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1.
A. A. Pan’kov 《Mechanics of Solids》2009,44(6):927-934
We develop the periodic componentmethod [1] and represent the solution of a stochastic boundary value elasticity problem for
a random quasiperiodic structure with a given disordering degree of inclusions in the matrix via the deviations from the corresponding
solution for a random structure with a smaller disordering degree. An example in which the tensor of elastic properties of
a composite is calculated is used to illustrate the asymptotic and differential approaches of the successive disordering method.
The asymptotic approach permits representing the quasiperiodic structure with a given chaos coefficient and the desired tensor
of effective elastic properties as a result of small successive disordering of an originally ideally periodic structure of
a composite with known tensor of elastic properties. In the differential approach, a differential equation is obtained for
the tensor of effective elastic properties as a function of the chaos coefficient. Its solution coincides with the solution
provided by the asymptotic approach. The solution is generalized to the case of piezoactive composites, and a numerical analysis
of the effective properties is performed for a PVF (polyvinylidene fluoride) piezoelectric with various quasiperiodic structures
on the basis of the cubic structure with spherical inclusions of a high-module elastic material. 相似文献
2.
A. A. Pan’kov 《Journal of Applied Mechanics and Technical Physics》1999,40(3):523-526
The problem of predicting the effective elastic properties of composites with prescribed random location and radius variation
in spherical inclusions is solved using the generalized self-consistent method. The problem is reduced to the solution of
the averaged boundary-value problem of the theory of elasticity for a single inclusion with an inhomogeneous transition layer
in a medium with desired effective elastic properties. A numerical analysis of the effective properties of a composite with
rigid spherical inclusions and a composite with spherical pores is carried out. The results are compared with the known solution
for the periodic structure and with the solutions obtained by the standard self-consistent methods.
Perm’ State Technical University, Perm’ 614600. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No.
3, pp. 186–190, May–June, 1999. 相似文献
3.
S. K. Kanaun 《Journal of Applied Mechanics and Technical Physics》1975,16(4):649-657
This paper is devoted to the calculation of effective elastic properties of a medium containing a random field of ellipsoidal inhomogeneities. It is assumed that the centers of the inclusions (the inhomogeneities) form a random spatial lattice, i.e., the field of inhomogeneities considered is strongly correlated. The interaction between the inhomogeneities is taken into account within the frame-work of the self-consistent field approximation. It hence turns out that the symmetry of the tensor of the elastic properties of the medium is determined by the symmetry of the elastic properties of the inclusion matrix, as well as by the symmetry of the spatial lattice formed by the mathematical expectations of the centers of the inclusions. 相似文献
4.
C. Pelissou J. Baccou Y. Monerie F. Perales 《International Journal of Solids and Structures》2009,46(14-15):2842-2855
A representative volume element (RVE) is related to the domain size of a microstructure providing a “good” statistical representation of typical material properties. The size of an RVE for the class of quasi-brittle random heterogeneous materials under dynamic loading is one of the major questions to be answered in this paper. A new statistical strategy is thus proposed for the RVE size determination. The microstructure illustrating the methodology of the RVE size determination is a metal matrix composite with randomly distributed aligned brittle inclusions: the hydrided Zircaloy constituting nuclear claddings. For a given volume fraction of inclusions, the periodic RVE size is found in the case of overall elastic properties and of overall fracture energy. In the latter case, the term “representative” is discussed since the fracture tends to localize. A correlation factor between the “elastic” RVE and the “fracture” RVE is discussed. 相似文献
5.
《International Journal of Solids and Structures》1999,36(18):2683-2705
The paper is concerned with composite materials which consist of a homogeneous matrix phase with a set of inclusions uniformly distributed in the matrix. The components of these materials are considered to be ideally elastic and exhibit piezoelectric properties. One of the variants of the self-consistent scheme, the Effective Field Method (EFM) is applied to calculate effective dielectric, piezoelectric and thermoelastic properties of such materials, taking into account the coupled electroelastic effects. At first the coupled thermoelectroelastic problem for a homogeneous medium with an isolated inclusion is solved. For an ellipsoidal inclusion and constant external field the solution of this problem is found in a closed analytic form. This solution is then used in the EFM to derive the effective thermoelectroelastic operator for the composite containing a random array of ellipsoidal inclusions. Explicit formulae for the electrothermoelastic constants are given for composites, reinforced by spheroidal inclusions. 相似文献
6.
In this paper, the elastic field created by randomly distributed inclusions is studied. The inclusions are considered to be randomly distributed in the material, and have random orientation and size. The random point field model is proposed to describe the randomness of inclusion position, orientation and size. As a special case, when phase transformation inclusions are uniformly distributed in the material, and have non-random orientation, the theory gives the same result as Mori and Tanaka (1973. Acta Metallurgica 21, 571). The elastic field created by randomly distributed dislocation loops is also considered in some detail, and it is found that the continuum theory of dislocation loops is applicable only when the size of the dislocation loop becomes infinitesimal. 相似文献
7.
