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The paper provides a detailed analysis of the current state of the problem. A mathematical model is presented to determine the dynamic behavior of earth dams, considering the viscoelastic properties of soil, using the hereditary Boltzmann-Volterra theory with the A.R. Rzhanitsyn kernel under periodic kinematic impacts. To solve the problems considered, the finite element method and complex arithmetics were used to reduce integrodifferential equations to a high-order complex algebraic equation. The accuracy of the methods was verified by solving test problems. Steadystate forced vibrations of the Pskem earth dam 195 m high are studied considering the real geometry and soil properties under resonant vibration modes. It was stated that the largest stress amplitudes in the body of the dam occur not only under the first resonance, but they can occur under other dense spectra of the eigenfrequencies of the dam, due to the interaction between close natural modes of vibration. The strength of various sections of the dam body was tested under kinematic impact using the Coulomb- Mohr theory of strength; the most dangerous sections of the dam were identified in terms of the highest stress.

The free vibrations of cantilever slender beams of polymers, which are viscoelastic materials, are theoretically described using the simple Euler–Bernoulli assumption. The comparison between the theory and the experimental data collected for a thermoplastic elastomer, polyether block amide, shows very satisfactory results. Consequently, the theory is used for a thoughtful analysis of the impact of the material parameters and the beam geometry on its free vibration. Finally, the comparison of the dynamic behaviors of two polymers, using the free vibration test and a simple uniaxial tension/relaxation test, is discussed.

Certain results about free energies of materials with memory are presented, both in the general case and within the theory of linear viscoelasticity. A new variational method is developed in both the time and frequency domains. In the latter case, explicit forms of a family of free energies, associated with a given state of a discrete spectrum viscoelastic material, are given, including both maximum and minimum free energies.

Abstract: This paper investigates the instability of a viscoelastic fluid in a saturated porous medium heated from below and subjected to an horizontal through-flow. The Oldroyd-B constitutive equation is used to describe the viscoelastic behavior of diluted polymeric solutions. In the absence of the horizontal flow, the onset of convection can be characterized either by stationary or oscillatory instabilities. A temporal stability analysis is carried out in order to study the combined influence of the viscoelastic properties of the fluid and the main flow on the linear characteristics of these two types of instabilities. It is shown that the presence of the through-flow has a destabilizing effect and that it favors the emergence of mobile transverse rolls (R.T.), among an infinity of three-dimensional unstable modes. The thresholds for the appearance of these R.T., as well as their wavelengths and frequencies, are determined as functions of the dimensionless parameters of the problem. [Copyright &y& Elsevier]

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Abstract: In this Note, we prove a Carleman''s estimate for the integro-differential hyperbolic system of the viscoelasticity problem and we use this estimate to obtain a stability result for the inverse problem of recovering a viscoelastic coefficient from a unique internal measure. To cite this article: M. de Buhan, A. Osses, C. R. Acad. Sci. Paris, Ser. I 347 (2009). [Copyright &y& Elsevier]

Abstract: The purpose of this study is to contribute to the knowledge of viscoelastic fluids flows in a contraction which are often studied numerically. A device has been conceived for an experimental study of the flow by Laser Doppler velocimetry. An isothermal flow through a rectangular duct including an abrupt contraction has been considered. We have characterized the isothermal flow for different values of Reynolds number and correlations of the axial velocity are presented. To cite this article: M. Mahfoud et al., C. R. Mecanique 336 (2008). [Copyright &y& Elsevier]

Abstract: The viscoelastic generalization of T and A integrals is presented in this Note. The analytical developments are based on conservative laws, the non-dependent integrals and the combination of real and virtual displacement and thermals fields inducing a quadrilinear form of the strain energy density. In order to simulate this integral parameter by finite element software, a modeling form ensuring the non-dependent path integral during crack growth process is presented. The introducing of viscoelastic behavior is realized with the generalized Kelvin Voigt model. To cite this article: R. Moutou Pitti et al., C. R. Mecanique 336 (2008). [Copyright &y& Elsevier]

Abstract: The main purpose of this Note is the development of a new integral Mv separating mixed mode fracture during a crack growth process in a viscoelastic media. The mathematical developments are based on conservative laws, the independent path integrals and the combination of real and virtual displacement fields inducing a bilinear form of the strain energy density. The uncoupling fracture mode is based on a generalization of the virtual work principle. The introduction of the viscoelastic behavior through an incremental formulation of the free energy allows the generalization of this path independent path integral. To cite this article: R. Moutou Pitti et al., C. R. Mecanique 335 (2007). [Copyright &y& Elsevier]

