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1.
A phenomenological model is proposed for describing the elastic deformation of a unidirectionally reinforced composite capable of accumulating scattered microdamages during its loading. The composite is considered as a homogeneous transversely isotropic solid. Its damaged state at every point is characterized by a centrally symmetric scalar function on the unit sphere (the damage function), which is used to account for variations in the elastic properties of the material during its deformation. The damage itself depends on the history of some equivalent strain, for which four simplified variants are suggested. The relation between strains and stresses is defined in a differential form. Dependences are presented for determining all unknown constants from simple mechanical experiments. As an example, an actual unidirectionally reinforced GFRP is considered, for which the main two-dimensional sections of corresponding failure surfaces are also constructed. 相似文献
2.
L. Nazarenko L. P. Khoroshun W. H. Müller B. R. Wille 《Mechanics of Composite Materials》2009,45(1):11-20
A model of deformation of stochastic composites subjected to microdamage is developed for the case of orthotropic materials
with microdamages accumulating in the fibers. The composite is treated as a matrix strengthened with elliptic fibers with
orthotropic elastic properties. The fractured microvolumes are modeled by a system of randomly distributed quasi-spherical
pores. The porosity balance equation and relations for determining the effective elastic moduli for the case of a fibrous
composite with orthotropic components are used as the fundamental relations. The fracture criterion is given as a limit value
of the intensity of average shear stresses occurring in the undamaged part of the material, which is assumed to be a random
function of coordinates and is described by the Weibull distribution. Based on an analytical and numerical approach, the algorithm
for determining the nonlinear deformation properties of such a material is constructed. The nonlinearity of composite deformations
is caused by the accumulation of microdamages in the fibers. By using a numerical solution, the nonlinear stress–strain diagrams
for an orthotropic composite in uniaxial tension are obtained.
Translated from Mekhanika Kompozitnykh Materialov, Vol. 45, No. 1, pp. 17–30, January–February, 2009. 相似文献
3.
The first part of the paper deals with homogenization models of unidirectional composites, in which each phase of the material
is bounded by parallel cylindrical surfaces. For a GFRP with epoxy resin and glass fibres, five elastic constants for six
models of the composite are calculated. In the second part, the results of strain gauge tests, photoelasticity investigations,
and scanning electron inspection are discussed. With these data, some elastic constants of the composite in tension and compression
are found. A comparison of experimental and analytical results is presented.
Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 2, pp. 195–206, March–April, 2008. 相似文献
4.
Incompressible elastic material with a periodic system of pores is considered. Processes are studied with a typical length
which is much more than the typical diameter of pores and the typical distance between pores. Porous material behaves as a
certain “effective” material without pores in such processes. The method of calculation of effective moduli based on mathematical
homogenization theory is described. The estimates for the effective moduli are proved. The results of numerical calculations
of effective moduli for materials with spherical and cubic pores are presented. The dependence of the effective moduli on
the volume fracture of pores is investigated. The explicit formulae for effective coefficients are deduced. Comparison with
the effective moduli for compressible materials is performed.
Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, October, 1995.
Lomonosov Moscow State University, Department of Mathematics and Mechanics, Moscow. Published in Mekhanika Kompozitnykh Materialov,
No. 5, pp. 579–587, September–October, 1996. 相似文献
5.
L. F. Fatullaeva 《Mechanics of Composite Materials》2007,43(6):513-520
The limiting state of a multilayer eccentric ring made of a nonlinearly elastic material and subjected to a uniform external
pressure is investigated. The topicality and importance of the problem are connected with the search for reserves of savings
in materials, with a simultaneous in crease in the load-carrying capacity of structures. Since rings often must have walls
of varying thickness, their critical buckling force is determined as a function of a parameter considering this fact. In solving
the problem, the geometric nonlinearity is also taken into account.
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Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 6, pp. 761–770, November–December, 2007. 相似文献
6.
A new micromacromechanical model of unit cells is suggested. In this model, a 3D-braided composite plate can be a cell system,
and the geometry of each cell strongly depends on its position in the cross section of the plate. Based on the Reddy higher-order
shear deformation theory of plates and the general von Karman-type equations, analytical solutions for the dynamic response
of simply supported 3D-braided rectangular plates resting on a two-parameter (Pasternak-type) elastic foundation and subjected
to transverse dynamic loads are found by using the perturbation method. The numerical illustrations concern the effects of
geometric parameters, fiber volume fraction, braiding angle, and foundation stiffness.
Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 6, pp. 861–880, November–December, 2008. 相似文献
7.
E. A. Aliyev 《Mechanics of Composite Materials》2007,43(6):521-534
Within the framework of a piecewise homogenous body model and with the use of a three-dimensional linearized theory of stability
(TLTS), the local near-surface buckling of a material system consisting of a viscoelastic (elastic) half-plane, an elastic
(viscoelastic) bond layer, and a viscoelastic (elastic) covering layer is investigated. A plane-strain state is considered,
and it is assumed that the near-surface buckling instability is caused by the evolution of a local initial curving (imperfection)
of the elastic layer with time or with an external compressive force at fixed instants of time. The equations of TLTS are
obtained from the three-dimensional geometrically nonlinear equations of the theory of viscoelasticity by using the boundary-form
perturbation technique. A method for solving the problems considered by employing the Laplace and Fourier transformations
is developed. It is supposed that the aforementioned elastic layer has an insignificant initial local imperfection, and the
stability is lost if this imperfection starts to grow infinitely. Numerical results on the critical compressive force and
the critical time are presented. The influence of rheological parameters of the viscoelastic materials on the critical time
is investigated. The viscoelasticity of the materials is described by the Rabotnov fractional-exponential operator.
Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 6, pp. 771–788, November–December, 2007. 相似文献
8.
James M. Hill Alexander I. Lee 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1989,40(1):128-132
Summary The governing equations for finite elastic deformations are highly nonlinear and there is still only a limited number of known exact solutions. In general for large elastic fully three dimensional deformations of the isotropic incompressible perfectly elastic neo-Hookean and Mooney materials, a non-trivial deformation for say the neo-Hookean strain-energy function, is frequently not well-defined for the general Mooney strain-energy function because the additional coupling imposes extra constraints on the deformation which are generally inconsistent with one another. Here we note two fully three dimensional deformations for which this is not the case. In both cases the resulting coupled systems of ordinary differential equations need to be integrated numerically but the deformations are nevertheless well-defined for the general Mooney material. The first deformation is simply noted because the details are given elsewhere. For the second deformation, the coupled system is derived and some new simple special solutions are given. Such deformations are important and noteworthy because of the scarcity of exact solutions in finite elasticity. 相似文献
9.
Bending of an elastic annular composite plate with a light filler lying on an elastic foundation is considered. The plate
is subjected to local loads. To describe the kinematics of the package, asymmetric across its thickness, the hypotheses of
broken normal is accepted. The reaction of foundation is described based on the Winkler model. A system of equilibrium equations
is constructed, and its exact solution in displacements is found. Numerical solutions for a metal-polymer sandwich plate are
presented.
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Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 1, pp. 109–120, January–February, 2007. 相似文献
10.
L. V. Nazarenko 《Journal of Mathematical Sciences》2010,168(5):653-664
The theory of long-term damageability of a homogeneous material is generalized to the case of an orthotropic fibrous composite
material with a stochastic structure. Equations of mechanics of microinhomogeneous media of this structure form the base of
the theory. The process of damage of components of a composite is modeled by the formation of stochastically located micropores.
The criterion of fracture of a unit microvolume is characterized by its long-term strength determined by the dependence of
the time of brittle fracture on the degree of closeness of the equivalent stress to its limit value, which characterizes the
short-term strength on the basis of the Huber–von Mises criterion accepted as an arbitrary function of coordinates. Efficient
deformation properties and the stress-strain state of an orthotropic fibrous composite with microdamages in components are
determined on the base of stochastic equations of elasticity of orthotropic media. For given macrostresses and macrostrains
and an arbitrary moment of time, balance equations of damage (porosity) of components are formulated. On the basis of the
iteration method, we construct algorithms for calculating dependences of microdamage of components of an orthotropic fibrous
material on time and dependences of macrostresses or macrostrains on time and obtain the corresponding curves for the case
of a bounded function of the long-term microstrength, which is approximated by an exponential law. 相似文献
11.
