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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2009, Volume 50, Issue 3, Pages 158–170 (Mi pmtf1752)  

This article is cited in 9 scientific papers (total in 9 papers)

Differential constitutive equations of incompressible media with finite deformations

A. L. Svistkova, B. Laukeb

a Institute of Continuous Media Mechanics, Ural Division, Russian Academy of Sciences, Perm’, 614013, Russia
b Leibniz-Institut für Polymerforschung Dresden e.V., Dresden, 01069, Germany
Full-text PDF (305 kB) Citations (9)
Abstract: A method is proposed for constructing a system of constitutive equations of an incompressible medium with nonlinear dissipative properties with finite deformations. A scheme of the mechanical behavior of a material is used, in which the points are connected by horizontally aligned elastic, viscous, plastic, and transmission elements. The properties of each element of the scheme are described with the use of known equations of the nonlinear elasticity theory, the theory of nonlinear viscous fluids, and the theory of plastic flow of the material under conditions of finite deformations of the medium. The system of constitutive equations is closed by equations that express the relation between the deformation rate tensor of the material and the deformation rate tensor of the plastic element. Transmission elements are used to take into account a significant difference between macroscopic deformations of the material and deformations of elements of the medium at the structural level.
Keywords: constitutive equations, finite deformations, elasticity, plasticity, viscosity incompressible medium, mechanical properties.
Received: 05.09.2006
Accepted: 13.02.2008
English version:
Journal of Applied Mechanics and Technical Physics, 2009, Volume 50, Issue 3, Pages 493–503
DOI: https://doi.org/10.1007/s10808-009-0066-2
Bibliographic databases:
Document Type: Article
UDC: 539.3
Language: Russian
Citation: A. L. Svistkov, B. Lauke, “Differential constitutive equations of incompressible media with finite deformations”, Prikl. Mekh. Tekh. Fiz., 50:3 (2009), 158–170; J. Appl. Mech. Tech. Phys., 50:3 (2009), 493–503
Citation in format AMSBIB
\Bibitem{SviLau09}
\by A.~L.~Svistkov, B.~Lauke
\paper Differential constitutive equations of incompressible media with finite deformations
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2009
\vol 50
\issue 3
\pages 158--170
\mathnet{http://mi.mathnet.ru/pmtf1752}
\elib{https://elibrary.ru/item.asp?id=11928593}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2009
\vol 50
\issue 3
\pages 493--503
\crossref{https://doi.org/10.1007/s10808-009-0066-2}
Linking options:
  • https://www.mathnet.ru/eng/pmtf1752
  • https://www.mathnet.ru/eng/pmtf/v50/i3/p158
  • This publication is cited in the following 9 articles:
    1. K.A. Mokhireva, A.L. Svistkov, “A new approach to describe the elastic behavior of filled rubber-like materials under complex uniaxial loading”, International Journal of Solids and Structures, 202 (2020), 816  crossref
    2. Dillon Presto, John Meyerhofer, Grant Kippenbrock, Suresh Narayanan, Jan Ilavsky, Sergio Moctezuma, Mark Sutton, Mark D. Foster, “Influence of Silane Coupling Agents on Filler Network Structure and Stress-Induced Particle Rearrangement in Elastomer Nanocomposites”, ACS Appl. Mater. Interfaces, 12:42 (2020), 47891  crossref
    3. V.N. Solodko, A.L. Svistkov, A.G. Pelevin, “Numerical modeling of viscoelastic behavior of filled rubber vulcanizates”, Comp. Contin. Mech., 7:2 (2014), 115  crossref
    4. O.K. Garishin, A.S. Korlyakov, V.V. Shadrin, “Study of visco-elastic-plastic properties of thermoplastic polymers. An integrated experimental and theoretical approach”, Comp. Contin. Mech., 7:2 (2014), 208  crossref
    5. J. Domurath, M. Saphiannikova, G. Heinrich, “Non‐Linear Viscoelasticity of Filled Polymer Melts: Stress and Strain Amplification Approach”, Macromolecular Symposia, 338:1 (2014), 54  crossref
    6. D. Livescu, “Numerical simulations of two-fluid turbulent mixing at large density ratios and applications to the Rayleigh–Taylor instability”, Phil. Trans. R. Soc. A., 371:2003 (2013), 20120185  crossref
    7. A.V. Shutov, J. Ihlemann, “A viscoplasticity model with an enhanced control of the yield surface distortion”, International Journal of Plasticity, 39 (2012), 152  crossref
    8. Jan Domurath, Marina Saphiannikova, Gilles Ausias, Gert Heinrich, “Modelling of stress and strain amplification effects in filled polymer melts”, Journal of Non-Newtonian Fluid Mechanics, 171-172 (2012), 8  crossref
    9. K. W. Stöckelhuber, A. S. Svistkov, A. G. Pelevin, G. Heinrich, “Impact of Filler Surface Modification on Large Scale Mechanics of Styrene Butadiene/Silica Rubber Composites”, Macromolecules, 44:11 (2011), 4366  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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