Hassani, S.; Alaoui Soulimani, A.; Ehrlacher, A. A nonlinear viscoelastic model: The pseudo-linear model. (English) Zbl 0919.73024 Eur. J. Mech., A, Solids 17, No. 4, 567-598 (1998). Summary: A large strain nonlinear viscoelastic model is developed. Called a “pseudo-linear” model, it identifies a suitable strain tensor which permits the Helmholtz free energy to be written as a quadratic form (linear behavior according to Boltzmann). To validate this model, we compare the pseudo-linear potential with a general Helmholtz free energy expression approximated by a fourth-order multiple integral expansion (Fréchet development). Furthermore, we are able to calculate the energy dissipation at any time. Cited in 1 Document MSC: 74D10 Nonlinear constitutive equations for materials with memory 74A15 Thermodynamics in solid mechanics 74A20 Theory of constitutive functions in solid mechanics Keywords:Fréchet development; strain tensor; Helmholtz free energy; quadratic form; fourth-order multiple integral expansion; energy dissipation PDFBibTeX XMLCite \textit{S. Hassani} et al., Eur. J. Mech., A, Solids 17, No. 4, 567--598 (1998; Zbl 0919.73024) Full Text: DOI References: [1] Alaoui Soulimani, A., Une méthode énergétique de modélisation de la viscoélasticité non linéaire en grandes déformations, (Thèse (1993), Ecole Nationale des Ponts et Chaussées: Ecole Nationale des Ponts et Chaussées Paris) [2] Bernstein, B.; Kearsley, E. A.; Zapas, L. J., A study of stress relaxation with finite strain, Transactions of the society of rheology, 7, 391-410 (1963) · Zbl 0139.42701 [3] Breuer, S.; Onat, E. 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