A. O. Kamins’kyi L. A. Kipnis M. V. Dudyk Yu. V. Dikhtyarenko 《Journal of Mathematical Sciences》2010,167(1):128-139
We perform calculation of the initial prefracture zone at the tip of a mode I crack that reaches a nonsmooth interface of
two dissimilar elastic media at its corner point by the Wiener–Hopf method. The zone is modeled by a line of normal displacement
fracture on a crack continuation. Expressions for the length of the prefracture zone and the potential energy accumulated
in it are obtained. Their numerical values are compared with the corresponding values for the prefracture zone in a bonding
material on the interface of the media, on the basis of which we draw a conclusion on the possible direction of development
of the zone. 相似文献
12.
L. V. Nazarenko 《Journal of Mathematical Sciences》2010,167(2):217-231
In the present work, a model of nonlinear deformation of stochastic composites under microdamaging is developed for the case
of a composite with orthotropic inclusions, when microdefects are accumulated in the matrix. The composite is treated as an
isotropic matrix strengthened by triaxial arbitrarily oriented ellipsoidal inclusions with orthotropic symmetry of the elastic
properties. It is assumed that the process of loading leads to accumulation of damage in the matrix. Fractured microvolumes
are modeled by a system of randomly distributed quasispherical pores. The porosity balance equation and relations for determining
the effective elastic modules in the case of orthotropic components are taken as basic relations. The fracture criterion is
specified as the limiting value of the intensity of average shear stresses acting in the intact part of the material. On the
basis of the analytic and numerical approach, we propose an algorithm for the determination of nonlinear deformation properties
of the investigated material. The nonlinearity of composite deformations is caused by the finiteness of deformations. By using
the numerical solution, the nonlinear stress–strain diagrams are predicted and discussed for an orthotropic composite material
for various cases of orientation of inclusions in the matrix. 相似文献
13.
M. H. B. M. Shariff 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,56(4):1112-1134
A general constitutive theory for anisotropic stress softening in compressible solids is presented. The constitutive equation
describes anisotropic strain induced behaviour of an initially “isotropic” virgin material. Parameters which characterise
damage are proposed together with a concept of damage function. In order to develop an anisotropic stress-softening theory
for compressible materials in close parallel to a recent incompressible anisotropic theory, the right stretch tensor is decomposed
into its isochoric and dilatational parts. The ’free’ energy is expressed as a function of the dilatation, modified principal
stretches, a volume change parameter and invariants of the dyadic products of the principal directions of the right stretch
tensor and two structural tensors. A class of free energy functions is discussed and a special form of this class which satisfies
the Clausius–Duhem inequality is proposed. Results of the theory applied to uniaxial tension, bulk compression and simple
shear deformations are given. A sequence of deformations involving shear, hydrostatic-compression and hydrostatic-tension
deformations is also investigated. In the case of hydrostatic-tension deformation, the stress softening is due to cavitation
damage. The theoretical results obtained are consistent with expected behaviour and compare well with experimental data. 相似文献
14.
R. M. Martynyak B. S. Slobodyan V. M. Zelenyak 《Journal of Mathematical Sciences》2009,160(4):470-477
A model of contact between an elastic half space and a rigid base with a shallow surface rectangular hole is proposed. The
hole contains an incompressible liquid and gas. The liquid occupies the middle part of the hole and forms a capillary bridge
between the opposite surfaces. The remaining volume of the hole is filled with gas under a constant pressure. The liquid completely
wets the surfaces of the bodies. The pressure drop at the liquid–gas interface caused by the surface tension is defined by
the Laplace formula. The corresponding plane contact problem for the elastic half space is essentially nonlinear because the
pressure of the liquid and the length of the capillary in the contact-boundary conditions are not known in advance and depend
on the external load. The problem is reduced to a system of three equations (a singular integral equation for the function
of height of the hole and two transcendental equations for the length of the capillary and the height of the meniscus). An
analytic-numerical procedure for the solution of these equations is proposed. Dependences of the length of the capillary and
the pressure drop at the liquid–gas interface on the external load, volume of liquid, and its surface tension are analyzed.
Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 51, No. 1, pp. 150–156, January–March, 2008. 相似文献
15.
R. Yu. Amenzadeh E. T. Kiyasbeyli L. F. Fatullaeva 《Mechanics of Composite Materials》2006,42(3):243-252
The loss of the load-carrying capacity of a nonlinearly elastic multilayer rod is investigated. The rod, whose layers have
various thickness and are made of different materials, is rigidly fixed at both its ends. Rigid contact conditions between
the layers are assumed. The problem posed is solved by using the variational method of mixed type in combination with the
Rayleigh-Ritz method. The initial analysis is reduced to the solution of the Cauchy problem for a nonlinear ordinary differential
equation solved for the first derivative. As the initial condition, the maximum initial eccentricity of the rod is assumed.
