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A thermodynamically consistent stress-rate type model of one-dimensional strain-limiting viscoelasticity

Erbay, H. A. and Sengul, Y. 2020. A thermodynamically consistent stress-rate type model of one-dimensional strain-limiting viscoelasticity. Zeitschrift für Angewandte Mathematik und Physik 71 (3) , 94. 10.1007/s00033-020-01315-7

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We introduce a one-dimensional stress-rate type nonlinear viscoelastic model for solids that obey the assumptions of the strain-limiting theory. Unlike the classical viscoelasticity theory, the critical hypothesis in the present strain-limiting theory is that the linearized strain depends nonlinearly on the stress and the stress rate. We show the thermodynamic consistency of the model using the complementary free energy and then using the Gibbs free energy. This allows us to take the stress and the stress rate as primitive variables instead of kinematical quantities such as deformation or strain. We also show that the non-dissipative part of the materials in consideration has a stored energy. We compare the new stress-rate type model with the strain-rate type viscoelastic model due to Rajagopal from the points of view of energy decay, the nonlinear differential equations of motion and Fourier analysis of the corresponding linear models.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Medicine
Publisher: Springer Verlag (Germany)
ISSN: 0044-2275
Date of Acceptance: 20 April 2020
Last Modified: 17 Nov 2021 09:13

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