均匀化方法在粘弹性多层复合材料中的应用

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多层复合材料的问题,在已有的线弹性多层材料的均匀化方法的基础上,应用弹性一粘弹性对应原理,在Carson域中求解粘弹性多层材料的问题。通过Burgers模型表示线粘弹性基体材料,反演得到了多层材料的有效松弛模量和有效泊松比在时间域中的表达式,并且与实验结果和其他结果进行了比较。     

一种颗粒复合材料物理性能计算模型与工程应用

结合傅里叶描述子法与格林函数法提出了任意形状夹杂物的Eshelby张量计算方法,基于分步夹杂法建立了一种具有任意形状颗粒的复合材料物理性能预测理论模型。通过傅里叶描述子法对扫描电镜(SEM)图像中颗粒形貌进行数学表征,构建由多个细观结构参数组合的几何模型;利用格林函数求解夹杂物Eshelby张量,考虑颗粒形态、大小和组分性能,研究细观结构对颗粒复合材料有效性能的影响。在此基础上,设计了一款颗粒复合材料物理性能预测软件。以铜铬合金为研究对象,分析重构的细观模型与预测的结果,并与有限元计算结果进行对比,验证了该计算模型的有效性和可靠性,以及在工程计算应用中的可行性。     

Hill–Mandel condition and bounds on lower symmetry elastic crystals

Despite advances in contemporary micromechanics, there is a void in the literature on a versatile method for estimating the effective properties of polycrystals comprising of highly anisotropic single crystals belonging to lower symmetry class. Basing on variational principles in elasticity and the Hill–Mandel homogenization condition, we propose a versatile methodology to fill this void. It is demonstrated that the bounds obtained using the Hill–Mandel condition are tighter than the Voigt and Reuss [1], [2] bounds, the Hashin–Shtrikman [3] bounds as well as a recently proposed self-consistent estimate by Kube and Arguelles [4] even for polycrystals with highly anisotropic single crystals.     

Computing overall elastic constants of polydisperse particulate composites from microtomographic data

In this paper, we use the well-known Hashin-Shtrikman-Willis variational principle to obtain the overall mechanical properties of heterogeneous polydisperse particulate composites. The emphasis is placed on the efficient numerical integration of complex three-dimensional integrals and on aspects of the anisotropic material response of real tomographically characterized packs. For this purpose, we numerically calculate the complete statistics of real packs, which are numerically or tomographically generated. We use the parallel adaptive sparse Smolyak integration method with hierarchical basis to integrate complex singular integrals containing the product of probability functions and the second derivative of Green's function. Selected examples illustrate both the numerical and physical facets of our work. First, we show the reduction of integral points for integration in spherical coordinates. Then, we comment on the parallel scalability of our method and on the numerical accuracy associated with the integration of a singular function. Next, we validate the solver against the experimental data and verify the results by comparing it to a closed-form expression. To investigate the ability of our scheme to capture the anisotropic nature of packs, we study a lattice type system. Finally, we report on the elastic constants computed for the modeled anisotropic particulate system that is tomographically characterized.     

Some exact results concerning thermoelastic properties of hollow sphere composites

1.IntroductionAsakindofwidelyusedlowdensitymaterials,compositeconsistingofamatrixanddistributedhollowsphereshaveattractedIncreasingresearchinterest.Relatedworkswhicharefocusedonthetheoreticalpredictionof.theeffectiveelasticmoduliofsuchcompositescanbefoundinLeeandWestmannl'1,QiuandWengl=],HuangandGibsonl31aswellasChercauoietal.HI.HuangandGibson13]havealsocarriedoutanexperimentalinvestigationonmechanicalbehavioursofthecomposites.Thepresentpapercontinuestheseinvestigationsandisfocusedonfindi…     

A Model for Predicting Effective Properties of Piezocomposites with Non-piezoelectric Inclusions

Most piezocomposites, which have been widely used in engineering, consist of piezoelectric inclusions and a non-piezoelectric matrix. Due to the limits of fabrication technology, it is hard to avoid the matrix intermingling with other non-piezoelectric inclusions, such as cavities. The non-piezoelectric inclusions can substantially affect performance of piezocomposites. In this paper we study the electromechanical fields in piezocomposites which are composed of a non-piezoelectric matrix embedded with both piezoelectric and non-piezoelectric inclusions. Closed-form relations are obtained for the effective electroelastic moduli of a piezocomposite with both piezoelectric and non-piezoelectric inclusions. The effective properties of a 1-3 type piezocomposite with non-piezoelectric spherical inclusions are analyzed carefully and explicit formulae for the effective electroelastic properties of a 1-3-0 piezocomposite are also obtained. The analysis shows that the effect of non-piezoelectric inclusions on the electroelastic properties of piezocomposites is significant and should not be neglected. The model proposed in this paper is expected to be useful for predicting and analyzing the overall electromechanical properties of piezocomposites with a non-piezoelectric matrix containing both piezoelectric and non-piezoelectric inclusions.     

