球形涂层粒子增强复合材料的有效模量

本文通过四相球模型和复合材料的等效介质理论,研究了球形涂层粒子增强复合材料的有效模量性质,得到了这种增强复合材料的有效体积模量和有效剪切模量的理论预测公式。这些结果在特殊情况下,可退化到三相球模型确定的球形粒子增强复合材料的有效模量公式。     

基于变体积约束的阻尼材料微结构拓扑优化研究北大核心CSCD

阻尼复合结构的抑振性能取决于材料布局和阻尼材料特性.该文提出了一种变体积约束的阻尼材料微结构拓扑优化方法,旨在以最小的材料用量获得具有期望性能的阻尼材料微结构.基于均匀化方法,建立阻尼材料三维微结构有限元模型,得到阻尼材料的等效弹性矩阵.逆用Hashin-Shtrikman界限理论,估计对应于期望等效模量的阻尼材料体积分数限,并构建阻尼材料体积约束限的移动准则.将获得阻尼材料微结构期望性能的优化问题转化为体积约束下最大化等效模量的优化问题,建立阻尼材料微结构的拓扑优化模型.利用优化准则法更新设计变量,实现最小材料用量下的阻尼材料微结构最优拓扑设计.通过典型数值算例验证了该方法的可行性和有效性,并讨论了初始微构型、网格依赖性和弹性模量等对阻尼材料微结构的影响.     

空心球复合材料热弹性性质的一些精确结果

本文基于所提出的基体均匀场方法研究了空心球增强复合材料的热弹性性质·导出了均匀边界条件激发的局部热场和力学场量的关系，并进而得到了复合材料等效热弹性性质之间的精确关系·对于具有某种特定内外径比的空心球所构成的宏观各向同性复合材料，如果基体和空心球的热膨胀系数相同，可以证明其等效体积模量和线膨胀系可以精确地确定·     

基于杂交应力元法的颗粒增强复合材料Monte-Carlo模拟

杂交应力元假设的高阶应力场可以用较疏的网格获得较高的计算精度.采用四叉树网格离散非均质计算域,四叉树杂交应力单元悬挂节点的位移协调条件自动满足,且得益于单元类型数量有限,单元刚度矩阵可以预计算,以便在实际计算时直接读取调用,大幅提高了计算效率.考虑夹杂的随机性对颗粒增强复合材料力学性能的影响,采用均匀化方法和Monte-Carlo方法,研究了随机夹杂的体积比、数量、长宽比对材料均质等效模量的影响,结果表明,复合材料的等效弹性模量随夹杂体积比、数量、长宽比的增大而增大,且对体积比最敏感.     

非完美界面弹性复合材料中的微分几何方法

首次用微分几何方法计算了含一般旋转椭球体嵌入相的非完美界面弹性复合材料的有效模量·用内蕴几何量表出了能量泛函中的全部界面积分项，由此得到了这种统一嵌入相模型的复合材料有效模量的上下界限·在三种极限情况，即球、盘和针状嵌入相下，本文的结果将退化到Ｈａｓｈｉｎ（１９９２）的结果·     

预测纳米纤维复合材料有效弹性性能的界面模型和界面相模型北大核心CSCD

基于广义自洽法,同时采用Gurtin-Murdoch界面模型和界面相模型研究了纳米纤维复合材料的有效弹性性能,获得了两种模型下有效体积模量的封闭解析解和计算有效面内剪切模量数值解的全部公式.基于界面模型的解答,讨论了有效体积模量和有效面内剪切模量的界面效应.证明了界面模型的解答可由界面相模型的解答退化得到,其中有效体积模量可以实现解析退化,有效面内剪切模量则可以数值退化.以含纳米孔洞的金属铝为例,比较了两种模型计算结果的差异.结果表明,当纳米孔洞半径较小时,两个模型的结果存在很大差异,而当半径较大时两个模型的结果差别不大.     

