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1.
In this study asphalt-aggregate mixes are treated as both viscoelastic and viscoplastic. Following a damage mechanics approach,
a nonlinear viscoelastic constitutive formulation is generated from a linear formulation by replacing ‘applied stresses’ with
‘effective viscoelastic stresses’. A non-dimensional scalar entity called ‘relative viscoelastic stiffness’ is introduced;
it is defined as the ratio of applied to effective viscoelastic stress and encapsulates different types of nonlinearities.
The paper proposes a computational scheme for exposing these nonlinearities by uncovering, through direct analysis of any
test data, changes experienced by the ‘relative viscoelastic stiffness’. In general terms, the method is based on simultaneous
application of creep and relaxation formulations while preserving the interrelationship between the corresponding time functions.
The proposed scheme is demonstrated by analyzing a uniaxial tension test and a uniaxial compression test (separately). Results
are presented and discussed, unveiling and contrasting the character of viscoelastic nonlinearities in both cases. A conceptual
viewpoint is offered to explain the observations, illustrating the requirements from any candidate constitutive theory. 相似文献
2.
The problem of describing of the viscoelastic properties of composite materials that consist of more than one viscoelastic
component is studied. It is supposed that the viscoelastic properties of the components are known. The difficulty in the application
of the mixture theory arises in the cases when the properties are described by integral operators with different integral
kernels. This difficulty is avoided by the approximations of the viscoelastic operators in the stress–strain relations. A
method is proposed to obtain appropriate approximations that reduce all the viscoelastic operators to a general kernel using
rational approximations of their Laplace transforms. The proposed method allows for the reduction of the approximation error
for related operators. Examples are given for the adjustment of viscoelastic functions in the cases of increase and decrease
of functions parameter. 相似文献
3.
N. J. L. Van Ruth J. F. Vega S. Rastogi J. Martínez-Salazar 《Journal of Materials Science》2006,41(12):3899-3905
Morphology and viscoelastic behaviour during the initial stages of crystallisation of isotactic polypropylene were explored
as a function of time and angular frequency by light microscopy and dynamic oscillatory rheology. Results were evaluated according
to the Krieger-Dougherty and Palierne models for viscoelastic suspensions of spheres. The data obtained from light microscopy
were introduced in the rheological models reproducing quite well the viscoelastic response during crystallisation. The Palierne
model was able to describe the behaviour of the system, though it was not possible to observe all the model’s features due
to a limited angular frequency range. Further, at high filler contents, an ‘equilibrium’ modulus needs to be introduced for
the model to fit the experimental data. The exponent required to model the changes occurring in the ‘equilibrium’ modulus
over time resembles that of chemical gelation more than physical gelation. 相似文献
4.
This paper presents a numerical method for solving the two-dimensional problem of a polygonal linear viscoelastic domain containing
an arbitrary number of non-overlapping circular holes of arbitrary sizes. The solution of the problem is based on the use
of the correspondence principle. The governing equation for the problem in the Laplace domain is a complex hypersingular boundary
integral equation written in terms of the unknown transformed displacements on the boundaries of the holes and the exterior
boundaries of the finite body. No specific physical model is involved in the governing equation, which means that the method
is capable of handling a variety of viscoelastic models. A truncated complex Fourier series with coefficients dependent on
the transform parameter is used to approximate the unknown transformed displacements on the boundaries of the holes. A truncated
complex series of Chebyshev polynomials with coefficients dependent on the transform parameter is used to approximate the
unknown transformed displacements on the straight boundaries of the finite body. A system of linear algebraic equations is
formed using the overspecification method. The viscoelastic stresses and displacements are calculated through the viscoelastic
analogs of the Kolosov–Muskhelishvili potentials, and an analytical inverse Laplace transform is used to provide the time
domain solution. Using the concept of representative volume, the effective viscoelastic properties of an equivalent homogeneous
material are then found directly from the corresponding constitutive equations for the average field values.
Several examples are given to demonstrate the accuracy of the method. The results for the stresses and displacements are compared
with the numerical solutions obtained by commercial finite element software (ANSYS). The results for the effective properties
are compared with those obtained with the self-consistent and Mori–Tanaka schemes. 相似文献
5.
