One-dimensional model describing the non-linear viscoelastic response of materials

Tomáš Bárta

Commentationes Mathematicae Universitatis Carolinae (2014)

  • Volume: 55, Issue: 2, page 227-246
  • ISSN: 0010-2628

Abstract

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In this paper we consider a model of a one-dimensional body where strain depends on the history of stress. We show local existence for large data and global existence for small data of classical solutions and convergence of the displacement, strain and stress to zero for time going to infinity.

How to cite

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Bárta, Tomáš. "One-dimensional model describing the non-linear viscoelastic response of materials." Commentationes Mathematicae Universitatis Carolinae 55.2 (2014): 227-246. <http://eudml.org/doc/261859>.

@article{Bárta2014,
abstract = {In this paper we consider a model of a one-dimensional body where strain depends on the history of stress. We show local existence for large data and global existence for small data of classical solutions and convergence of the displacement, strain and stress to zero for time going to infinity.},
author = {Bárta, Tomáš},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {viscoelasticity; integrodifferential equation; classical solution; global existence; implicit constitutive relations; viscoelasticity; integro-differential equation; classical solution; global existence; implicit constitutive relations},
language = {eng},
number = {2},
pages = {227-246},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {One-dimensional model describing the non-linear viscoelastic response of materials},
url = {http://eudml.org/doc/261859},
volume = {55},
year = {2014},
}

TY - JOUR
AU - Bárta, Tomáš
TI - One-dimensional model describing the non-linear viscoelastic response of materials
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2014
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 55
IS - 2
SP - 227
EP - 246
AB - In this paper we consider a model of a one-dimensional body where strain depends on the history of stress. We show local existence for large data and global existence for small data of classical solutions and convergence of the displacement, strain and stress to zero for time going to infinity.
LA - eng
KW - viscoelasticity; integrodifferential equation; classical solution; global existence; implicit constitutive relations; viscoelasticity; integro-differential equation; classical solution; global existence; implicit constitutive relations
UR - http://eudml.org/doc/261859
ER -

References

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  2. Dafermos C.M., Nohel J.A., A nonlinear hyperbolic Volterra equation in viscoelasticity, . Contributions to analysis and geometry (Baltimore, Md., 1980), pp. 87–116, Johns Hopkins Univ. Press, Baltimore, Md., 1981. Zbl0588.35016MR0648457
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  8. Málek J., Mathematical properties of flows of incompressible power-law-like fluids that are described by implicit constitutive relations, Electron. Trans. Numer. Anal. 31 (2008), 110–125. Zbl1182.35182MR2569596
  9. Málek J., Průša P., Rajagopal K.R., 10.1016/j.ijengsci.2010.06.013, Internat. J. Engrg. Sci. 48 (2010), no. 12, 1907–1924. Zbl1231.76073MR2778752DOI10.1016/j.ijengsci.2010.06.013
  10. Muliana A., Rajagopal K.R., Wineman A.S., A new class of quasi-linear models for describing the nonlinear viscoelastic response of materials, Acta Mechanica (2013), 1–15. 
  11. Průša V., Rajagopal K.R., 10.1016/j.jnnfm.2012.06.004, Journal of Non-Newtonian Fluid Mechanics 181-182 (2012), 22–29. DOI10.1016/j.jnnfm.2012.06.004
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  13. Renardy M., Hrusa W.J., Nohel J.A., Mathematical Problems in Viscoelasticity, Pitman Monographs and Surveys in Pure and Applied Mathematics, 35, Longman Scientific & Technical, Harlow; John Wiley & Sons, Inc., New York, 1987. Zbl0719.73013MR0919738
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