高体积百分比颗粒增强聚合物材料的有效粘弹性性质

聚合物材料通常表现为粘弹性性质．为了改进聚合物材料的力学性能,通常将某种无机材料以颗粒或纤维的形式填充到聚合物中,从而得到增强、增韧的聚合物基复合材料．提出了一个新的细观力学模型,用于预测颗粒增强聚合物复合材料的有效粘弹性性质,尤其针对高体积百分比的颗粒夹杂复合材料,该方法基于Laplace变换和双夹杂相互作用的弹性模型．计算了玻璃微珠/ED-6复合材料的有效松弛模量以及恒应变率下的应力应变关系．计算结果表明在高体积百分比下该文方法比基于Mori Tanaka方法预测的粘弹性效应明显减弱．     

具有非均匀界面相的颗粒和纤维增强复合材料弹性静力学问题的解析解

通过将以位移表示的平衡方程转化为黎卡提方程,得到了具有非均匀界面相的颗粒和纤维增强复合材料非均匀界面相内弹性场的解析解·　所得的解析解是弹性模量呈幂次方变化的非均匀界面相解的通用形式·　任意给定1个幂指数,可以得到具有非均匀界面相的颗粒和纤维增强复合材料体积模量的解析表达式·　通过改变幂指数及幂次方项的系数,此解析解可适用于具有多种不同性质的非均匀界面相·　结果表明:界面相模量和厚度对复合材料模量有很大的影响,当界面相存在时,粒子将出现一种"尺寸效应"·     

残余界面应力对粒子填充热弹性纳米复合材料有效热膨胀系数的影响

根据黄筑平等人提出的基于“3个构形”的表/界面能理论,研究了热弹性纳米复合材料的有效性质,重点讨论了残余界面应力对纳米尺度夹杂填充的热弹性复合材料有效热膨胀系数的影响．首先,给出了由第一类Piola-Kirchhoff界面应力表示的热弹性界面本构关系和Lagrange描述下的Young-Laplace方程;其次,采用Hashin复合球作为代表性体积单元,推导了在参考构形下复合球内部由残余界面应力诱导的残余弹性场,并进一步计算了从参考构形到当前构形的变形场;最后,基于以上计算得到了热弹性复合材料有效体积模量和有效热膨胀系数的解析表达式．研究表明,残余表/界面应力对复合材料的热膨胀系数有重要影响．     

横观各向同性基体复合材料的等效弹性常数

细观力学的一个主要研究内容是求复合材料的等效弹性性能.常见的细观力学模型解析公式一般假定基体各向同性且只存在纤维和基体两相材料,实际复合材料的基体和纤维之间往往存在一个横观各向同性的界面相,该三相复合材料的等效性能可由两个两相复合材料性能的组合得到,这就需要求出横观各向同性基体复合材料的等效弹性常数.该文基于两相同心圆柱模型,首先导出了横观各向同性基体内应力与增强纤维内应力之间桥联矩阵的解析公式,与基于数值积分Eshelby张量得到的Mori-Tanaka桥联矩阵相符,再进一步获得了横观各向同性基体复合材料的5个弹性常数显式表达式.文中还给出了扩展的桥联模型显式公式.选用适当的桥联参数,两种模型所得结果十分接近.     

A Comparison of homogenization, Hashin-Shtrikman bounds and the Halpin-Tsai Equations

In this paper we study a unidirectional and elastic fiber composite. We use the homogenization method to obtain numerical results of the plane strain bulk modulus and the transverse shear modulus. The results are compared with the Hashin-Shtrikman bounds and are found to be close to the lower bounds in both cases. This indicates that the lower bounds might be used as a first approximation of the plane strain bulk modulus and the transverse shear modulus. We also point out the connection with the Hashin-Shtrikman bounds and the Halpin-Tsai equations. Optimal bounds on the fitting parameters in the Halpin-Tsai equations have been formulated.     

Modeling viscoelastic response of particulate polymeric composites with high volume fractions of fillers

A generalized self-consistent method is extended to particulate viscoelastic composites with elastomeric matrices and high volume fractions of elastic inclusions. It is shown that the effective bulk modulus of a composite coincides with the bulk modulus of particles. A quadratic operator equation is derived for an analog of the effective shear relaxation kernel. This equation is explicitly solved using the Laplace transform method. The influence of material and geometrical parameters of a composite on its effective viscoelastic moduli is analyzed numerically.     

On bounds for bulk arrival queues

This paper gives a simple and effective approach pf deriving bounds for bulk arrival queues by making use of the bounds for single arrival queues. With this approach, upper bounds of mean actual/virtual waiting times and mean queue length at random epochs can be derived for the bulk arrival queues GI^X/G/1 and GI^X/G/c (lower bounds can be derived in a similar way). The merit of this approach is shown by comparing the bounds obtained with some existing results in the literature.     

