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Viscoplasticity

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Encyclopedia of Continuum Mechanics

Synonyms

Creep plasticity; Rate-dependent plasticity; Rate-sensitive plasticity

Definition

Viscoplasticity is the theory which describes the rate-dependent (rate-sensitive) plastic behavior of solids. Rate dependence should be understood as a material sensitivity to rate of the deformation induced by external loads or shortly as a sensitivity to rate of external loads. It is important that rate-independent plastic response can be obtained as a limit case of viscoplastic flow. Furthermore, viscoplasticity belongs to implicit nonlocal models (Sumelka and Lodygowski, 2017) and can also be interpreted as the regularization of rate-independent flow (Simo and Hughes, 1997). Another important property is the dispersive nature of viscoplastic waves, what is crucial from the point of view of strain localization phenomena (Glema, 2004). In consequence, viscoplastic material shows not only instantaneous permanent deformation, due to applied loads, but undergoes also a creep flow.

General Remarks

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References

  • Andrade E (1910) On the viscous flow in metals, and allied phenomena. Proc R Soc A 84(A567):1–12

    Article  Google Scholar 

  • Bodner S, Partom Y (1975) Constitutive equations for elastic-viscoplastic strain-hardening materials. J Appl Mech (ASME) 42(2):385–389

    Article  Google Scholar 

  • Chaboche J (1977) Viscoplastic constitutive equations for the description of cyclic and anisotropic behaviour of metals. Bull Polish Acad Sci Tech Sci 25(1):33–42

    Google Scholar 

  • Freudenthal A, Geiringer H (1953) The mathematical theories of the inelastic continuum. In: FlĂŒgge S (ed) Elasticity and Plasticity/ElastizitĂ€t und PlastizitĂ€t. Encyclopedia of Physics/Handbuch der Physik. Springer, Berlin, pp 229–433

    Google Scholar 

  • Glema A (2004) Analysis of wave nature in plastic strain localization in solids, Rozprawy, vol 379. Publishing House of Poznan University of Technology (in Polish), Poznan, Poland

    Google Scholar 

  • Glema A, Lodygowski T, Sumelka W, Perzyna P (2009) The numerical analysis of the intrinsic anisotropic microdamage evolution in elasto-viscoplastic solids. Int J Damage Mech 18(3):205–231

    Article  Google Scholar 

  • Heeres O, Suiker A, de Borst R (2002) A comparison between the perzyna viscoplastic model and the consistency viscoplastic model. Eur J Mech A/Solids 21(1):1–12

    Article  Google Scholar 

  • Hohenemser K, Prager W (1932) Fundamental equations and definitions concerning the mechanics of isotropic continua. J Rheol 3:16. https://doi.org/10.1122/1.2116434

    Article  Google Scholar 

  • Imatani S (1990) Studies on inelastic constitutive relationship for high temperature materials and its application to finite element analysis. Ph.D Dissertation, Kyoto Unversity, Kyoto

    Google Scholar 

  • Johnson G, Cook W (1983) A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. In: Proceedings of the sevens international symposium on ballistics, The Hague, pp 541–547

    Google Scholar 

  • Klepaczko J (1975) Thermally activated flow and strain rate history effects for some polycrystalline f.c.c. metals. Mater Sci Eng 18(1):121–135

    Article  Google Scholar 

  • KƂosowski P, Woznica K (2007) Elastic-viscoplastic non-linear constitutive models in selected applications of structures analysis. Publishing house of Gdanska University of Technology, Gdansk (in Polish)

    MATH  Google Scholar 

  • Liao M, Lai Y, Liu E, Wan X (2017) A fractional order creep constitutive model of warm frozen silt. Acta Geotech 12(2):377–389

    Article  Google Scholar 

  • LitoƄski J (1977) Plastic flow of a tube under adiabatic torsion. Bulletin de l’Academie, Polonaise des Sciences – Serie des Sciences Techniques XXV(1):7–14

    Google Scholar 

  • Ɓodygowski T (1996) Theoretical and numerical aspects of plastic strain localization. D.Sc. thesis, vol 312. Publishing House of Poznan University of Technology

    Google Scholar 

  • Ludwik P (1909) Elemente der Technologischen Mechanik. Springer, Berlin

    Book  Google Scholar 

  • Malvern L (1951) The propagation of longitudinal waves of plastic deformation in a bar of material exhibiting a strain-rate effects. J Appl Mech (ASME) 18:203–208

    MathSciNet  Google Scholar 

  • Norton F (1929) The creep of steel at high temperature. McGraw-Hill, New York

    Google Scholar 

  • Odquist F (1933) Die verfestigung von flußeisenĂ€hnlichen körpern. ein beitrag zur plastizitĂ€tstheorie. Zeitschrift fĂŒr Angewandte Mathematik und Mechanik 13(5):360–363

    Article  Google Scholar 

  • Perzyna P (1963) The constitutive equations for rate sensitive plastic materials. Q Appl Math 20:321–332

    Article  MathSciNet  Google Scholar 

  • Perzyna P (2005) The thermodynamical theory of elasto-viscoplasticity. Eng Trans 53:235–316

    MathSciNet  MATH  Google Scholar 

  • Perzyna P (2010) The thermodynamical theory of elasto-viscoplasticity for description of nanocrystalline metals. Eng Trans 58(1–2):15–74

    Google Scholar 

  • Perzyna P (2012) Multiscale constitutive modelling of the influence of anisotropy effects on fracture phenomena in inelastic solids. Eng Trans 60(3):225–284

    MathSciNet  Google Scholar 

  • Simo J, Hughes T (1997) Computational inelasticity. Interdisciplinary applied mathematics, vol 7. Springer, New York

    Google Scholar 

  • Sumelka W (2014) Fractional viscoplasticity. Mech Res Commun 56:31–36

    Article  Google Scholar 

  • Sumelka W, Ɓodygowski T (2017) Implicit nonlocality in the framework of the viscoplasticity. In: Voyiadjis G (ed) Handbook of nonlocal continuum mechanics for materials and structures. Springer, Cham. https://doi.org/10.1007/978-3-319-22977-5_17-1

    MATH  Google Scholar 

  • Sun Y, Shen Y (2017) Constitutive model of granular soils using fractional-order plastic-flow rule. Int J Geomech 17(8):04017025. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000904

    Article  Google Scholar 

  • Tanimura S, Ishikawa K (1991) A constitutive equation describing strain hardening, strain rate sensitivity, temperature dependence and strain rate history effect. Springer, Dordrecht, pp 417–420

    Google Scholar 

  • Xiao R, Sun H, Chen W (2017) A finite deformation fractional viscoplastic model for the glass transition behavior of amorphous polymers. Int J Non-linear Mech 93:7–14

    Article  Google Scholar 

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Correspondence to Wojciech Sumelka .

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Sumelka, W., Ɓodygowski, T. (2018). Viscoplasticity. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_226-1

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  • DOI: https://doi.org/10.1007/978-3-662-53605-6_226-1

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