The work is devoted to the problem of plane monochromatic longitudinal wave propagation through a homogeneous elastic medium
with a random set of spherical inclusions. The effective field method and quasicrystalline approximation are used for the
calculation of the phase velocity and attenuation factor of the mean (coherent) wave field in the composite. The hypotheses
of the method reduce the diffraction problem for many inclusions to a diffraction problem for one inclusion and, finally,
allow for the derivation of the dispersion equation for the wave vector of the mean wave field in the composite. This dispersion
equation serves for all frequencies of the incident field, properties and volume concentrations of inclusions. The long and
short wave asymptotics of the solution of the dispersion equation are found in closed analytical forms. Numerical solutions
of this equation are constructed in a wide region of frequencies of the incident field that covers long, middle, and short
wave regions of propagating waves. The phase velocities and attenuation factors of the mean wave field are calculated for
various elastic properties, density, and volume concentrations of the inclusions. Comparisons of the predictions of the method
with some experimental data are presented; possible errors of the method are indicated and discussed. 相似文献
8.
《International Journal of Solids and Structures》2005,42(14):3971-3997
The work is dedicated to the problem of plane monochromatic shear wave propagation through elastic matrix composite materials with a homogeneous random set of spherical inclusions. The effective field method (EFM) and quasi-crystalline approximation are used for the calculation of phase velocity and attenuation factor of the mean wave field propagating through the composite. The version of the method developed in the work allows us to obtain the dispersion equation for the wave vector of the mean wave field that serves for all frequencies of the incident field, properties and volume concentrations of the inclusions. The long- and short-wave asymptotic solutions of the dispersion equation are found in closed analytical forms. Numerical solutions of this equation are constructed in a wide region of frequencies that covers the long-, middle- and short-wave regions of the propagating waves. The phase velocities and attenuation factors of the mean wave field in the composites are analyzed for various elastic properties, density and volume concentrations of the inclusions. Comparisons of the predictions of the method with some numerical computation of the effective parameters of matrix composites are presented; possible errors in predictions of the velocities and attenuation factors of the mean wave field in the composites are indicated and discussed. 相似文献
9.
Jumpol Paiboon D.V. Griffiths Jinsong Huang Gordon A. Fenton 《International Journal of Solids and Structures》2013,50(20-21):3233-3241
The purpose of the study is to investigate the influence of porosity and void size on effective elastic geotechnical engineering properties with a 3D model of random fields and finite element. The random field theory is used to generate models of geomaterials containing spatially random voids with controlled porosity and void size. A “tied freedom” analysis is developed to evaluate the effective Young’s modulus and Poisson’s ratio in an ideal block material of finite elements. To deliver a mean and standard deviation of the elastic parameters, this approach uses Monte-Carlo simulations and finite elements, where each simulation leads to an effective value of the property under investigation. The results are extended to investigate an influence of representative volume element (RVE). A comparison of the effective elastic stiffness of 2D and 3D models is also discussed. 相似文献
10.
双周期圆柱形夹杂纵向剪切问题的精确解 总被引:7,自引:1,他引:7
研究无限介质中矩形排列双周期圆柱形夹杂的纵向剪切问题.利用Eshelby等效夹杂理论并结合双周期与双准周期解析函数工具,为这类考虑夹杂相互影响的问题提供了一个严格又实用的分析方法,求得了问题的全场级数解.作为退化情形得到单夹杂问题的经典解答,双周期孔洞、双周期刚性夹杂及单行(列)周期弹性夹杂等问题也可作为特殊情况被解决.数值结果揭示了这类非均匀材料力学性质随微结构参数变化的规律. 相似文献
11.
含正交排列夹杂和缺陷材料的等效弹性模量和损伤 总被引:3,自引:0,他引:3
研究含正交排列夹杂和缺陷材料的等效弹性模量和损伤,推导了以Eshelby-Mori-Tanaka方法求解多相各向异性复合材料等效弹性模量的简便计算公式,针对含三相正交椭球状夹杂的正交各向异性材料,得到了由细观参量(夹杂的形状、方位和体积分数)表示的等效弹性模量的解析表达式.在此基础上,提出了一个宏细观结合的正交各向异性损伤模型,从而建立了以细观量为参量的含损伤材料的应力应变关系.最后,对影响材料损伤的细观结构参数进行了分析. 相似文献
12.
含夹杂复合材料宏观性能研究 总被引:10,自引:1,他引:10
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。 相似文献
13.
