturbation expansion, which is related to the Clausius-Mossotti approximation of electrostatics, was obtained in the form of simple algebraic expressions for the elastic moduli. Explicit expressions were derived for the case of a simple cubic array of spheres, and comparison was made with some accurate results. Here, we present explicit expressions for the effective elastic moduli of base-centered and face-centered cubic arrays as well, and make a comparison with other estimates and with accurate numerical results. The simple algebraic expressions provide accurate results at low volume fractions of the inclusions and are good estimates at moderate volume fractions even when the contrast is high.     

含柔性涂层的颗粒增强复合材料弹性模量估计

采用线弹簧型弱界面模型来模拟柔性涂层,研究柔性涂层对复合材料宏观弹性模量的影响。首先利用Mori-Tanaka方法和弱界面球形夹杂问题的弹性解,获得单夹杂内部的平均应力和平均应变,进而求得具有柔性涂层的复合材料的宏观弹性模量,并研究界面柔度对复合材料弹性模量的影响。