Thermomechanical properties of smart composites

The smart composite materials reinforced by SMA show a high performance and special deformation behavior. The thermomechanical constitutive formulas of the composites are derived by means of Eshelby's equivalent inclusion method and Mori-Tanaka's mean field concept. The interaction between the inclusion and crack and toughening mechanism are considered and the energy release rate of a crack in the smart composite is calculated. This work shows that there are the multiple mechanisms contributing to the toughening of the smart composite materials reinforced by SMA.This project is supported by the National Natural Science Foundation of China.     

Mechanical properties of lattice grid composites

An equivalent continuum method only considering the stretching deformation of struts was used to study the in-plane stiffness and strength of planar lattice grid com- posite materials. The initial yield equations of lattices were deduced. Initial yield surfaces were depicted separately in different 3D and 2D stress spaces. The failure envelope is a polyhedron in 3D spaces and a polygon in 2D spaces. Each plane or line of the failure envelope is corresponding to the yield or buckling of a typical bar row. For lattices with more than three bar rows, subsequent yield of the other bar row after initial yield made the lattice achieve greater limit strength. The importance of the buckling strength of the grids was strengthened while the grids were relative sparse. The integration model of the method was used to study the nonlinear mechanical properties of strain hardening grids. It was shown that the integration equation could accurately model the complete stress-strain curves of the grids within small deformations.     

石墨烯及其复合材料纳米力学研究进展

石墨烯是一种由碳原子构成的二维晶体,是目前已知最薄但却有着极高强度的纳米材料.由于在强度、导热性、电子输运和光学上显示出不同寻常的特性,石墨烯迅速成为材料科学、物理、化学和力学等学科的研究热点.与此同时,石墨烯复合材料的研究也迅速兴起.论文综述了近年来石墨烯及其复合材料的力学特性的研究进展.根据力学行为的差异,我们主要阐述了石墨烯面内力学特性、离面力学特性、原子尺度修饰和石墨烯复合材料力学特性的研究进展:石墨烯的面内拉伸力学特性通过纳米压痕等技术得到了测量,其断裂行为在微纳尺度下不能完全使用连续介质力学模型进行解释,在多层石墨烯情况下会出现超润滑现象;石墨烯的可控离面位移对于改变其物理特性有重要的意义,石墨烯上的屈曲受到手性和尺度的影响,在高频器件中存在着非连续性的离面响应;适当的原子尺度修饰可以改善石墨烯的拉伸和扭转力学特性;石墨烯可以改善复合材料的力学特性,如提高强度、韧性等,其主要强化效应是通过与基体材料的离面、面内力学行为结合产生的.最后,论文对石墨烯及其复合材料的力学研究进行了总结和展望.     

A stochastic homogenization approach to estimate bone elastic properties

The mechanical properties of bone tissue depend on its hierarchical structure spanning many length scales, from the organ down to the nanoscale. Multiscale models allow estimating bone mechanical properties at the macroscale based on information on bone organization and composition at the lower scales. However, the reliability of these estimates can be questioned in view of the many uncertainties affecting the information which they are based on. In this paper, a new methodology is proposed, coupling probabilistic modeling and micromechanical homogenization to estimate the material properties of bone while taking into account the uncertainties on the bone micro- and nanostructure. Elastic coefficients of bone solid matrix are computed using a three-scale micromechanical homogenization method. A probabilistic model of the uncertain parameters allows propagating the uncertainties affecting their actual values into the estimated material properties of bone. The probability density functions of the random variables are constructed using the Maximum Entropy principle. Numerical simulations are used to show the relevance of this approach.     

Antiplane magneto-electro-elastic effective properties of three-phase fiber composites

In the present work, applying the asymptotic homogenization method (AHM), the derivation of the antiplane effective properties for three-phase magneto-electro-elastic fiber unidirectional reinforced composite with parallelogram cell symmetry is reported. Closed analytical expressions for the antiplane local problems on the periodic cell and the corresponding effective coefficients are provided. Matrix and inclusions materials belong to symmetry class 6mm. Numerical results are reported and compared with the eigenfunction expansion-variational method (EEVM) and other theoretical models. Good agreements are found for these comparisons. In addition, with the herein implemented solution, it is possible to reproduce the effective properties of the reduced cases such as piezoelectric or elastic composites obtaining good agreements with previous reports.     

