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On the linear theory of viscoelasticity 总被引:4,自引:0,他引:4
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Within the theory of linear viscoelasticity, we seek solutions to the inversion problem of the constitutive equation respectively inL
2 and in the spaceS of the tempered distributions. Successively we study the quasi-static problem inS. Both problems admit one and only one solution if the relaxation function satisfies Graffi's inequality. Finally we show that the inversion problem and the quasi-static one are deeply connected and that every counterexample about the existence or uniqueness of the solutions for the first problem also provides a counterexample for the latter.
Sommario Nell'ambito della viscoelasticità lineare, si studia il problema dell'invertibilità della equazione costitutiva rispettivamente inL 2 e nello spazioS delle distribuzioni temperate. Successivamente si studia il problema quasi statico inS. Entrambi i problemi ammettono una ed una sola soluzione se la funzione di rilassamento soddisfa la disuguaglianza di Graffi. Infine si mostra che i due problemi sono strettamente correlati in quanto ogni problema quasi statico è riconducibile ad un problema di invertibilità.相似文献
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I.IntroductionQuasi-staticdisplacementbasedtechniqueofinverseanalysisfortheconstitutlveparametersisbeingwidlyusedintheundergroundengineeringandsomeotherfields.Anumberofprogresshasbeenachievedinthefieldofidentificationfortheviscoelasticconstitutiveparallleters.XueandYang(1986)l'].Liu(1986)l=lemployedintegraltransformationtechniquetoidentifyviscoelasticconstitutiveparameters;a3-DinverseanalysisfortheviscoelasticconstitutiveparameterswasconductedbyYang(199I)l'];YallgandWu(1996)l'Jproposedagen… 相似文献
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In the present paper the linear theory of micropolar viscoelasticity is considered. The explicit expression of fundamental solution of the system of equations of steady vibrations is constructed by means of elementary functions and its basic properties are established. The Green's formulas in the considered theory are obtained. The formulas of integral representations of Somigliana-type of regular vector and regular (classical) solution are presented. The representation formulas of Galerkin-type solution of the system of nonhomogeneous equations and of the general solution of the system of homogeneous equations by means of eight metaharmonic functions are presented. The completeness of these solutions is proved. 相似文献
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The viscoelastic relaxation modulus is a positive-definite function of time. This property alone allows the definition of
a conserved energy which is a positive-definite quadratic functional of the stress and strain fields. Using the conserved
energy concept a Hamiltonian and a Lagrangian functional are constructed for dynamic viscoelasticity. The Hamiltonian represents
an elastic medium interacting with a continuum of oscillators. By allowing for multiphase displacement and introducing memory
effects in the kinetic terms of the equations of motion a Hamiltonian is constructed for the visco-poroelasticity.
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B. E. Pobedrya 《Moscow University Mechanics Bulletin》2012,67(5-6):134-137
Some features of the behavior of viscoelastic materials whose existence leads to the choice of nonlinear constitutive relations are discussed. A classification of such constitutive relations is given and a number of requirements imposed by practice on their adequacy are formulated. A nonlinear theory of viscoelasticity is proposed; this theory offers the advantages over the theory in which stresses are expressed in terms of strains by integral operators of increasing multiplicity. By a one-dimensional example, it is shown that the constitutive operator relations are reciprocal. 相似文献
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This paper establishes three minimum principles and transformed minimum principles concerning Laplace transformation in the linear dynamic theory of viscoelasticity. 相似文献
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A generalization of Pobedrya’s viscoelasticity constitutive relations is considered for an isotropic material with an elastic
behavior of the material volume. Two model problems are discussed for a specimen under uniform compression and uniaxial tension.
The resulting expressions for strains are used to formulate some necessary conditions for a nonrelaxing behavior of the material
volume. The case of an arbitrary low loading of the specimen is examined. It is proved that the obtained nonrelaxing conditions
are not only necessary but are also sufficient. 相似文献
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The main aim of this work is to develop a consistent formulation of the rheological behavior for different anisotropic polymer
systems. The unified theory of anisotropic viscoelasticity is developed based on the symmetry principles. The Maxwell rheological
equation is extended to nonsymmetric anisotropic liquids. Transitions from the most general anisotropy to particular cases
of anisotropy are established. It appears that the coupled relaxation of symmetric and antisymmetric stresses is a natural
phenomenon in nonsymmetric viscoelasticity. Within the concept of an internal state variable, a stress–order relation is derived
for a fully nonlinear case. The order tensor dynamics is also considered. A simple method of deriving the equation of the
internal rotational motion is developed for the general macroscopic anisotropy.
This paper was presented at the 3rd Annual Rheology Conference, AERC 2006, April 27–29, 2006, Crete, Greece 相似文献
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The plane displacement boundary value problem of quasi-static linear orthotropic thermoelasticity is discussed. The thermoelastic system on a bounded simply-connected domain is decoupled. The decoupled temperature equation is investigated by using an accurate estimate and the contractive mapping principle. Representation of solution of the field equation is obtained, and some solvability results are proved. The results are of both theoretical and numerical interest. 相似文献
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An analytic method is proposed to find material functions for the linear moment theory of viscoelasticity with consideration of the structure of the composite material under study. 相似文献