Lidiya Nazarenko Leonid Khoroshun Wolfgang H. Müller Ralf Wille 《Continuum Mechanics and Thermodynamics》2009,20(7):429-458
In the present paper, we will illustrate the application of the method of conditional moments by constructing the algorithm
for determination of the effective elastic properties of composites from the given elastic constants of the components and
geometrical parameters of inclusions. A special case of two-component matrix composite with randomly distributed unidirectional
spheroidal inclusions is considered. To this end it is assumed that the components of the composite show transversally isotropic
symmetry of thermoelastic properties and that the axes of symmetry of the thermoelastic properties of the matrix and inclusions
coincide with the coordinate axis x
3. As a numerical example a composite based on carbon inclusions and epoxide matrix is investigated. The dependencies of Young’s
moduli, Poisson’s ratios and shear modulus from the concentration of inclusions and for certain values which characterize
the shape of inclusions are analyzed. The results are compared and discussed in context with other theoretical predictions
and experimental data.
相似文献
14.
The propagation and attenuation of elastic waves in a random anisotropic two-phase medium is studied using statistical averaging procedures and a self-consistent multiple scattering theory. The specific geometry and orientation of the inhomogeneities (second phase) are incorporated into the formulation via the scattering matrix of each inhomogeneity. The anisotropy of the composite medium is due to the specific orientation of the non-symmetric inclusions. At low frequencies, analytical expressions are derived for the effective wave number in the average medium as a function of the geometry and the material properties and the angle of orientation of the inclusions. The results for the special cases of oriented cracks may find applications in geophysics and material science. The formulation is ideally suited for numerical computation at higher frequencies as evidenced by the results presented for composites reinforced by fibers of elliptical cross section. 相似文献
15.
C. B. Demakos 《Archive of Applied Mechanics (Ingenieur Archiv)》1999,69(4):240-256
Summary The objective of this paper is to evaluate the averaged elastic properties of 3-D grained composites in which identical inclusions
form a prismatic network interacting with the matrix material. The inclusions are of ellipsoidal shape with transverse circular
sections located at the nodes of a doubly-periodic lattice with an orthogonal elementary cell. When the arrays of inclusions
are set at equal spacings in normal directions through the thickness of the matrix, the material formed is an anisotropic
composite with tetragonal symmetry at planes transverse to the fiber axis.
The longitudinal and transverse elastic and shear moduli as well as the longitudinal Poisson's ratios of such composites are
evaluated in this paper. The averaged properties are studied in terms of the aspect ratio and volume fraction of the inclusions
as well as the relative rigidity of the constituent phases. Employing the Eshelby's theory for the stress field around a single
ellipsoidal inhomogeneity, which is surrounded by the effective anisotropic material, and considering the Mori-Tanaka's concept
for the mutual interaction of the neighboring inclusions, we may evaluate the averaged elastic properties of grained composites
with aligned ellipsoidal inclusions at finite concentrations.
The results provided in a closed-form solution concern the stiffness of 3-D grained composites with parallely dispersed ellipsoidal
inclusions forming a prismatic network inside the principal material. It is shown that the stiffness is affected by both the
geometry of the inclusions and their concentration. The use of different composite models in the analysis shows that intense
variations of stiffness occur mainly in hard composites weakened by soft ellipsoidal inclusions. These findings come in full
verification with experimental or theoretical results from the literature.
Received 10 February 1998; accepted for publication 27 November 1998 相似文献
16.
Igor V. Andrianov Vladyslav V. Danishevs'kyy Dieter Weichert 《European Journal of Mechanics - A/Solids》2002,21(6):556
We propose an asymptotic approach for evaluating effective elastic properties of two-components periodic composite materials with fibrous inclusions. We start with a nontrivial expansion of the input elastic boundary value problem by ratios of elastic constants. This allows to simplify the governing equations to forms analogous to the transport problem. Then we apply an asymptotic homogenization method, coming from the original problem on a multi-connected domain to a so called cell problem, defined on a characterizing unit cell of the composite. If the inclusions' volume fraction tends to zero, the cell problem is solved by means of a boundary perturbation approach. When on the contrary the inclusions tend to touch each other we use an asymptotic expansion by non-dimensional distance between two neighbouring inclusions. Finally, the obtained “limiting” solutions are matched via two-point Padé approximants. As the results, we derive uniform analytical representations for effective elastic properties. Also local distributions of physical fields may be calculated. In some partial cases the proposed approach gives a possibility to establish a direct analogy between evaluations of effective elastic moduli and transport coefficients. As illustrative examples we consider transversally-orthotropic composite materials with fibres of square cross section and with square checkerboard structure. The obtained results are in good agreement with data of other authors. 相似文献
17.
