双周期电磁弹性纤维增强复合材料的纵向剪切问题

利用等效夹杂法并结合双 (准) 周期解析函数理论,为双周期电磁弹性圆截面纤维复合材料的纵向剪切问题发展了实用有效的解析方法,获得了全场的级数解,给出了应力、电位移和磁感应强度的显式结果。利用数值算例讨论了该类非均匀材料微结构对其电磁弹性性能的影响。本文方法为电磁弹性复合材料的性能分析和微结构设计提供了一个实用有效的计算工具。      

一种通用的计算复合材料刚度的有限元方法

根据复合材料宏观有效模量的定义,本文通过在复合材料细观模型的边界施加六组特定形式的均匀边界条件,以三维有限元作为数值分析手段,对各种细观模型及增强相力学特性,可一次性全部解出复合材料的所有弹性系数。通过计算典型代表体元细观模型,验证了本文数值方法的准确性和优越性。     

高模碳纤维细观力学分析

将碳纤维视为由微晶和无定型碳所构成的二相复合材料,以Mori-Tanaka方法研究了碳纤维微观结构对弹性模量的影响。对四种高模碳纤维M35JB、M40JB、M46JB及M55JB的微观量进行了测量。微晶的长细比由XRD实验测得,碳纤维石墨化程度由拉曼光谱分析得到。影响碳纤维弹性模量的因素包括:微晶的长细比、体积分数及取向度。通过计算细观力学模型得到了四种高模碳纤维的微晶体积分数。研究发现:碳纤维石墨化程度越高,微晶体积分数越大。碳纤维弹性模量随着微晶取向度、体积分数和长细比的增加而增加,且对这三种因素做了比较,微晶取向度和体积分数对弹性模量的影响高于微晶长细比对弹性模量的影响,只有当微晶取向度接近100%时,其对弹性模量的影响才有可能被微晶长细比超越。微晶取向度和体积分数增加的最初阶段,取向度对弹性模量的影响较大,随着两影响因素的增加,取向度对弹性模量的影响最终被体积分数超越。     

高体积含量颗粒增强复合材料的一个细观力学模型Ⅰ: 弹性分析与等效模量

提出了一种高体积含量颗粒增强复合材料的细观力学模型。该模型将颗粒简化为同质、同尺寸的弹性圆球, 两颗粒之间的粘接材料(基体) 简化为连接颗粒的一段圆柱体, 假设了圆柱形基体中的细观位移分布形式, 在此基础上分析了一对颗粒之间弹性的细观应力场和细观弹性系数, 将颗粒对的细观弹性系数在空间各个方向上平均, 得到材料的宏观弹性常数, 并建立了宏、细观分析之间的联系。最后用本模型分析了一种实际材料(两种体积含量) , 弹性常数的预测与实验吻合良好, 研究还发现颗粒的空间分布方式对材料宏观弹性常数的影响不大, 而对细观应力的影响显著。      

基于细观力学的纤维沥青混凝土有效松弛模量

为了研究纤维沥青混凝土的本构模型,将其视为以沥青混合料为粘弹性基体,纤维为弹性夹杂的两相复合材料。对基于复合材料细观力学理论建立的有效模量表达式进行了修正,提出了纤维沥青混凝土的割线有效松弛模量。以聚酯纤维沥青混凝土为例进行了有效松弛模量的解析分析和模拟蠕变实验的有限元分析,分析结果与试验数据的比较表明,该文提出的割线有效松弛模量模型对于纤维沥青混凝土粘弹性力学行为具有很好的预测能力。应用该模型对路面弯沉变形进行了有限元分析,结果表明:纤维的加入有效的改善了沥青混凝土路面的粘弹性性能。     

双周期涂层纤维增强复合材料反平面剪切问题

研究了双周期含涂层纤维增强复合材料在远场反平面载荷作用时的问题 , 利用 Eshelby等效夹杂方法和 Laurent 级数展开技术 , 并结合双准周期 Riemann边值问题理论 , 获得了其全场解析解 , 得到了应力场和有效模量表达式。与有限元结果的对照显示出本方法的效率和精度。考察了涂层参数对复合材料细观应力场和宏观有效性能的影响。当涂层刚度较大时 , 涂层内存在高的应力集中 , 且涂层刚度越大、 涂层相对厚度越小 , 应力集中系数越大。纤维刚度对复合材料有效模量的影响也取决于涂层性能 , 非常软或非常硬的涂层都大大限制了纤维刚度对复合材料有效模量的贡献。      

