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1.
An explicit expression of the effective moduli for composite materials filled with coated inclusions
The obvious shortcoming of the generalized self-consistent method (GSCM) is that the effective shear modulus of composite
materials estimated by the method can not be expressed in an explicit form. This is inconvenient in engineering applications.
In order to overcome that shortcoming of GSCM, a reformation of GSCM is made and a new micromechanical scheme is suggested
in this paper. By means of this new scheme, both the effective bulk and shear moduli of an inclusion-matrix composite material
can be obtained and be expressed in simple explicit forms. A comparison with the existing models and the rigorous Hashin-Shtrikman
bounds demonstrates that the present scheme is accurate. By a two-step homogenization technique from the present new scheme,
the effective moduli of the composite materials with coated spherical inclusions are obtained and can also be expressed in
an explicit form. The comparison with the existing theoretical and experimental results shows that the present solutions are
satisfactory. Moreover, a quantitative comparison of GSCM and the Mori-Tanaka method (MTM) is made based on a unified scheme.
The project supported by the National Natural Science Foundation of China under the Contract NO. 19632030 and 19572008, and
China Postdoctoral Science Foundation 相似文献
2.
3.
《应用数学和力学(英文版)》2017,(11)
In order to apply classical micromechanics in predicting the effective properties of nanocomposites incorporating interface energy, a concept of equivalent inclusion(EI) is usually adopted. The properties of EI are obtained by embedding a single inclusion with the interface into an infinite matrix. However, whether such an EI is universal for different micromechanics-based methods is rarely discussed in the literature. In this paper, the interface energy theory is used to study the applicability of the above mentioned EI. It is found that some elastic properties of the EI are related only to the properties of the inclusion and the interface, whereas others are also related to the properties of the matrix. The former properties of the EI can be applied to both the classical Mori-Tanaka method(MTM) and the generalized self-consistent method(GSCM). However, the latter can be applied only to the MTM. Two kinds of new EIs are proposed for the GSCM and used to estimate the effective mechanical properties of nanocomposites. 相似文献
4.
Size-dependent effective elastic constants of solids containing nano-inhomogeneities with interface stress 总被引:1,自引:0,他引:1
The fundamental framework of micromechanical procedure is generalized to take into account the surface/interface stress effect at the nano-scale. This framework is applied to the derivation of the effective moduli of solids containing nano-inhomogeneities in conjunction with the composite spheres assemblage model, the Mori-Tanaka method and the generalized self-consistent method. Closed-form expressions are given for the bulk and shear moduli, which are shown to be functions of the interface properties and the size of the inhomogeneities. The dependence of the elastic moduli on the size of the inhomogeneities highlights the importance of the surface/interface in analysing the deformation of nano-scale structures. The present results are applicable to analysis of the properties of nano-composites and foam structures. 相似文献
5.
《International Journal of Solids and Structures》2007,44(21):6805-6825
The classical generalized self-consistent model (GSCM) is recognized to be suitable and efficient for estimating the effective moduli of an isotropic composite consisting of an isotropic host matrix and an isotropic inclusion phase. The present work aims to enlarge the scope of the GSCM so that it becomes applicable to a good number of important situations where the phases cannot be differentiated as the host matrix and inclusions. This objective is achieved first by inserting into the unknown effective medium a coated composite sphere whose core is made of the unknown effective medium and whose coatings are formed of the constituent phases and then by imposing an energy equivalency condition. The equations thus obtained to characterize the effective bulk and shear moduli involve a microstructural parameter which turns out to be capable of describing in some sense how far a microstructure is from the host matrix/inclusion morphology. The important case of two-phase composites is studied in detail to illustrate the salient features of the proposed model. 相似文献
6.
