非对称铺层复合材料层合板的双稳态特性半解析研究

非对称铺层的复合材料层合板在存在热残余应力的情况下，具有双稳态性质．层合板的两个稳态之间仅需要一个适当的激励就可以互相转化，因此该结构在变体飞机上应用广泛．基于经典层合板理论，本文引入几何大变形建立了具有双稳态性质的复合材料层合板的能量泛函，提出了一个高阶的位移场函数，用瑞利里兹法推导出一组关于位移场函数系数的非线性方程组．结合牛顿迭代法和消元法求解非线性方程组，得到了层合板面外位移场．同时利用有限元软件ABAQUS，对复合材料层合板双稳态机理进行了数值模拟．选取了几组具有代表性的铺层进行计算，以有限元结果为基准，比较了本文的位移场结果与前人的结果，验证了高阶位移场函数的准确性．     

编织复合材料弹性性能的细观力学模型

提出了编织复合材料弹性性能分析的细观力学模型，这个力学模型考虑了实际编织结构中的纬向和经向纤维束的曲屈，相邻纤维束之间的间隙和纤维束的横截面尺寸对编织复合材料弹性性能的影响，并探讨了在纤维束间纯树脂区内孔隙的含量和两种叠层结构对材料弹性性能的影响．理论计算结果与实测值的比较，表明所提出的细观力学模型是合理的．根据理论分析的结果，提出了优化单层和叠层编织结构的结构参数选择方法     

含夹杂复合材料宏观性能研究

本文综述并评价了有关含夹杂复合材料的有效弹性模量研究的代表性工作，包括自洽理论，微分法，Ｅｓｈｅｌｂｙ－Ｍｏｒｉ－Ｔａｎａｋａ法，Ｈａｓｈｉｎ和Ｓｈｔｒｉｋｍａｎ的变分法等。指出上述理论由于没有充分考虑复合材料内部的微结构特征，如夹杂的形状、几何尺寸、分布和夹杂间的相互影响，在夹杂的体积份数较大，如大于０．３时已不能有效地预报复合材料的有效弹性模量，随后介绍了近来才发展起来的一种新方法─—相关函数积分法，理论与实验的结果的比较表明，该方法在夹杂体积份数较大时仍然有效。     

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．     

非局部弹性理论概述及在当代材料背景下的一些进展

局部作用原理在发展经典连续介质力学的本构关系中起着重要的作用，由此导出的简单物质理论得到了广泛的应用．然而，随着科技的发展，各种具有微结构的新材料不断涌现，理论和实验表明，非局部理论可以更好地刻画这些材料的宏观力学行为．本文简要介绍了一些传统的非局部弹性理论，包括Eringen 理论、Kunin 理论、Mindlin 理论；阐述了针对复合材料发展的，具有时间-空间非局部特征的Willis 方程、最新的时间-空间耦合非局部弹性动力学理论以及近场动力学理论．时间-空间非局部理论反映了复合材料宏观性能固有的非局部特征，而具有空间非局部特征的近场动力学理论便于处理具有不连续性的问题．最后，本文讨论了非局部理论的发展中值得关注的一些问题.     

复合材料宏观性能的细观力学研究

本文利用Ｍｏｒｉ－Ｔａｎａｋａ平均场理论，从细观力学的角度讨论了建立复合材料宏观性能与微观结构联系的方法．这方面的工作对复合材料的优化和设计有着重要指导意义     

改进的二维高精度通用单胞模型

基于复合材料细观力学周期性假设,利用高阶理论的改进算法,对高精度通用单胞模型的计算方法进行了改进．模型中用界面的平均量代替细观位移函数中解系数,并利用细观单元力学方程的分析与求解,建立了细观平均量与复合材料宏观平均量间的联系．改进高精度通用单胞模型的求解方程数目减少了大约60％,求解时间大大缩短;并且消除了亚子胞的概念,同时解耦了横向与纵向的方程．该模型的计算结果与试验结果及理论计算结果具有较好的一致性．     

复合材料的宏观性能与参数设计

本文综述了预测复合材料宏观性能──有效刚度的几类方法：自洽模型、单胞模型以及它们的结合──自洽有限元法．阐述了复合材料发生弹塑性变形时的有关力学问题．基于细观力学的定量分析结果，探讨了面向材料宏观刚度的细观结构参数设计的基本原则，以期对建立复合材料细观结构设计的力学和数学模型有所启发．     