粘弹性复合材料中的渐近均匀化方法

主要研究了由各向同性线弹性加强体和各向同性线粘弹性基体组成的复合材料的问题。在已有的线弹性多层材料的渐近均匀化方法的基础上,应用弹性-粘弹性对应原理,在Carson域中求解粘弹性问题,通过两次运用均匀化方法,得到一类单向强化复合材料的有效模量的表达式。反演可得到单向强化复合材料的有效松弛模量在时间域中的表达式,并且与其它结果进行了比较。     

基于共焦点椭球构型的复合材料有效性质预测

介绍了共焦点椭球构型,给出了基于该构型对空间任意取向复合材料模量的解析计算公式,并将其同Mori-Tanaka(MT)法、Ponte-Castaneda-Willis (PCW)方法以及Hashin-Shtrikman(HS)界限进行了比较。数值结果显示,基于该构型的预测处于MT法和PCW法所预测的值之间,并且与MT法所预测的值接近。此外,还对纤维不同的角度平均方法对有效性质的影响做了讨论。     

一种基于帘线/橡胶复合材料细观力学的精确建模方法

为研究适应性底座的受压膨胀力学特性,提出了一种基于纤维帘线/橡胶复合材料细观力学的精确建模方法.该方法建立在帘线与橡胶材料参数的准确取值这一基础上,其中橡胶材料采用Mooney-Rivilin本构模型进行描述,通过拉伸试验验证了本构模型的准确性,基于束帘线拉伸试验规律对帘线拉伸模量进行了修正.通过上述方法,对适应性橡胶底座受压膨胀过程进行了数值模拟与试验研究.结果表明:这一精确建模方法能够较好地模拟底座的受压膨胀特性,能够获取底座中帘线与橡胶材料的应力、应变的分布以及二者的变化规律.研究工作为适应性底座的进一步研究和实际应用提供了技术支撑.     

平面应力作用下复合材料的蠕变分析

本文对受平面应力作用下的复合材料的细观蠕变进行了研究,分析了纤维与基体的性能,纤维取向以及纤维体积百分含量等对复合材料蠕变性能的影响,从细观角度提出了控制复合材料蠕变的具体措施.     

多层次等效的Mori-Tanaka法预测含空腔点阵增强芯层的等效弹性模量

提出了兼具力学和声学性能的夹层吸声复合材料-含空腔点阵增强夹芯结构;为了预测含空腔点阵增强结构芯层的等效弹性模量,建立了包含空腔、点阵增强柱和泡沫基体的三相复合材料的细观力学多层次等效数理模型,结合点阵增强柱和空腔周期性分布的特点建立代表性体积单元,利用Mori-Tanaka方法进行两次单相夹杂等效处理,获取了含空腔点阵增强芯层等效弹性模量的解析解,与试验数据和细观力学有限元法结果对比均吻合较好。采用有限元软件ANSYS建立了含空腔点阵增强夹芯结构的实际模型和等效模型,并将芯层等效模量解析结果作为等效模型芯层的材料参数,计算弯曲变形和固有频率并进行对比分析,弯曲变形位移和中低频固有频率的相对误差不超过2%,满足工程精度要求。进一步利用该等效方法,分别探讨了点阵增强柱和空腔体积比对芯层等效弹性模量的影响规律。结果表明,上述方法能较准确地预测含空腔点阵增强结构芯层的等效弹性模量,且数理模型清晰,公式简单,计算快速。     

Numerical analysis of doubly periodic array of cracks/rigid-line inclusions in an infinite isotropic medium using the boundary integral equation method

In this paper, the boundary integral equation approaches are used to study the doubly periodic array of cracks/rigid-line inclusions in an infinite isotropic plane medium. For the doubly periodic rigid-line inclusion problems, the special integral equation containing the axial and shear forces within the rigid-line inclusion is used. The doubly periodic crack problems are dealt with using the displacement discontinuous integral equation approach. Stress intensity factors, effective elastic properties for doubly periodic array of cracks/rigid-line inclusions are calculated and compared with the available numerical solutions.     

A modification of the Mori-Tanaka estimate of average elastoplastic behavior of composites and polycrystals with interfacial debonding

A modification of the Mori-Tanaka method is proposed to evaluate the average elastoplastic behavior of composites and polycrystals in a virtual matrix. The virtual matrix is an elastic material in which real matrix material and inhomogeneities are embedded, and its volume vanishes as a limit after homogenization. With regard to elasticity, depending on the choice of material properties of this virtual matrix, many kinds of average moduli between the classical bounds can be predicted. In this paper, we extend the application of this method to elastoplastic materials. Furthermore, Weng’s approximate model of interfacial debonding between the inclusions and the matrix is installed, because of its very simple criterion for the initiation of debonding to simulate progressive debonding phenomena. Several numerical examples without interfacial debonding show the applicability of the virtual matrix concept to elastoplastic materials. The characteristics of the model and its overall behaviors are described through the use of typical numerical simulations with debondings. Finally, comparisons with experimental results including debondings demonstrate the eligibility of the proposed method and models, and the application of the present method to designing a hybrid FRP is overviewed.     

