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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 1, Pages 65–95 (Mi vsgtu1543)  

This article is cited in 4 scientific papers (total in 4 papers)

Mechanics of Solids

Analysis of properties of creep curves generated by the linear viscoelasticity theory under arbitrary loading programs at initial stage

A. V. Khokhlov

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

Abstract: The general equation of creep curves family generated by the linear integral constitutive relation of viscoelasticity (with an arbitrary creep compliance function) under arbitrary non-decreasing stress histories at initial stage of loading up to a given stress level is derived and analyzed. Basic qualitative properties of the theoretic creep curves and their dependence on a rise time magnitude, on a loading program shape at initial stage and on creep function characteristics are studied analytically in the uni-axial case assuming creep compliance is an increasing convex-up function of time. Monotonicity and convexity intervals of creep curves, their asymptotic behavior at infinity and conditions for convergence to zero of the deviation from the creep curve under instantaneous (step) loading to a constant stress with time tending to infinity are examined. Two-sided bounds have been obtained for such creep curves and for deviation from the creep curve under step loading and for differences of creep curves with different initial programs of loading up to a given stress level. The uniform convergence of the theoretic creep curves family (with fixed loading law at initial stage) to the creep curve under step loading with the rise time tending to zero has been proved. The analysis revealed the importance of convexity restriction imposed on a creep compliance and the key role of its derivative limit value at infinity. It is proved that the derivative limit value equality to zero is the criterion for memory fading.
General properties and peculiarities of the theoretic creep curves and their dependence on loading program shape at initial stage are illustrated by the examination of the classical rheological models (consisting of two or three spring and dashpot elements), fractional models and hybrid models (with piecewise creep function). The main classes of linear models are considered and specific features of their theoretic creep curves are marked. The results of the analysis are helpful to examine the linear viscoelasticity theory abilities to provide an adequate description of basic rheological phenomena related to creep and to indicate the field of applicability or non-applicability of the linear theory considering creep test data for a given material. The results constitutes the analytical foundation for obtaining precise two-sided bounds and correction formulas for creep compliance via theoretic or experimental creep curves with initial stage of loading (ramp loading, in particular) and for development of identification, fitting and verification techniques.

Keywords: linear viscoelasticity, creep compliance, theoretic creep curves, initial loading stage influence, loading program shape, rise time, ramp loading, two-sided bounds, deviation asymptotics, convergence, fading memory, regular and singular models, fractional models

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/vsgtu1543

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Bibliographic databases:

Document Type: Article
UDC: 539.372
MSC: 74D05, 74A20
Received: April 23, 2017
Revised: August 11, 2017
Accepted: December 18, 2017
First online: March 29, 2018

Citation: A. V. Khokhlov, “Analysis of properties of creep curves generated by the linear viscoelasticity theory under arbitrary loading programs at initial stage”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 22:1 (2018), 65–95

Citation in format AMSBIB
\Bibitem{Kho18}
\by A.~V.~Khokhlov
\paper Analysis of properties of creep curves generated by the linear viscoelasticity theory under arbitrary loading programs at initial stage
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2018
\vol 22
\issue 1
\pages 65--95
\mathnet{http://mi.mathnet.ru/vsgtu1543}
\crossref{https://doi.org/10.14498/vsgtu1543}
\zmath{https://zbmath.org/?q=an:07038276}
\elib{http://elibrary.ru/item.asp?id=35246683}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Khokhlov, “Osobennosti povedeniya poperechnoi deformatsii i koeffitsienta Puassona izotropnykh reonomnykh materialov pri polzuchesti, opisyvaemye lineinoi teoriei vyazkouprugosti”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 10:4 (2018), 65–77  mathnet  crossref  elib
    2. A. V. Khokhlov, “Sravnitelnyi analiz svoistv krivykh polzuchesti, porozhdaemykh lineinoi i nelineinoi teoriyami nasledstvennosti pri stupenchatykh nagruzheniyakh”, Matematicheskaya fizika i kompyuternoe modelirovanie, 21:2 (2018), 27–51  crossref  elib
    3. A. V. Khokhlov, “Modelirovanie zavisimosti krivykh polzuchesti pri rastyazhenii i koeffitsienta Puassona reonomnykh materialov ot gidrostaticheskogo davleniya s pomoschyu nelineino-nasledstvennogo sootnosheniya Rabotnova”, Mekhanika kompozitsionnykh materialov i konstruktsii, 24:3 (2018), 407–436  elib
    4. A. V. Khokhlov, “Dvustoronnie otsenki dlya funktsii relaksatsii lineinoi teorii nasledstvennosti cherez krivye relaksatsii pri ramp-deformirovanii i metodiki ee identifikatsii”, Izvestiya Rossiiskoi akademii nauk. Mekhanika tverdogo tela, 2018, no. 3, 81–104  crossref  elib
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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