反平面剪切作用下双材料滑动界面的细观力学模型 总被引:1,自引:0,他引:1
非理想粘结界面对多相材料力学性能具有重要影响。对于双材料间含众多随机分布微裂纹的界面,宏观上可以等效为连续损伤的弱界面,其两侧的面力连续而位移有间断。只有切线方向的位移间断,而法线方向位移连续的弱界面称之为滑动界面。在反平面剪切的作用下,我们证明了对于含有随机分布微裂纹的弹性双材料界面在宏观上等效为线弹簧型滑动界面,并获得了滑动界面柔度的一般表达式。利用Mori—Tanaka方法和广义自洽方法,我们研究了滑动界面柔度系数和微裂纹密度的关系。对这两种方法所得的结果进行比较发现,Mori—Tanaka方法得到的界面柔度比广义自洽方法得到的界面柔度大。当裂纹密度比较小时,这两种方法求得的界面柔度很接近。两种方法的结果都表明,界面柔度随裂纹密度的增加而增加。Mori—Tanaka方法比广义自治方法求解更为简便。 相似文献
7.
Classical micromechanical methods for calculating the effective moduli of a heterogeneous material are generalized to include the interface (surface) effect. By using Hashin‘s Composite Sphere Assemblage (CSA) model, a new expression of the bulk modulus for a particle-reinforced composite is derived. It is emphasized that the present study is within the finite-deformation framework such that the effective properties are not influenced by the interface stress itself solely, but influenced by the change of the interface stress due to changes of the shape and size of the interface, itence some inadequacies in previous papers are pointed out. 相似文献
8.
《International Journal of Solids and Structures》2007,44(7-8):2225-2243
Under investigation is a heterogeneous material consisting of an elastic homogeneous isotropic matrix in which layered elastic isotropic inclusions or pores are embedded. The generalized self-consistent model (GSCM) is extended so as to be capable of estimating the apparent elastic properties of a finite-size specimen smaller than a representative volume element (RVE). The kinematical or static apparent shear modulus is determined as a root of a cubic polynomial equation instead of a quadratic polynomial equation as in the classical GSCM of Christensen and Lo [Christensen, R.M., Lo, K.H., 1979. Solutions for effective shear properties in three phase sphere and cylinder models. J. Mech. Phys. Solids 27, 315–330]. It turns out that the extended GSCM establishes a link between the composite sphere assemblage model (CSAM) of Hashin [Hashin, Z., 1962. The elastic moduli of heterogeneous materials. J. Appl. Mech. 29, 143–150] and the classical GSCM. Demanding that the normalized distance between the kinematical and static apparent moduli of a finite-size specimen be smaller than a certain tolerance, the minimum RVE size is estimated in a closed form. 相似文献
9.
A UNIFIED ENERGY APPROACH TO A CLASS OF MICROMECHANICS MODELS FOR MICROCRACKED SOLIDS 总被引:2,自引:0,他引:2
Y.Huang K.C.Hwang 《Acta Mechanica Solida Sinica》1995,8(2):110-120
Micromechanics models have been developed for the determination ofthe elastic moduli of microcracked solids based on different approaches andinterpretations,including the dilute or non-interacting solution,the Mori-Tanakamethod,the self-consistent method,and the generalized self-consistent method.It isshown in the present study that all these micromechanics models can be unified withinan energy-equivalence framework,and that they differ only in the way in which themicrocrack opening and sliding displacements are evaluated.Relevance to thedifferential methods and the verification of these models are discussed. 相似文献
10.
Z.H. Tong S.H. Lo C.P. Jiang Y.K. Cheung 《International Journal of Solids and Structures》2008,45(20):5205-5219
A three-phase cylindrical model for analyzing fiber composite subject to in-plane mechanical load under the coupling effects of multiple physical fields (thermo, electric, magnetic and elastic) is presented. By introducing an eigenstrain corresponding to the thermo-electro-magnetic-elastic effect, the complex multi-field coupling problem can be reduced to a formal in-plane elasticity problem for which an exact closed form solution is available. The present three-phase model can be applied to fiber/interphase/matrix composites, such that a lot of interesting thermo-electro-magnetism and stress coupling phenomena induced by the interphase layer are revealed. The present model can also be applied to fiber/matrix composites, in terms of which a generalized self-consistent method (GSCM) is developed for predicting the effective properties of piezoelectric–magnetic fiber reinforced composites. The effective piezoelectric, piezomagnetic, thermoelectric and magnetoelectric moduli can be expressed in compact explicit formulae for direct references and applications. A comparison of the predictions by the GSCM with available experimental data is presented, and interesting magnification effects and peculiar product properties are discussed. As a theoretical basis for the GSCM, the equivalence of the three sets of different average field equations in predicting the effective properties are proved, and this fact provides a strong evidence of mathematical rigor and physical realism in the formulation. 相似文献
11.