复合材料有效弹性性质分析方法eeeeee

建立复合材料的有效性质与微结构参数的关联,是复合材料优化设计的基础。本文具体针对有效弹性性质,重点介绍了建立有效性的基本思路 和主要分析方法。首先讨论了代表单元的概念,然后分别从复合材料有效性质的普适关系、界限理论和近似方法三个不同的视角较全面的介绍了建立非均质材料有效性质的方法、主要结果和最新进展。重点从构型的概念和微结构分布形式上分析了各种模型间及分析方法之间的联系与差别。最后还就建立非均质材料有效性质中存在的问题和研究热点做了简单的介绍。     

Micromechanics of particle-reinforced elasto-viscoplastic composites: Finite element simulations versus affine homogenization

The micromechanics of elasto-viscoplastic composites made up of a random and homogeneous dispersion of spherical inclusions in a continuous matrix was studied with two methods. The first one is an affine homogenization approach, which transforms the local constitutive laws into fictitious linear thermo-elastic relations in the Laplace–Carson domain so that corresponding homogenization schemes can apply, and the temporal response is computed after a numerical inversion of Laplace transform. The second method is the direct numerical simulation by finite elements of a three-dimensional representative volume element of the composite microstructure. The numerical simulations carried out over different realizations of the composite microstructure showed very little scatter and thus provided – for the first time – “exact” results in the elasto-viscoplastic regime that can be used as benchmarks to check the accuracy of other models. Overall, the predictions of the affine homogenization model were excellent, regardless of the volume fraction of spheres, of the loading paths (shear, uniaxial tension and biaxial tension as well as monotonic and cyclic deformation), particularly at low strain rates. It was found, however, that the accuracy decreased systematically as the strain rate increased. The detailed information of the stress and strain microfields given by the finite element simulations was used to analyze the source of this difference, so that better homogenization methods can be developed.     

The effective properties of composites with fiber-end cracks

The paper describes use of self-consistent finite element method (SCFEM) for predicting effective properties of fiber composite with partially debonded interface. The effective longitudinal Young's modulus and shear modulus for unidirectional fiber reinforced composites with fiber-end cracks are calculated. Numerical results show that the effective properties are considerably influenced by the fiber-end cracks. The effects of microstructural parameters, such as fiber volume fraction, modulus ratio of the constituents and fiber aspect, on the effective properties of the composites were discussed. The project supported by the National Natural Science Foundation of China     

PVC/纳米Al2O3复合材料的力学性能研究

通过熔融共混方法制备了PVC/纳米Al2O3复合材料,研究了纳米粒子对PVC的增强、增韧效果。采用细观力学方法理论上求解了纳米复合材料的有效弹性模量,比较并分析了试验值和理论计算值的偏差。     

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.     

考虑损伤界面的多相复合材料总体平均力学性能的预测

在广义自洽有限元迭代法￣［１］的基础上研究了损伤界面对多相复合材料的总体平均横向力学性能的影响。给出了对于不同体分比和损伤界面性质的典型复合材料的数值结果。数值分析表明损伤界面的厚度及其损伤程度对复合材料总体平均横向平面应变体积模量和剪切模量有显著影响。本文还计算了损伤界面区域的局部应力场。     

Three-phase plane composites of minimal elastic stress energy: High-porosity structures

The paper establishes exact lower bound on the effective elastic energy of two-dimensional, three-material composite subjected to the homogeneous, anisotropic stress. It is assumed that the materials are mixed with given volume fractions and that one of the phases is degenerated to void, i.e., the effective composite is porous. Explicit formula for the energy bound is obtained using the translation method enhanced with additional inequality expressing certain property of stresses. Sufficient optimality conditions of the energy bound are used to set the requirements which have to be met by the stress fields in each phase of optimal effective material regardless of the complexity of its microstructural geometry. We show that these requirements are fulfilled in a special class of microgeometries, so-called laminates of a rank. Their optimality is elaborated in detail for structures with significant amount of void, also referred to as high-porosity structures. It is shown that geometrical parameters of optimal multi-rank, high-porosity laminates are different in various ranges of volume fractions and anisotropy level of external stress. Non-laminate, three-phase microstructures introduced by other authors and their optimality in high-porosity regions is also discussed by means of the sufficient conditions technique. Conjectures regarding low-porosity regions are presented, but full treatment of this issue is postponed to a separate publication. The corresponding “G-closure problem” of a three-phase isotropic composite is also addressed and exact bounds on effective isotropic properties are explicitly determined in these regions where the stress energy bound is optimal.     

金属颗粒磁带宏观性质的细观力学估计

金属颗粒之间的磁场相互作用对金属颗粒磁带的高密度记录性能有显著的影响. 为了有效 地估计该影响，在单畴颗粒的Stoner-Wohlforth模型基础上将新近提出的细观力学相 互作用直推法(Zheng & Du, J. Mech. Phys. Solid. 2001) 推广到非均匀磁记录材料中，得到了磁带宏观性质的率形式解析表达， 能有效地计及颗粒之间的相互作用、颗粒形状的统计分布和体积分数对磁介质性能的 影响. 得到的理论结果与数值模拟和有关的实验观测结果相当一致.     

纤维复合材料损伤过程的数值模拟

利用界面断裂力学和有限元法数值模拟纤维增强复合材料的细观损伤过程，研究各种主要破坏模式之间的相互转变和影响，指出以断裂能和混合度表示的界面性能是控制复合材料损伤过程的主要细观参数。分析了界面韧度对破坏性能的影响，探讨了基于破坏模式控制的复合材料韧度设计的新途径。