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1.
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
2.
A. Loghman A. Ghorbanpour Arani A. R. Shajari S. Amir 《Archive of Applied Mechanics (Ingenieur Archiv)》2011,81(12):1853-1864
Time-dependent creep stress redistribution analysis of rotating disk made of Al–SiC composite is investigated using Mendelson’s
method of successive elastic solution. All mechanical and thermal properties except Poisson’s ratio are radial dependent based
on volume fraction percent of SiC reinforcement. The material creep behavior is described by Sherby’s constitutive model using
Pandey’s experimental results on Al–SiC composite. Loading is an inertia body force due to rotation and a distributed temperature
field due to steady-state heat conduction from inner to outer surface of the disk. Using equations of equilibrium, stress
strain, and strain displacement, a differential equation, containing creep strains, for displacement is obtained. History
of stresses and deformations are calculated using method of successive elastic solution. It is concluded that the uniform
distribution of SiC reinforcement does not considerably influence on stresses. However, the minimum and most uniform distribution
of circumferential and effective thermoelastic stresses belongs to composite disk of aluminum with 0% SiC at inner surface
and 40% SiC at outer surface. It has also been found that the stresses, displacement, and creep strains are changing with
time at a decreasing rate so that after almost 50 years the solution approaches the steady-state condition. 相似文献
3.
4.
The resonant-based identification of the in-plane elastic properties of orthotropic materials implies the estimation of four
principal elastic parameters: E
1
, E
2
, G
12
, and ν
12
. The two elastic moduli and the shear modulus can easily be derived from the resonant frequencies of the flexural and torsional
vibration modes, respectively. The identification of the Poisson’s ratio, however, is much more challenging, since most frequencies
are not sufficiently sensitive to it. The present work addresses this problem by determining the test specimen specifications
that create the optimal conditions for the identification of the Poisson’s ratio. Two methods are suggested for the determination
of the Poisson’s ratio of orthotropic materials: the first employs the resonant frequencies of a plate-shaped specimen, while
the second uses the resonant frequencies of a set of beam-shaped specimens. Both methods are experimentally validated using
a stainless steel sheet. 相似文献
5.
The objective of this article is to derive a macroscopic Darcy’s law for a fluid-saturated moving porous medium whose matrix
is composed of two solid phases which are not in direct contact with each other (weakly coupled solid phases). An example of this composite medium is the case of a solid matrix, unfrozen water, and an ice matrix within the pore space.
The macroscopic equations for this type of saturated porous material are obtained using two-space homogenization techniques
from microscopic periodic structures. The pore size is assumed to be small compared to the macroscopic scale under consideration.
At the microscopic scale the two weakly coupled solids are described by the linear elastic equations, and the fluid by the linearized Navier–Stokes equations with appropriate
boundary conditions at the solid–fluid interfaces. The derived Darcy’s law contains three permeability tensors whose properties
are analyzed. Also, a formal relation with a previous macroscopic fluid flow equation obtained using a phenomenological approach
is given. Moreover, a constructive proof of the existence of the three permeability tensors allows for their explicit computation
employing finite elements or analogous numerical procedures. 相似文献
6.
《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
7.
This paper examines the numerical displacements and stresses developed around a disc under horizontal prescribed displacements
and at the interface separating it from the surrounding elastic soil. Since the geometry of the problem exhibits axial symmetry
and the loading is non-axisymmetric, the semi-analytical FE approach is used as it proves to be efficient and economical.
First, both analytical and numerical expressions for soil reaction are established and compared. Results of comparison show
a very good agreement. Then, for different values of the soil Poisson’s ratio, normal radial stresses, orthoradial stresses
and shear stresses distributions along radial distance reaching 20r
d (r
d is the disc radius) are presented for a disc that has either perfectly smooth or perfectly rough interfaces with the elastic
medium. The paper finishes by showing the effect of the soil Poisson’s ratio as well as the relative soil/interface stiffness
on the stresses developed at the interface locations. 相似文献
8.
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
9.