Abstract: We present a Cosserat-based 3D–1D dimensional reduction for the viscoelastic finite strain model introduced by P. Neff. The reduced 1D model preserves observer invariance. We prove the existence and uniqueness of the solution of the reduced coupled minimization/evolution problem. To cite this article: J. Beyrouthy, C. R. Acad. Sci. Paris, Ser. I 345 (2007). [Copyright &y& Elsevier]

Abstract: In this note, one considers a 1-d.o.f. oscillator consisting of a mass and a viscoelastic spring, the rheology of which is represented by a generalized so-called Biot''s model with parameters. It is proved that its independent eigenmotions are of the following nature: two eigenmotions damped with or without oscillations (as in the case of classical viscous damping) and n eigenmotions damped without oscillations which are induced by the viscoelastic rheology. To cite this article: P. Muller, C. R. Mecanique 333 (2005). [Copyright &y& Elsevier]

Abstract: The aim of the present Note is to differentiate the relative contributions of the aggregation and the percolation phenomena to the viscoelastic behaviour of composites. This separation is performed through the development of a micromechanical model, by taking into account the percolation concept. To cite this article: P. Mélé et al., C. R. Mecanique 333 (2005). [Copyright &y& Elsevier]

A bone remodeling model taking into account the viscoelastic properties of the material is proposed. The nonlinear equations governing the evolution of the bone apparent density are solved by a finite difference method in the unidimensional case of a n-unit elements model. The results show the effects of the viscous damping on the structure for a controlled mechanical loading. To cite this article: S. Baïotto, M. Zidi, C. R. Mecanique 332 (2004). [Copyright &y& Elsevier]

This paper is concerned with incompressible viscoelastic fluids which obey a differential constitutive law of White–Metzner type. We establish the existence and uniqueness of local solutions in 3-D as well as the global existence of small solutions. We then deduce the existence and asymptotic stability of small periodic and stationary solutions. Finally, we prove that the 2-D results obtained in Hakim (J. Math. Anal. Appl. 185 (1994) 675–705) remain true without any restriction on the smallness of the retardation parameter which is the linking coefficient between the equation of velocity (Navier–Stokes equation) and the transport equation verified by the extra-stress tensor. To cite this article: L. Molinet, R. Talhouk, C. R. Acad. Sci. Paris, Ser. I 338 (2004). [Copyright &y& Elsevier]

Fatigue of bituminous asphalts is one of the main types of pavement destruction. This phenomenon was studied extensively in Europe (RILEM) and in the United States (SHRP). There are no standardized tests in Quebec to assess asphalt fatigue resistance. In France, a new approach based on the determination of damage rates due to fatigue has been developed for a tension–compression test on asphalt core samples to study their fatigue strength. This paper presents a summary of the knowledge on asphalt fatigue. Damage rate analyses, developed by the DGCB (Département de Génie Civil et du Bâtiment) of the ENTPE at Lyon, is detailed and applied to stone matrix asphalt (SMA). Results show the validity of the approach by damage and the good fatigue damage strength of the SMA. [ABSTRACT FROM AUTHOR]

We extend the previous work by Benallal et al. on the relationship between structure and rheological properties of linear polymer melts. The aim of this paper is to quantify the effect of the chemical structure on the viscoelastic properties. We show that these properties are governed by the monomer dimensions and the interaction energy. To cite this article: A. Allal et al., C. R. Physique 3 (2002) 1451–1458. [Copyright &y& Elsevier]

Let α be a positive number. The one-dimensional viscoelastic problem utt−uxx−αuxxt=f, x∈(−∞,0], t∈[0,+∞), with unilateral boundary conditions u(0,·)⩾0, (ux+αuxt)(0,·)⩾0, (u(ux+αuxt))(0,·)=0, can be reduced to the following variational inequality: λ1*w=g+b, w⩾0, b⩾0, 〈w,b〉=0. Here λˆ1(ω) is the causal determination of iω√ of 1+iαω. We show that the energy losses are purely viscous; this result is a consequence of the relation 〈w˙,b〉=0; since a priori, b is a measure and w˙ is defined only almost everywhere, this relation is not trivial. To cite this article: A. Petrov, M. Schatzman, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 983–988. [Copyright &y& Elsevier]