Free damped vibrations of a linear viscoelastic oscillator based on Rabotnov’s model involving one fractional parameter and
several relaxation (retardation) times are investigated. The analytical solution is obtained in the form of two terms, one
of which governs the drift of the system’s equilibrium position and is defined by the quasi-static processes of creep occurring
in the system, and the other term describes damped vibrations around the equilibrium position and is determined by the systems’s
inertia and energy dissipation. The drift is governed by an improper integral taken along two sides of the cut of the complex
plane. Damped vibrations are determined by two complex conjugate roots of the characteristic equation, which are located in
the left half-plane of the complex plane. The behaviour of the characteristic equation roots as function of the system’s parameters
is shown in the complex plane.
Dedicated to the bright memory of Academician Yury N. Rabotnov. 相似文献
6.
Two higher-order fractional viscoelastic material models consisting of the fractional Voigt model (FVM) and the fractional
Maxwell model (FMM) are considered. Their higher-order fractional constitutive equations are derived due to the models’ constructions.
We call them the higher-order fractional constitutive equations because they contain three different fractional parameters
and the maximum order of equations is more than one. The relaxation and creep functions of the higher-order fractional constitutive
equations are obtained by Laplace transform method. As particular cases, the analytical solutions of standard (integer-order)
quadratic constitutive equations are contained. The generalized Mittag–Leffler function and H-Fox function play an important
role in the solutions of the higher-order fractional constitutive equations. Finally, experimental data of human cranial bone
are used to fit with the models given by this paper. The fitting plots show that the models given in the paper are efficient
in describing the property of viscoelastic materials. 相似文献
7.
On the direct estimation of creep and relaxation functions 总被引:1,自引:0,他引:1
Two alternative approaches for estimating linear viscoelastic material functions from a single experiment under random excitation
are derived and analyzed. First, Boltzmann’s superposition integral is discretized into a system of linear equations. Due
to the ill-posedness of the resulting matrix equation, Tikhonov’s regularization is introduced. Second, the integral is transformed
into a recursive formula, using a Prony series representation of viscoelastic material functions, in which gradient-based
optimization is applied. Numerical results are provided to compare and verify the applicability of the presented numerical
procedures. 相似文献
8.
Nonlinear parametric vibration of axially accelerating viscoelastic strings is investigated via an approximate analytical
approach. The standard linear solid model using the material time derivative is employed to describe the string viscoelastic
behaviors. A coordinate transformation is introduced to derive Mote’s model of transverse motion from the governing equation
of the stationary string. Mote’s model leads to Kirchhoff’s model by replacing the tension with the averaged tension over
the string. An asymptotic perturbation approach is proposed to study principal parametric resonance based on the two models.
The amplitude and the existence conditions of the steady-state responses are determined by locating the nonzero fixed points
in the modulation equations resulting from the solvability condition. Numerical results are presented to highlight the effects
of the material parameters, the axial-speed fluctuation amplitude, and the initial stress on steady-state responses. 相似文献
9.
I. A. Makarov 《Journal of Engineering Physics and Thermophysics》2000,73(5):910-914
Flow between two plates is investigated numerically in the phase of reaching a steady-state value for a Newtonian fluid. Certain
features of the application of the method of finite elements are discussed. The time of reaching the steady state by the flow
is determined, which is constant for a wide range of parameters and fluids. It is noted that the results obtained can serve
as the ‘point of departure’ for comparing the considered flow with similar flows of viscoelastic and viscoplastic fluids and
that the difference between the times of reaching the steady state by the flows can be used to evaluate the degree of non-Newtonian
behavior of one fluid or another or of the model.
Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 73, No. 5, pp. 927–931, September–October, 2000. 相似文献
10.
Daniel Tscharnuter Michael Jerabek Zoltan Major Reinhold W. Lang 《Mechanics of Time-Dependent Materials》2011,15(1):1-14
Due to the viscoelastic behavior of polymers mechanical properties are strongly affected by the loading history. To obtain
the time-dependent Poisson’s ratio without further data manipulation, stress relaxation tests have to be carried out. Only
few results for viscoelastic materials have been published to date, but the theory of Poisson’s ratio in the framework of
linear viscoelasticity has received some attention with respect to loading histories other than relaxation, i.e. creep and
constant rate of strain tests. 相似文献
11.