《International Journal of Solids and Structures》1999,36(25):3861-3885
We consider a linear elastic composite medium, which consists of a homogeneousmatrix containing aligned ellipsoidal uncoated or coated inclusions arranged in a doubly periodicarray and subjected to inhomogeneous boundary conditions. The hypothesis of effective fieldhomogeneity near the inclusions is used. The general integral equation obtained reduces theanalysis of infinite number of inclusion problems to the analysis of a finite number of inclusions insome representative volume element (RVE) . The integral equation is solved by a modifiedversion of the Neumann series; the fast convergence of this method is demonstrated for concreteexamples. The nonlocal macroscopic constitutive equation relating the cell averages of stress andstrain is derived in explicit iterative form of an integral equation. A doubly periodic inclusion fieldin a finite ply subjected to a stress gradient along the functionally graded direction is considered.The stresses averaged over the cell are explicitly represented as functions of the boundaryconditions. Finally, the employed of proposed explicit relations for numerical simulations oftensors describing the local and nonlocal effective elastic properties of finite inclusion pliescontaining a simple cubic lattice of rigid inclusions and voids are considered. The local andnonlocal parts of average strains are estimated for inclusion plies of different thickness. Theboundary layers and scale effects for effective local and nonlocal effective properties as well as foraverage stresses will be revealed. 相似文献
18.
O. C. Valdiviezo-Mijangos V. M. Levin F. J. Sabina 《Archive of Applied Mechanics (Ingenieur Archiv)》2009,79(1):51-67
This paper deals with the problem of multiple scattering by a random distribution of spherical solid particles in a solid.
The material properties of both media are taken as thermoelastic. The radii of the inclusions may be different. The self-consistent
method in its variant of the effective medium is used to find the dispersion and attenuation of quasi-elastic, quasi-thermal
and shear waves. The single scattering problem required by this technique is solved approximately by means of the Galerkin
method applied to an integral equation using the Green function. Numerical results display a characteristic resonance phenomena
which appears in the interval where the results are approximately valid, that is, for very long waves down to wavelengths
about twice the largest diameter of the spheres. Examples are shown, for composites with two sets of inclusions, which have
either a very similar or dissimilar size. Comparisons are made with the elastic counterpart. Among the material properties,
the mass density ratio, inclusion to matrix, seems to play an important and simple role. Frequency intervals are distinguished
and shown to depend on that ratio, where the attenuation and dispersion of quasi-elastic and P-waves are either very close
to each other or not at all. The same applies to shear waves in either composite. The mass density ratio also displays a simple
monotonic decreasing behaviour as a function of the frequency at the first attenuation maximum and velocity minimum. These
results may be of interest for the nondestructive testing characterization of particulate composites. 相似文献
19.
V. A. Buryachenko F. G. Rammerstorfer 《Archive of Applied Mechanics (Ingenieur Archiv)》2001,71(4-5):249-272
Summary We consider a linearly thermoelastic composite medium, which consists of a homogeneous matrix containing a statistically
inhomogeneous random set of ellipsoidal uncoated or coated inclusions, where the concentration of the inclusions is a function
of the coordinates (functionally graded material). Effective properties, such as compliance and thermal expansion coefficient,
as well as first statistical moments of stresses in the components are estimated for the general case of inhomogeneity of
the thermoelastic inclusion properties. The micromechanical approach is based on the Green function technique as well as on
the generalization of the multiparticle effective field method (MEFM), previously proposed for the research of statistically
homogeneous random structure composites. The hypothesis of effective field homogeneity near the inclusions is used; nonlocal
effects of overall constitutive relations are not considered. Nonlocal dependences of local effective thermoelastic properties
as well as those of conditional averages of the stresses in the components on the concentration of the inclusions are demonstrated.
Received 11 November 1999; accepted for publication 4 May 2000 相似文献
20.
《International Journal of Solids and Structures》2007,44(3-4):1304-1315
For a composite with thin interface layers between inclusions and the matrix, the effective elastic properties and the effective conductivity (thermal or electric) are almost unaffected by the layers, provided (1) the layer thickness is much smaller than the inclusion sizes and (2) the contrast between the properties of the layers and either of the phases is not overly high. For composites with nanoparticles, the interface thickness may be comparable to the particle sizes. Therefore, the effect of interfaces on the overall properties may be substantial. The controlling parameters are (1) the ratio of the interface thickness to particle sizes and (2) variability of the properties across the interface thickness. Explicit expressions constructed in the present work show that the overall elastic/conductive properties are affected, mostly, by the interface thickness (normalized to the size of the core particle) and are much less sensitive to the extent of the variation and its exact character. Similarities and differences between the elasticity and the conductivity problems are discussed. 相似文献