Abstract
By introducing a functional derivative and the line integral of a functional the author supplies an energy proof of the nonlinear theory of viscoelasticity. The stress potential for small strains, analogous to the potential proposed by Coleman for large strains [7], is considered for comparison.
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Literature cited
M. Frechet, "Sur les Fonctionnelles continues," Ann. de l'Ecole Normale Sup., 3rd Series, 27 (1910).
B. E. Pobedrya, Mekhan. Polim., No. 3, 427 (1967).
B. E. Pobedrya, Mekhan. Polim., No. 4, 645 (1967).
A. A. Il'yushin and P. M. Ogibalov, Mekhan. Polim., No. 2, 170 (1966).
M. M. Soldatov, Mekhan. Polim., No. 4, 498 (1966).
V. V. Moskvitin and V. V. Kolokol'chikov, Mekhan. Polim., No. 4, 603 (1969).
B. Coleman, Arch. Rat. Mech. Anal.,17, No. 3, 230 (1964).
W. Noll, J. Rat. Mech. Anal.,4, No. 1, 3 (1955).
L. A. Lyusternik and V. I. Sobolev, Elements of Functional Analysis [in Russian], Moscow (1965).
B. Coleman and M. Gurtin, Mekhanika, No. 2, 136 (1967).
Additional information
Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 4, pp. 633–642, July–August, 1970.
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Kolokol'chikov, V.V. Stress potential in the nonlinear theory of viscoelasticity. Polymer Mechanics 6, 552–560 (1970). https://doi.org/10.1007/BF00856303
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DOI: https://doi.org/10.1007/BF00856303