Effective elastoplastic properties of the periodic composites

The article presented deals with the homogenization of composite materials with elastoplastic constituents. The transformation field analysis (TFA) approach is presented and applied to compute the effective nonlinear behavior of multicomponent periodic composite structure. Computational implementation of the method consists in special utilization of the program ABAQUS, which makes it possible to homogenize n-component periodic composites with relatively general configuration of the periodicity cell. Numerical example of homogenization of a three-component periodic composite shows the comparison between the nonlinear behavior of a real composite and of a homogenized one in a specific boundary problem defined on its representative volume element (RVE).     

An eigenfunction expansion-variational method for the anti-plane electroelastic behavior of three-phase fiber composites

The anti-plane electroelastic behavior of three-phase piezoelectric composites (fiber/interphase/matrix) with doubly periodic microstructures is dealt with. A new variational functional for a unit cell is constructed by incorporating the periodic boundary conditions into the energy functional. Then, by combining with the eigenfunction expansions of the complex potentials satisfying the fiber-interphase-matrix interfacial conditions, an eigenfunction expansion-variational method based on a unit cell is developed. The numerical results of the effective electroelastic moduli show a rapid convergence of the present method. A unified first-order approximation formula is also provided, where an equivalent parameter matrix reflecting the overall influence of the electroelastic properties of the fiber and interphase on the effective properties, is found. The equivalent parameter matrix can greatly simplify the complicated relation of the effective electroelastic properties to the internal structure of a three-phase fiber composite. Though the equivalent parameter matrix is extracted in the first-order approximation formula, its validity is also verified in the high-order numerical results.     

A new method of shear stiffness prediction of periodic Timoshenko beams

This article interprets the new implementation of an asymptotic homogenization method for effective bending stiffness of heterogeneous beam structures with periodic microstructure along its axial direction in an intuitionistic way. With this interpretation, the authors then develop a new method of evaluating effective shear stiffness for their Timoshenko beam model. This method can be easily implemented numerically in commercial software. Different kinds of elements and modeling techniques available in commercial software can be applied to model the unit cell. Several examples are given to demonstrate the effectiveness of this new method.     

On accuracy improvement of microscopic stress/stress sensitivity analysis with the mesh superposition method for heterogeneous materials considering geometrical variation of inclusions

In this paper, a new method is proposed for improving accuracy of microscopic stress analysis/stress sensitivity analysis of heterogeneous materials considering a geometrical variation of inclusions using the mesh superposition method-based approach. In particular, the analysis, which considers a location variation of inclusions in heterogeneous materials with location change of a local mesh, is a target problem. This problem must be accurately solved for, eg, reliability evaluation with the multiscale stochastic stress analysis considering a microscopic geometrical variation of composites. The influence of a geometrical random variation of inclusions on the stress field is not negligible; further, a finite element mesh must be substantially updated for the evaluation of stress field for a significant realization. Therefore, the mesh superposition method based approach is adopted. In this paper, a problem point in the stress/stress sensitivity analysis considering the geometrical variation of inclusions when using the mesh superposition method is discussed, and improved approaches based on an improved formulation and a relocalization analysis are proposed. The proposed approaches are applied to a stress/stress sensitivity analysis of a heterogeneous material associated with a microstructure of composites. With the numerical results, effectiveness of the proposed approach is discussed.     

Modeling of inclusions with interphases in heterogeneous material using the infinite element method

A two-dimensional heterogeneous infinite element method (HIEM) for modeling heterogeneous materials, like imbedded inclusions with surrounding interphases, is proposed in this paper. The special element, called heterogeneous infinite element (HIE), was formulated based on the conventional finite element method (FEM) using the similarity stiffness property and matrix condensing operations. An HIE-FE coupling scheme was also developed and implemented using the commercial software ABAQUS to conduct a complete elastostatic analysis.

The proposed approach was first validated so that heterogeneous material containing circular inclusions can be studied. The displacement and stress distribution around the inclusions were accurately captured. The approach was then applied to analyze the effective modulus of the single-cell and 2 × 2-cell square models with the presence of interphases. The effects of varying the modulus and thickness of the interphases were also examined. Finally, the influences of the shape and orientation of the inclusions are investigated. Results show that different arrangements in the model can have marked influences on the evaluation of the effective elastic modulus for periodic fiber-reinforced composites.