Recently Zheng & Hwang established a series of independence theorems concerning with planar effective elastic properties.
It is manifested that the estimation of the effective elastic properties of microcracked solids through the generalized self-consistent
method (GSCM) contradicts with these independence theorems. In this paper it is shown that such contradiction is actually
caused by the approximate algorithm adopted, while the exact solution of GSCM is consistent with these rigorously established
independence theorems. Since only an approximate algorithm in GCSM is available in dealing with problems involving non-circular
inclusions or holes, an intrinsic GSCM is proposed, which can be performed based on an approximate algorithm and the corresponding
estimations are consistent with the independence theorems. 相似文献
12.
Zhai Jun Luo Haian 《Acta Mechanica Solida Sinica》1997,10(2):108-117
This paper presents a direct Mori-Tanaka approach to calculate the effective moduli ofparticle-reinforced composites and fiber-reinforced composites with spring like imperfect interfaces.Bya comparison between these results and those obtained from the approximate Mori-Tanaka method de-veloped by Qu for composites with slightly weakened interface,the validity of the Qu's method is re-vealed. 相似文献
13.
Yang Qingsheng 《Acta Mechanica Sinica》1998,14(2):171-178
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 相似文献
14.
The effective electroelastic moduli of microcavity-weakened piezoelectric plates are investigated by the dilute, self-consistent, Mori-Tanaka and differential micromechanics theories. The results of perturbed heat intensity, strain and electric field (SEF) due to the presence of voids are obtained for two-dimensional (2-D) piezoelectric plates with microcavities of various shapes, and then the above four micromechanics models can be established with the results. These models can be applicable to a wide range of microcavities such as ellipse, circle, crack, triangle, square and pentagon. Some numerical results are presented to illustrate the applicability of these models. 相似文献
15.
Based on the general solution given to a kind of linear tensor equations, the spin of a symmetric tensor is derived in an
invariant form. The result is applied to find the spins of the left and the right stretch tensors and the relation among different
rotation rate tensors has been discussed. According to work conjugacy, the relations between Cauchy stress and the stresses
conjugate to Hill's generalized strains are obtained. Particularly, the logarithmic strain, its time rate and the conjugate
stress have been discussed in detail. These results are important in modeling the constitutive relations for finite deformations
in continuum mechanics.
The project is supported by the National Natural Science Foundation of China and the Chinese Academy of Sciences (No. 87-52). 相似文献
16.
Based on both the spring layer interface model and the Gurtin-Murdoch surface/interface model, the anti-plane shear problem is studied for piezoelectric composites containing coated nano-elliptical fibers with imperfect interfaces. By using the complex function method and the technique of conformal mapping, the exact solutions of the electroelastic fields in fiber, coating, and matrix of piezoelectric nanocomposites are derived under far-field anti-plane mechanical and in-plane electrical loads. Furthermore, the generalized self-consistent method is used to accurately predict the effective electroelastic moduli of the piezoelectric nanocomposites containing coated nano-elliptical fibers with imperfect interfaces. Numerical examples are illustrated to show the effects of the material constants of the imperfect interface layers, the aspect ratio of the fiber section, and the fiber volume fraction on the effective electroelastic moduli of the piezoelectric nanocomposites. The results indicate that the effective electroelastic moduli of the piezoelectric nanocomposites can be significantly reduced by the interfacial debonding, but it can be improved by the surface/interface stresses at the small scale, which provides important theoretical reference for the design and optimization of piezoelectric nanodevices and nanostructures. 相似文献
17.
