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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2018, Volume 22, Number 2, Pages 293–324 (Mi vsgtu1573)  

Mechanics of Solids

Properties of stress-strain curves generated by the nonlinear Maxwell-type viscoelastoplastic model under loading and unloading at constant stress rates

A. V. Khokhlov

Lomonosov Moscow State University, Institute of Mechanics, Moscow, 119192, Russian Federation

Abstract: A physically nonlinear Maxwell-type constitutive relation for non-aging rheonomic materials is studied analytically to find out the set of basic rheological phenomena that it simulates, to indicate its application field and to develop identification techniques and ways of tuning and further modifications. Under minimal primary restrictions on two material functions of the relation, the general equation of theoretic stress-strain curves family produced by the model under loading and unloading at constant stress rates is derived and analyzed in uni-axial case. Intervals of monotonicity and convexity of loading and unloading curves, conditions for existence of extremum and inflection points, magnitudes of maximal strain, strain rate jumps and plastic strain arising as a result of loading- unloading cycle are considered and their dependences on material functions and on stress rate and maximal stress are examined. The main qualitative properties of stress-strain curves and unloading responses generated by the constitutive equation are compared to typical properties of test loading-unloading curves of viscoelastoplastic materials in order to elucidate capabilities of the model, to obtain necessary phenomenological restrictions which should be imposed on the material functions and to find convenient indicators of applicability (or non-applicability) that can (and should) be checked examining test data of a material.

Keywords: elastoviscoplasticity, stress-strain curves, stress rate, unloading response, rate sensitivity, instantaneous modulus, equilibrium stress-strain curve, tension compression asymmetry, superplasticity, polymers

Funding Agency Grant Number
Russian Foundation for Basic Research 17-08-01146_а
This work was supported by the Russian Foundation for Basic Research (project no. 17–08–01146_a).


DOI: https://doi.org/10.14498/vsgtu1573

Full text: PDF file (1389 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Document Type: Article
UDC: 539.372
MSC: 74D05, 74A20
Received: October 18, 2017
Revised: March 28, 2018
Accepted: June 11, 2018
First online: June 29, 2018

Citation: A. V. Khokhlov, “Properties of stress-strain curves generated by the nonlinear Maxwell-type viscoelastoplastic model under loading and unloading at constant stress rates”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 22:2 (2018), 293–324

Citation in format AMSBIB
\Bibitem{Kho18}
\by A.~V.~Khokhlov
\paper Properties of stress-strain curves generated by the nonlinear Maxwell-type viscoelastoplastic model under loading and unloading at constant stress rates
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2018
\vol 22
\issue 2
\pages 293--324
\mathnet{http://mi.mathnet.ru/vsgtu1573}
\crossref{https://doi.org/10.14498/vsgtu1573}


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  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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