The modified nonlinear relations for the estimation of elastic constants of Al2O3–NiAl composite material are developed. The concept of microstructure and interconnectivity of phases at the interface is
used. Hashin–Shtrikman relations are described in their actual form and modified version of Hashin–Shtrikman relations for
bulk and shear moduli are discussed. These relations for elastic and mechanical properties are applied mainly for Al2O3–NiAl composite material. Theoretical predictions using modified relations are compared with Hashin–Shtrikman bounds and experimental
results of elastic properties for Al2O3–NiAl matrix-inclusion-based composite. It is found that the predicted values of elastic and mechanical properties using modified
relations are quite close to the experimental results. 相似文献
10.
《International Journal of Plasticity》1996,12(6):781-804
The effective elastoplastic behavior of a two-phase composite consisting of partially debonded elastic inclusions and a ductile matrix is investigated by a homogenization method. The method drew information from a recent study by the authors on the effective elastic moduli of the said composite and from an energy approach suggested by Qui and Weng, J. Appl. Mech., 59, 261 [1992] to address the homogenized plastic state of the heterogeneously deformed ductile matrix. Two types of partial debonding configuration are considered; the first is on the top and bottom of the aligned oblate inclusions and the other is on the lateral surface of the prolate ones, with special reference to spherical inclusions for both types of debonding. The transversely isotropic elastoplastic properties of the partially debonded composite are found to be highly dependent upon the debonding mode and the volume concentration and shape of inclusions. A damage mechanics based on Weibull's statistical function is also proposed to study the progressive partial debonding of the initially bonded composite under pure tension and under biaxial tension, respectively, for these two types of partial debonding. It is found that the interfacial strength, particle concentration, inclusion shape and debonding mode all play significant role in the overall response of the heterogeneous system during the progressive debonding process. 相似文献
11.
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
12.
We consider the regularized Ericksen model of an elastic bar on an elastic foundation on an interval with Dirichlet boundary
conditions as a two-parameter bifurcation problem. We explore, using local bifurcation analysis and continuation methods,
the structure of bifurcations from double zero eigenvalues. Our results provide evidence in support of Müller’s conjecture
(Müller, Calc. Var. 1:169–204, 1993) concerning the symmetry of local minimizers of the associated energy functional and describe in detail the structure of
the primary branch connections that occur in this problem. We give a reformulation of Müller’s conjecture and suggest two
further conjectures based on the local analysis and numerical observations. We conclude by analysing a “loop” structure that
characterizes (k,3k) bifurcations.
相似文献
13.
An investigation is presented on the suitability and accuracy of a thermoelastic technique for the analysis of fatigue cracks.
The stress intensity factor ranges ΔK
I and ΔK
II are determined from thermoelastic data recorded from around the tip of a sharp slot in a steel specimen under biaxial load,
in order to assess the accuracy of the technique. ΔK
I and ΔK
II are determined to within 4% and 9% of a theoretical prediction, respectively. The results from a similar test on a fatigue
crack under biaxial load are also presented. These show that thermoelastic stress analysis is a rapid and accurate way of
analyzing mixed-mode fatigue cracks. A discussion is given on the potential of thermoelastic stress analysis of propagating
cracks. 相似文献
14.
Michal Kotoul 《Journal of the mechanics and physics of solids》2002,50(5):1099-1124
The Mori-Tanaka approach is used to modelling metal particulate-reinforced brittle matrix composites under cyclic compressive loading. The J2-flow theory is considered as the relevant physical law of plastic flow in inclusions. Ratchetting of the composite is prevented by the strong constraint exerted by the matrix on the inclusions, even under the assumption of evanescent kinematic hardening. However, the weakening constraint power of the matrix caused by microfracture damage around inclusions is closely coupled with the plasticity of inclusion and leads to ratchetting even when the plastic deformation of inclusions is described by an isotropic hardening rule. A detailed parametric study has revealed that ratchetting is followed by either plastic or elastic shakedown, depending on the load amplitude, composite parameters and the mean length of microcracks. 相似文献
15.
The paper gives explicit expressions of the elastic T-stress components T
I, T
II, and T
III for an elliptic crack in an unbounded body under uniform pressure and bending and expressions of all the T-stress components for parabolic and tunnel cracks under uniform loading. These formulas are derived by analyzing the asymptotic
behavior of the stress components near the crack front using special harmonic functions. The dependence of the T-stresses on Poisson’s ratio, semiaxes and parametric angle of the elliptic crack is studied. The expressions of T
I, T
II, and T
III for a penny-shaped crack under arbitrary uniform pressure and bending follow as a special case from the respective expressions
for an elliptic crack
__________
Translated from Prikladnaya Mekhanika, Vol. 43, No. 8, pp. 57–70, August 2007. 相似文献
16.
