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Validation et formulation variationnelle d'une loi de comportement viscoélastique non linéaire en grandes déformations

Abstract : We develop a large strain nonlinear viscoelastic model, called pseudo-linear model. It is based on the choice of a suitable strain tensor which permits to write the Helmholtz free energy as a quadratic form and the constitutive equation as a single convolution equation. To validate this model, we compare the pseudolinear potential with a general Helmholtz free energy approximated by a fourth order multiple integral expansion. The memory functions are chosen in exponential form with one characteristic time by decade. This comparison shows that the two models are in good agreements. The proposed model can easily evaluate the dissipation function of the material. This is illustrated in the case of harmonic vibrations. Then, we develop a variational formulation based on the total energy minimum principle. A numerical integration procedure using the finite element method is proposed, based on a linear approximation in the time domain. The comparison between the numerical results and the theoretical predictions are in good agreements for common behaviours.
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Seddiq Hassani. Validation et formulation variationnelle d'une loi de comportement viscoélastique non linéaire en grandes déformations. Matériaux. Ecole Nationale des Ponts et Chaussées, 1997. Français. ⟨tel-00529389⟩

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