葵花杆填充板静曲力学性能研究

本文运用复合材料刚度合理分配法，在理论分析和实验的基础上给出了新的计算公式，揭示了葵花杆填充板的力学性能，为广泛使用该材料提供了理论依据．     

葵花杆填充板静曲力学性能研究

本文运用复合材料刚度合理分配法，在理论分析和实验的基础上给出了新的计算公式，揭示了葵花杆填充板的力学性能，为广泛使用该材料提供了理论依据．     

考虑碳纳米管非均匀分布的复合材料电导率计算

碳纳米管作为导电相在机敏复合材料中广泛应用,但碳纳米管为团簇材料,在基体中很难均匀分散。本文考虑碳纳米管的非均匀分布特性,提出了计算碳纳米管复合材料电导率的数值方法。通过引入随机谐和函数,建立了碳纳米管体积分数的三维随机场模型。基于细观力学的有效介质理论、Mori-Tanaka方法和H-S界限理论,考虑碳纳米管之间的隧穿效应,发展了复合材料微小体积单元的电导率计算方法。在此基础上,构建了考虑碳纳米管非均匀分布的复合材料等效电导率三维有限元计算模型。数值分析结果与试验值能够很好吻合,表明这一方法可以准确计算碳纳米管复合材料的电导率。本文进一步分析了碳纳米管非均匀分布对复合材料电导率的影响。     

The homogenization method for the study of variation of Poisson's ratio in fiber composites

Summary Materials with specific microstructural characteristics and composite structures are able to exhibit negative Poisson's ratio. This fact has been shown to be valid for certain mechanisms, composites with voids and frameworks and has recently been verified for microstructures optimally designed by the homogenization approach. For microstructures composed of beams, it has been postulated that nonconvex shapes (with reentrant corners) are responsible for this effect. In this paper, it is numerically shown that mainly the shape, but also the ratio of shear-to-bending rigidity of the beams do influence the apparent (phenomenological) Poisson's ratio. The same is valid for continua with voids, or for composites with irregular shapes of inclusions, even if the constituents are quite usual materials, provided that their porosity is strongly manifested. Elements of the numerical homogenization theory and first attempts towards an optimal design theory are presented in this paper and applied for a numerical investigation of such types of materials. Received 11 March 1997; accepted for publication 12 September 1997     

Anisotropic strength of composites

The present investigation is concerned with the development of a theory of strength of anisotropic composite materials and the establishment of sound experimental procedures for the confirmation of the predicted results. A general theory is stated whereby the strength of laminated as well as unidirectional composite materials subjected to any state of combined stress can be predicted once the basic strength characteristics of a unidirectional layer have been determined. The transversely isotropic layer is treated in detail and, based on the understanding of the mechanical behavior of laminated composites, the procedure outlined for determining the strength of laminated systems. An experimental program was conducted, using glass-filament-reinforced resin test spceimens, and data obtained confirmed the results predicted for the strength of unidirectional composites. Based on the results of the analysis presented, composites may then be designed to incorporate an optimum utilization of the inherent strength characteristics of the constitutent materials.     

On two models in the three-dimensional theory of stability of composites

A comparative analysis is made of the infinite-fiber and finite-fiber models in the three-dimensional theory of stability of composites. The results analyzed have been obtained using the three-dimensional linearized theory of stability of deformable bodies. A historical sketch is given of the theory of stability for and approaches used in the mechanics of laminated and fibrous composite materials Translated from Prikladnaya Mekhanika, Vol. 44, No. 8, pp. 3–31, August 2008.     

Electroelastic behavior of doubly periodic piezoelectric fiber composites under antiplane shear

The piezoelectric composites with a doubly periodic parallelogrammic array of piezoelectric fibers are dealt with under antiplane shear coupled with inplane electrical load. A rigorous analytical method is developed by using the doubly quasi-periodic Riemann boundary value problem theory integrated with the eigenstrain and eigen-electrical-field concepts. The numerical results are presented and a comparison with finite element calculations, experimental data and micromechanical analysis is made to demonstrate the efficiency and accuracy of the present method. Subsequently, the present solutions are used to study two important topics in piezoelectric fiber composites, i.e., (1) stress and electrical field fluctuations in the microstructure, (2) the macroscopic effective electroelastic moduli. The relation between the macroscopic properties of the composites and their microstructural parameters is discussed and many interesting electroelastic interaction phenomena are revealed, which are useful to estimate and optimize the performance of piezoelectric composites.     