Since piezoelectric ceramic/polymer composites have been widely used as smart materials and smart structures, it is more and
more important to obtain the closed-from solutions of the effective properties of piezocomposites with piezoelectric ellipsoidal
inclusions. Based on the closed-from solutions of the electroelastic Eshelby's tensors obtained in the part I of this paper
and the generalized Budiansky's energy-equivalence framework, the closed-form general relations of effective electroelastic
moduli of the piezocomposites with piezoelectric ellipsoidal inclusions are given. The relations can be applicable for several
micromechanics models, such as the dilute solution and the Mori-Tanaka's method. The difference among the various models is
shown to be the way in which the average strain and the average electric field of the inclusion phase are evaluated. Comparison
between predicted and experimental results shows that the theoretical values in this paper agree quite well with the experimental
results. These expression can be readily utilized in analysis and design of piezocomposites.
The project supported by the National Natural Science Foundation of China 相似文献
18.
Recently, some new quadrilateral finite elements were successfully developed by the Quadrilateral Area Coordinate (QAC) method.
Compared with those traditional models using isoparametric coordinates, these new models are less sensitive to mesh distortion.
In this paper, a new displacement-based, 4-node 20-DOF (5-DOF per node) quadrilateral bending element based on the first-order
shear deformation theory for analysis of arbitrary laminated composite plates is presented. Its bending part is based on the
element AC-MQ4, a recent-developed high-performance Mindlin-Reissner plate element formulated by QAC method and the generalized
conforming condition method; and its in-plane displacement fields are interpolated by bilinear shape functions in isoparametric
coordinates. Furthermore, the hybrid post-processing procedure, which was firstly proposed by the authors, is employed again
to improve the stress solutions, especially for the transverse shear stresses. The resulting element, denoted as AC-MQ4-LC,
exhibits excellent performance in all linear static and dynamic numerical examples. It demonstrates again that the QAC method,
the generalized conforming condition method, and the hybrid post-processing procedure are efficient tools for developing simple,
effective and reliable finite element models.
The project is supported by the National Natural Science Foundation of China (10502028), the Special Foundation for the Authors
of the Nationwide (China) Excellent Doctoral Dissertation (200242), and the Science Research Foundation of China Agricultural
University (2004016). 相似文献
19.
Recent developments in nanotechnology make it possible to fabricate nanofibers and identify their mechanical fibers. In particular,
nanofibers are used as reinforcement in composites. The present work concerns unidirectional nanofibrous composites with cylindrically
anisotropic phases and aims to analytically estimate their effective thermoelastic moduli. This objective is achieved by extending
the classical generalized self-consistent model to the setting of thermoelasticity, to the case of cylindrically anisotropic
phases, and to the incorporation of interface stress effect. Analytical closed-form estimations are derived for all the effective
thermoelastic moduli, showing that these moduli depend on the fiber cross-section size. Numerical examples are provided to
illustrate this size-dependent effect. 相似文献
20.
H.L. Duan 《Journal of the mechanics and physics of solids》2006,54(7):1401-1425
This paper first presents the Eshelby tensors and stress concentration tensors for a spherical inhomogeneity with a graded shell embedded in an alien infinite matrix. The solution is then specialized to inhomogeneous inclusions in finite spherical domains with fixed displacement or traction-free boundary conditions. The Eshelby tensors in the infinite and finite domains and the stress concentration tensors are especially useful for solving many problems in mechanics and materials science. This is demonstrated on two examples. In the first example, the strain distributions in core-shell nanoparticles with eigenstrains induced by lattice mismatches are calculated using the Eshelby tensors in the finite domains. In the second example, the Eshelby and stress concentration tensors in the three-phase configuration are used to formulate the generalized self-consistent prediction of the effective moduli of composites containing spherical particles within the framework of the equivalent inclusion method. The advantage of this micromechanical scheme is that, whilst its predictions are almost identical to the classical generalized self-consistent method and the third-order approximation, the expressions for the effective moduli have simple closed forms. 相似文献