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Adequacy of a nonlinear theory of viscoelasticity

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Abstract

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.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119899, Russia

    B. E. Pobedrya

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  1. B. E. Pobedrya
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Additional information

Original Russian Text © B.E. Pobedrya, 2012, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2012, Vol. 67, No. 5, pp. 65–69.

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Pobedrya, B.E. Adequacy of a nonlinear theory of viscoelasticity. Moscow Univ. Mech. Bull. 67, 134–137 (2012). https://doi.org/10.3103/S002713301205007X

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  • DOI: https://doi.org/10.3103/S002713301205007X

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