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IssuesArchive of Issues2020-5pp.664-672

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N.S. Stetsenko, "Nonlinear Effects Simulated by a Viscoelastic Maxwell-Type Model for Finite Deformations," Mech. Solids. 55 (5), 664-672 (2020)
Year 2020 Volume 55 Number 5 Pages 664-672
DOI 10.3103/S0025654420300044
Title Nonlinear Effects Simulated by a Viscoelastic Maxwell-Type Model for Finite Deformations
Author(s) N.S. Stetsenko (Lomonosov Moscow State University, Moscow, 119992, Russia,
Abstract For viscoelastic materials, a generalization of the elementary Maxwell model to the case of finite deformations is investigated using the one-parameter set of Gordon-Showalter objective derivatives. Using the obtained constitutive relations, we consider the problems of simple shear, uniaxial tension-compression, and shear vibrations given by the sawtooth function. It is shown that the obtained analytical solutions of these problems significantly depend on the parameters of the model and, thus, consideration of the set of objective derivatives, the special cases of which are the Oldroyd, Cotter-Rivlin, and Jaumann derivatives, expands the possibilities of describing the behavior of the material. It is shown that the analyzed model predicts the appearance of the Poynting, Kelvin, and Weissenberg effects, exhibits non-Newtonian viscosity, reveals a nonzero normal stress difference in the simple shear problem, simulates viscosity decrease as a function of shear rate with an increase in shear thinning and an escalation in viscosity as a function of tensile strain rate with increasing extensional thickening strain rate.
Keywords finite deformations, viscoelastic models, non-Newtonian viscosity, Poynting effect, Kelvin effect, Weissenberg effect, normal stress differences, shear thinning, extensional thickening
Received 14 October 2019Revised 18 October 2019Accepted 21 October 2019
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