Latif K. Talybly 《Mechanics of Time-Dependent Materials》2010,14(3):253-259
A problem on the action of a normal concentrated force on the surface of viscoelastic half-space (Boussinesq’s viscoelastic
problem) is solved. The relations of the theory of linear isotropic viscoelasticity are used as determining relations. The
two relaxation functions corresponding to shift and volumetric expansion states are accepted to be independent. The forms
of these functions are not defined concretely. Exact formulae for displacements, strains and stresses components are represented.
The used solution method may be used for the solution of a series of problems of the theory of linear isotropic viscoelasticity
as well. 相似文献
12.
One-dimensional wave-propagation is analysed in a non-homogeneous, isotropic, linearly viscoelastic semi-infinite medium,
by the theory of singular surfaces. The characteristics of the medium at any point are assumed to be dependent upon the position
of the point. The solution for the stress field, which is valid even after the wave-front has passed, is obtained in the form
of Taylor’s series by prescribing the time dependent stress boundary condition in the form of a Maclaurin’s series.
Furthermore, it is shown that the higher order discontinuities satisfy the same propagation conditions as the stress waves
and all the discontinuities decay as they traverse the material.
An application of inhomogeneity varying exponentially with position has been analysed. Diagrams for the above example with
arbitrarily chosen parameters are presented. 相似文献
13.
14.
A. V. Pavlov 《Measurement Techniques》1999,42(12):1146-1151
The triangular-norms method is used to construct algebras that are adequate to optical systems in approximations of geometrical
and Fourier optics. The elements of the algebras are defined. Implication operators are defined for both approximations with
interpretation of a measurement as a modus ponens inference.
Russia. Translated from Izmeritel’naya Tekhnika, No. 12, pp. 27–31, December, 1999. 相似文献
15.
The impact of a rigid body upon an elastic isotropic plate is investigated for the case when the equations of motion take
rotary inertia and shear deformation into account. The impactor is considered as a mass point, and the contact between it
and the plate is established through a buffer involving a linear-spring–fractional-derivative dashpot combination, i.e., the
viscoelastic features of the buffer are described by the fractional-derivative Maxwell model. It is assumed that a transient
wave of transverse shear is generated in the plate, and that the reflected wave has insufficient time to return to the location
of the spring’s contact with the plate before the impact process is completed. To determine the desired values behind the
transverse-shear wave front, one-term ray expansions are used, as well as the equations of motion of the impactor and the
contact region. As a result, we are led to a set of two linear differential equations for the displacements of the spring’s
upper and lower points. The solution of these equations is found analytically by the Laplace-transform method, and the time-dependence
of the contact force is obtained. Numerical analysis shows that the maximum of the contact force increases, tending to the
maximal contact force when the fractional parameter is equal to unity. 相似文献
16.
Vladimir V. Mokeyev 《International journal for numerical methods in engineering》2001,50(9):2271-2282
A generalized complex eigenvector method which can be used to a linear dynamic analysis of viscoelastic structures is described. Here dynamic analysis is understood as transient analysis and frequency response analysis. The generalized complex eigenvector method is based on finite element discretization of structure, approximation of viscoelastic properties by differential operators and mode superposition technique. Coefficients of differential operator are defined from the condition of best coincidence of complex characteristic of viscoelastic material and complex characteristic of differential operator in preset frequency range. Advantage of this method is that it allows to take into account the real changes of the viscoelastic property in frequency range. Also, the generalized complex eigenvector method permit to describe a viscoelastic properties by two functions (complex Young's modulus, complex Poisson's ratio). The method is verified with the help of comparing with solutions obtained by complex modulus method. An influence of viscoelastic Poisson's ratio on transient and frequency responses of structure is demonstrated. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
17.