Transient waves in composite materials

A continuum theory for transient wave propagation in three-dimensional composite materials is given. The derived model provides a set of governing equations for the prediction of dynamic response of elastic composites to impulsive loadings. Pulse propagation normal to the direction of layering in periodically bilaminated media, and normal to the fiber direction in unidirectional long-fiber composites are obtained as special cases. The dynamic response of the composite is determined solely from the materials properties of the constituents (assumed in general to be orthotropic) and their geometrical dimensions. The predicted propagating transient waves are checked with exact solutions for impacted laminated composites, and with measured data for a fiber-reinforced material. Applications are given for pulse propagation in particulate composites and in tri-othogonally fiber-reinforced materials.     

Onset of failure in finitely strained layered composites subjected to combined normal and shear loading

A limiting factor in the design of fiber-reinforced composites is their failure under axial compression along the fiber direction. These critical axial stresses are significantly reduced in the presence of shear stresses. This investigation is motivated by the desire to study the onset of failure in fiber-reinforced composites under arbitrary multi-axial loading and in the absence of the experimentally inevitable imperfections and finite boundaries.By using a finite strain continuum mechanics formulation for the bifurcation (buckling) problem of a rate-independent, perfectly periodic (layered) solid of infinite extent, we are able to study the influence of load orientation, material properties and fiber volume fraction on the onset of instability in fiber-reinforced composites. Two applications of the general theory are presented in detail, one for a finitely strained elastic rubber composite and another for a graphite-epoxy composite, whose constitutive properties have been determined experimentally. For the latter case, extensive comparisons are made between the predictions of our general theory and the available experimental results as well as to the existing approximate structural theories. It is found that the load orientation, material properties and fiber volume fraction have substantial effects on the onset of failure stresses as well as on the type of the corresponding mode (local or global).     

On the theory of stability of laminated composites

The stability-loss problem for laminated composites is considered for infinite layers with constant thicknesses and parallel interfaces. It is assumed that composites of periodic structure are compressed along the layers and in the perpendicular direction. A spatial problem is investigated using the three-dimensional linearized theory of deformable-body stability in the general case of elastic and elastoplastic compressible and incompressible isotropic and orthotropic bodies under finite and small (two variants of theory) precritical strains. The concept of a plane of points with equal phases of stability-loss form along layers is introduced. A method is proposed for solution of the problem when this plane is oriented arbitrarily with respect to the layer direction. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 4, pp. 3–10, April, 1999.     

织物及织物复合材料本构理论与试验研究进展

织物复合材料具有高的抗损伤性, 各方向的性能优于层合复合材料, 因而引起人们的重视.织物增强复合材料由于其高比强度、易于制造和充分发展的织物技术等优点使其已经广泛用于航空、汽车和运动产品. 由于使用这些材料越来越普遍, 自动化生产替代了手工生产, 用精确的方法模拟材料的变形是必不可少的. 为了精确的反映材料的行为, 那么就需要描述材料力学性质的本构方程,而作为验证本构模型的试验是伴随着本构模型的发展而发展的.本文首先综述了织物及织物复合材料的发展和现状, 接着重点介绍了织物及织物复合材料的本构理论的研究发展, 并对织物及织物复合材料的斜拉伸试验、像框试验等内容进行了介绍. 最后根据织物复合材料的最新进展对其未来的发展趋势进行了展望.      

Asymptotic homogenization of three-dimensional thermoelectric composites

Thermoelectric composites are promising for high efficiency energy conversion between thermal flows and electric conduction, though their effective behaviors remain poorly understood due to nonlinear thermoelectric coupling. In this paper, we develop an asymptotic homogenization theory to analyze the effective behavior of three-dimensional (3D) thermoelectric composites, built on the observation that the equations governing microscopic field fluctuations in the composite are actually linear instead of nonlinear after separation of length scales. A set of solutions similar to Green's function method are used to construct the unit cell problem, and appropriate interfacial continuity conditions and boundary conditions are derived. The homogenized governing equations are then developed for thermoelectric composites, and they are further reduced for a special case wherein the heat flow and electric conduction in the composite remains one-dimensional (1D) at macroscopic scale, even though the composite itself is 3D in general. The general homogenization theory is implemented using finite element method, and a key constant in the constructed solutions is determined using the reformulated eigenvalue problem. The algorithm is validated, and is applied for a number of case studies for the effective behavior of thermoelectric composites.