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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]

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: 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]