Calculation of deformative and thermal properties of multiphase composite materials filled with composite or hollow spherical inclusions by the effective medium method

A theoretical investigation was carried out to examine the possibilities of a structural approach to prediction of elastic constants, creep functions, and thermal properties of multiphase polymer composite materials filled with composite or hollow spherical Inclusions of several types. The problem of determining effective properties of the composite was solved by generalizing the effective medium method, a variant of the self-consistent method, for the case of a four-phase kernel-shell-matrix-equivalent homogeneous medium model. Exact analytical expressions for the bulk modulus thermal expansion coefficient, thermal conductivity coefficient, and specific heat were obtained. The solution for the shear modulus is given in the form of a nonlinear equation whose coefficients are the solution of a system of 12 linear equations.To be presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, October 1995.Published in Mekhanika Kompozitnykh Materialov, Vol. 31, No. 4, pp. 462–472, July–August, 1995.     

Effect of hydrostatic pressure on certain thermodynamic properties of polymeric materials

By means of a thermodynamic approach it is demonstrated that the mechanical properties of homogenous polymeric materials depend only on specific volume. Expressions are derived for the entropy and volume coefficient of thermal expansion as functions of hydrostatic pressure and temperature. It is shown that for both crystalline and amorphous polymeric materials the bulk modulus depends on reduced temperature.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 825–829, September–October, 1970.     

Exact relations for effective tensors of composites: Necessary conditions and sufficient conditions

Typically the elastic and electrical properties of composite materials are strongly microstructure dependent. So it comes as a nice surprise to come across exact formulae for effective moduli that are universally valid no matter what the microstructure. Such exact formulae provide useful benchmarks for testing numerical and actual experimental data and for evaluating the merit of various approximation schemes. They can also be regarded as fundamental invariances existing in a given physical context. Classic examples include Hill's formulae for the effective bulk modulus of a two‐phase mixture when the phases have equal shear moduli, Levin's formulae linking the effective thermal expansion coefficient and effective bulk modulus of two‐phase mixtures, and Dykhne's result for the effective conductivity of an isotropic two‐dimensional polycrystalline material. Here we present a systematic theory of exact relations embracing the known exact relations and establishing new ones. The search for exact relations is reduced to a search for matrix subspaces having a structure of special Jordan algebras. One of many new exact relations is for the effective shear modulus of a class of three‐dimensional polycrystalline materials. We present complete lists of exact relations for three‐dimensional thermoelectricity and for three‐dimensional thermopiezoelectric composites that include all exact relations for elasticity, thermoelasticity, and piezoelectricity as particular cases. © 2000 John Wiley & Sons, Inc.     

On characterizing the set of possible effective tensors of composites: The variational method and the translation method

A general algebraic framework is developed for characterizing the set of possible effective tensors of composites. A transformation to the polarization-problem simplifies the derivation of the Hashin-Shtrikman variational principles and simplifies the calculation of the effective tensors of laminate materials. A general connection is established between two methods for bounding effective tensors of composites. The first method is based on the variational principles of Hashin and Shtrikman. The second method, due to Tartar, Murat, Lurie, and Cherkaev, uses translation operators or, equivalently, quadratic quasiconvex functions. A correspondence is established between these translation operators and bounding operators on the relevant non-local projection operator, T₁. An important class of bounds, namely trace bounds on the effective tensors of two-component media, are given a geometrical interpretation: after a suitable fractional linear transformation of the tensor space each bound corresponds to a tangent plane to the set of possible tensors. A wide class of translation operators that generate these bounds is found. The extremal translation operators in this class incorporate projections onto spaces of antisymmetric tensors. These extremal translations generate attainable trace bounds even when the tensors of the two-components are not well ordered. In particular, they generate the bounds of Walpole on the effective bulk modulus. The variational principles of Gibiansky and Cherkaev for bounding complex effective tensors are reviewed and used to derive some rigorous bounds that generalize the bounds conjectured by Golden and Papanicolaou. An isomorphism is shown to underlie their variational principles. This isomorphism is used to obtain Dirichlet-type variational principles and bounds for the effective tensors of general non-selfadjoint problems. It is anticipated that these variational principles, which stem from the work of Gibiansky and Cherkaev, will have applications in many fields of science.