In the case of zero eccentricity, the Shanley critical force for an axially compressed rod is determined. For a three-layer
rod whose outer layers have equal thickness and are made of the same material, numerically, for various degrees of nonlinearity,
the effect of physicomechanical and geometric parameters on the critical load of buckling instability is determined. It is
found that, by matching the heterogeneity of the rod, it is possible to raise its load-carrying capacity.
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Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 3, pp. 347–360, May–June, 2006. 相似文献
16.
Y. I. Kunets V. V. Matus V. V. Mykhas’kiv A. Boström Ch. Zhang 《Mechanics of Composite Materials》2008,44(2):165-172
The problem of interaction of a plane time-harmonic SH-wave with an elastic fiber of quasi-square or quasi-triangular cross
section, when an interface crack is present between an infinite elastic matrix and the fiber, is considered. The modified
null-field method taking into account the asymptotic behavior of the solution at crack tips is exploited for obtaining numerical
results. The effects of fiber shape, fiber/matrix material combination, debonding (crack size), and direction of wave incidence
on the scattering amplitude in the far zone are analyzed.
Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 2, pp. 245–254, March–April, 2008. 相似文献
17.
Z. A. Yanson 《Journal of Mathematical Sciences》2007,142(6):2689-2696
The whispering gallery modes propagating along the surface of an anisotropic elastic body are investigated with the use of
space-time caustic expansions and space-time ray series. Each surface mode modulated in amplitude and frequency, is interpreted
as a wave packet, with its amplitude’s maximum moving at a group velocity. On the boundary surface, asymptotic expressions
for the group velocity (as a function of time and coordinates) are derived, which are in agreement with analogous formulas
for Rayleigh waves of SV type in the isotropic case. Bibliography: 6 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 332, 2006, pp. 299–312. 相似文献
18.
R. A. Kayumov 《Mechanics of Composite Materials》1999,35(5):409-418
Laminated nonthin shells made of nonlinearly elastic fiber composites are considered. The composite material is assumed to
be transversely isotropic in planes perpendicular to reinforcement. The asymptotic method and the condition of material stability
are applied to analyze the structure of constitutive relations. To introduce a small parameter, the high stiffness in the
reinforcement direction of the fiber composite is used. This allows us to obtain simplified constitutive relations containing
functions with one or two arguments instead of five as in the initial general case.
Kazan State Architectural Building Academy, Tatarstan, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35,
No. 5, pp. 615–628, September–October, 1999. 相似文献
19.
An anisotropic medium is considered in which, upon loading, scattered microdamages accumulate giving rise to nonlinear and
residual strains. The damage at a point of the medium is characterized by a scalar function on a unit sphere, referred to
as the damage function. This function is approximated by a fourth-rank tensor used for specifying the relation between the
increments of strains and stresses. The calculation dependences are presented in detail for a unidirectional composite, which
is taken to be a homogeneous transversely isotropic medium. Determination of the unknown constants is illustrated by the example
of an actual fiberglass plastic.
Institute of Polymer Mechanics, University of Latvia, Riga, LV-1006, Latvia. Translated from Mekhanika Kompozitnykh Materialov,
Vol. 35, No. 5, pp. 561–574, September–October, 1999. 相似文献
20.
The transient creep of a UD composite with a quadratic arrangement of elastic fibers of quadratic cross section is investigated.
The deformational properties of the composite are determined from the known properties of its constituents. A structural model
of the UD composite is developed, whose minimal elementary cell contains four elements. The stress-strain state of the elements
is assumed homogeneous. Two types of basic and resolving governing equations of transient creep are deduced, which are based
on static or kinematic assumptions. In each of the cases, a formula for the longitudinal elastic shear modulus of the composite
is found. The stationary solutions of creep equations allow one to obtain formulas of the steady-state creep of the composite
in a form similar to Norton’s law. Numerical calculations are also performed, and a comparison of the results with data given
in the literature bears witness to the efficiency of the models developed and the solutions obtained.
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Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 4, pp. 437–448, July–August, 2007. 相似文献