With respect to obtaining the effective elastic moduli of the composite, the present theory differs from both Eshelby's equivalent
inclusion method and Hill's self-consistent one, both of which only consider the mechanical properties of the matrix and inclusions
(fibers). In fact, the inclusion-inclusion interaction is more pronounced when the volume fraction of inclusions of the composite
increases. Hence, in this paper the effective elastic moduli of the composite are derived by taking into account the shapes,
sizes and distribution of inclusions, and the interactions between inclusions. In addition, it is more convincing to assume
short-fibers as cylindrical inclusions as in the present paper than as ellipsoidal ones as in others[7,8]. Finally, numerical results are given. 相似文献
17.
Constitutive equations for a linear thermoelastic dielectric are derived from the energy balance equation assuming dependence of the stored energy function on the strain tensor, the polarization vector, the polarization gradient tensor and entropy. A method is indicated for constructing a hierarchy of constitutive equations for materials with arbitrary symmetry by introducing various thermodynamic potentials. Maxwell's relations are constructed for the thermodynamic potential WL. The entropy inequality is used to obtain stability conditions for an elastic dielectric in equilibrium under prescribed boundary constraints. Frequencies are explicitly determined for a plane wave propagating along the x1-axis in an infinite centro-symmetric isotropic thermoelastic dielectric. 相似文献
18.
I. V. Andrianov H. Topol D. Weichert 《Archive of Applied Mechanics (Ingenieur Archiv)》2009,79(11):999-1007
In A fibre-reinforced 2D composite material with elastic fibres and viscoelastic, isotropic matrix is studied. Starting from
the solution of a reference-problem with elastic matrix material the elastic matrix parameters are substituted by their viscoelastic
correspondents in the Laplace domain. For simplification the time-dependent solution is approximated by using limiting value
theorems that give information about the time-dependent solution for t → 0 and t → ∞. Then the method of asymptotically equivalent functions is used and illustrated with examples of a steel fibre in a PMMA
matrix. The analytical solutions are compared with their numerical counterparts. In summary it can be stated that this paper
is a further contribution to the vast literature about the application of the correspondence principle to the solution of
special problems of the linear viscoelasticity. 相似文献
19.
H. Brito-Santana R. Rodríguez-Ramos R. Guinovart-Díaz J. Bravo-Castillero F. J. Sabina G. A. Maugin 《Archive of Applied Mechanics (Ingenieur Archiv)》2009,79(3):189-204
Using the spherical and deviator decomposition of the polarization and strain tensors, we present a general algorithm for
the calculation of variational bounds of dimension d for any type of anisotropic linear elastic composite as a function of the properties of the comparison body. This procedure
is applied in order to obtain analytical expressions of bounds for multiphase, linear elastic composites with cubic symmetry
where the geometric shapes of the inclusions are arbitrary. For the validation, it can be proved that for the isotropic particular
case, the bounds coincide with those recently reported by Gibiansky and Sigmund. On the other hand, based on this general
procedure some, classical bounds reported by Hashin for transversely isotropic composites, are reproduced. Numerical calculations
and some comparisons with other models and experimental data are shown. 相似文献
20.
Chao Hu Xueqian Fang Wenhu Huang 《Archive of Applied Mechanics (Ingenieur Archiv)》2008,78(3):177-190
A new approach is proposed to investigate the propagation of a plane compressional wave in matrix composite materials with
high volume concentrations of particles. The theory of quasicrystalline approximation and Waterman’s T matrix formalism are employed to treat the multiple scattering resulting from the particles in composites. The addition theorem
for spherical Bessel functions is used to accomplish the translation between different coordinate systems. The Percus–Yevick
correlation function widely applied in the molecular theory of liquids is employed to analyze the interaction of the densely
distributed particles. The analytical expression for the Percus–Yevick correlation function is also given. The closed form
solution for the effective propagation constant is obtained in the low frequency limit. Only numerical solutions are obtained
at higher frequencies. Numerical examples show that the phase velocities in the composite materials with low volume concentration
are in good agreement with those in previous literatures. The effects of the incident wave number, the volume fraction and
the material properties of the particles and matrix on the phase velocity are also examined. 相似文献