This paper presents a homogenised finite element formulation for the transient dynamic analysis of asymmetric and symmetric
unconstrained layer damping beams in which the viscoelastic material is characterised by a five-parameter fractional derivative
model. This formulation is based on the weighted residual method (Galerkin’s approach) providing a fractional matrix equation
of motion. The application of Grünwald-Letnikov’s definition of the fractional derivatives allows to solve numerically the
fractional equation by means of two different implicit formulations. Numerical examples for a cantilever beam with viscoelastic
treatment are presented comparing the response provided by the proposed homogenised formulation with that of Padovan, based
on the principle of virtual work. Different damping levels and load cases are analysed, as well as the influence of the truncation
and time-step. From the numerical applications it can be concluded that the presented formulation allows to reduce significantly
the degrees of freedom and consequently the computational time and storage needs for the transient dynamic analysis of structural
systems in which damping treatments have been applied by means of viscoelastic materials characterised by fractional derivative
models. 相似文献
18.
Relaxation behavior of neat and particulate filled polypropylene in uniaxial and multiaxial compression 总被引:1,自引:0,他引:1
M. Jerabek D. Tscharnuter Z. Major K. Ravi-Chandar R. W. Lang 《Mechanics of Time-Dependent Materials》2010,14(1):47-68
The recently developed confined compression test was used to measure the viscoelastic bulk and shear relaxation moduli of
neat, glass bead and talc filled polypropylene. In this paper further modifications of the test are introduced and a criterion
for the assessment of the quality of experimental data is suggested. As expected, shear as well as the bulk relaxation moduli
were found to increase with the addition of particles. In order to determine the pressure sensitivity of the material, unconfined
compression tests were also performed and compared with the confined tests through interconversion of the measured moduli.
In agreement with earlier results on other polymers, it turned out that the relaxation response is significantly retarded
at higher confinement levels. It is shown that the effect of filler particles on the long-term behavior depends on the specific
uniaxial or multiaxial stress state. Poisson’s ratio was calculated by interconversion from the bulk and shear relaxation
modulus; these results show that with a single test in the confined configuration, a complete viscoelastic characterization
of the material can be obtained. 相似文献
19.
In a previous paper (Lu et al., Mechanics of Time-Dependent Materials, 7, 2003, 189–207), we described methods to measure
the creep compliance of polymers using Berkovich and spherical indenters by nanoindentation. However, the relaxation modulus
is often needed in stress and deformation analysis. It has been well known that the interconversion between creep compliance
and relaxation function presents an ill-posed problem, so that converting the creep compliance function to the relaxation
function cannot always give accurate results, especially considering that the creep data at short times in nanoindentation
are often not reliable, and the overall nanoindentation time is short, typically a few hundred seconds. In this paper, we
present methods to measure Young’s relaxation functions directly using nanoindentation. A constant-rate displacement loading
history is usually used in nanoindentations. Using viscoelastic contact mechanics, Young’s relaxation modulus is extracted
using nanoindentation load-displacement data. Three bulk polymers, Polymethyl Methacrylate (PMMA), Polycarbonate (PC) and
Polyurethane (PU), are used in this study. The Young’s relaxation functions measured from the nanoindentation are compared
with data measured from conventional tensile and shear tests to evaluate the precision of the methods. A reasonably good agreement
has been reached for all these materials for indentation depth higher than a certain value, providing reassurance for these
methods for measuring relaxation functions. 相似文献
20.
Rostand Moutou Pitti Frédéric Dubois Christophe Petit 《International Journal of Fracture》2010,161(2):187-198
This paper deals with the generalization of T-integral to crack growth process in viscoelastic materials. In order to implement this expression in a finite element software,
a modelling form of this integral, called Aθ, is developed. The analytical formulation is based on conservative law, independent path integral, and a combination of real,
virtual displacement fields, and real, virtual thermal fields introducing, in the same time, a bilinear form of free energy
density F. According to the generalization of Noether’s method, the application of Gauss Ostrogradski’s theorem combined with curvilinear
cracked contour, T
v
is obtained. By introducing a volume domain around crack tip, the modelling expression Aθ is also defined.. Finally, the viscoelastic generalization through a thermodynamic approach, called A
v
, is introduced by using a discretisation of the creep tensor according to a generalized Kelvin Voigt representation. 相似文献