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An alternative material model using a generalized J2 finite-strain flow plasticity theory with isotropic hardening

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Języki publikacji
EN
Abstrakty
EN
In this paper an alternative material model using a generalized J2 finite-strain flow plasticity theory with isotropic hardening is presented. The model is based on a new nonlinear continuum mechanical theory of finite deformations of elasto-plastic media which allows for the development of objective and thermodynamically consistent material models. As a result, the constitutive equation, the evolution equation and even the ‘normality rule’, characterising the plastic flow in the material during return mapping, can be expressed in various forms, using several instances of the yield surface and corresponding pairs of stress measures and strain rates, respectively, which are conjugate with respect to the internal mechanical power and its arbitrary higher order time derivative. Therefore the results of the material model when used in numerical analyses are not affected by the description and particularities of the material model formulation. Here, we briefly outline the nonlinear continuum theory along with a detailed description of the material model and finally present the model in a numerical example using a cross-shaped specimen in biaxial tension.
Rocznik
Strony
339--353
Opis fizyczny
Bibliogr. 30 poz., rys., tab.
Twórcy
autor
  • Slovak University of Technology in Bratislava Námestie slobody 17, 812 31 Bratislava, SLOVAKIA
autor
  • Slovak University of Technology in Bratislava Námestie slobody 17, 812 31 Bratislava, SLOVAKIA
Bibliografia
  • [1] Maugin G.A. (1992): The Thermodynamics of Plasticity and Fracture. – Cambidge: Cambridge University Press.
  • [2] Simo J.C. and Hughes T.J.R. (1998): Computational Inelasticity. – New York: Springer.
  • [3] De Souza Neto E.A., Perić D. and Owen D.R.J. (2008): Computational Methods for Plasticity. Theory and Applications. – Singapore: John Wiley and Sons Ltd..
  • [4] Nemat-Nasser S. (2004): Plasticity, a Treatise on Finite Deformation of Heterogenous Inelastic Materials. – Cambridge: Cambridge University Press.
  • [5] Bertran A. (2013): Elasticity and Plasticity of Large Deformations. An Introduction, 3rd ed. – Spinger, Berlin, Heidelberg.
  • [6] Owen D.R.J. and Hinton E. (1980): Finite Elements in Plasticity. Theory and Practice. – Swansea: Pineridge Press.
  • [7] Belytschko T., Liu W.K. and Moran B. (2000): Nonlinear Finite Elements for Continua and Structures. – Chichester: John Wiley and Sons Ltd.
  • [8] Crisfield M.A. (2000): Non-Linear Finite Element Analysis of Solids and Structures. Essentials. Vol.1. – Chichester: John Wiley and Sons Ltd..
  • [9] Crisfield M.A. (2001): Non-Linear Finite Element Analysis of Solids and Structures. Advanced Topics. – Vol.2. Chichester: John Wiley and Sons Ltd..
  • [10] Bathe K.J. (1995): Finite Element Procedures. – New Jersey: Prentice-Hall Inc., Englewood Cliffs.
  • [11] Truesdell C. and Toupin R.A. (1960): The Classical Field Theories. Handbook der Physic, III/1. – Berlin: Springer-Verlag.
  • [12] Truesdell C. and Noll W. (1965): The Nonlinear Field Theories. Handbook der Physic, III/3. – Berlin: Springer-Verlag.
  • [13] Gurtin M.E. (1981): An Introduction to Continuum Mechanics. – Orlando: Academic Press.
  • [14] Marsden J.E. and Hughes T.J.R. (1994): Mathematical Foundations of Elasticity. – New York: Dover.
  • [15] Ogden R.W. (1984): Non-Linear Elastic Deformations. – West Sussex: Ellis Horwood Ltd.
  • [16] Cairlet P. (1988): Mathematical Elasticity. Three-Dimensional Elasticity. – Vol.1. Amsterdam: North-Holland Publishing Company.
  • [17] Asaro R.J. (1983): Micromechanics of Crystals and Polycrystals, Advances in Applied Mechanics. – Vol.23. New York: Academic Press.
  • [18] Taylor G.I. (1938): Analysis of Plastic Strain in a Cubic Crystal. – In Stephen Timoshenko 60th Anniversary Volume, ed., J.M. Lessels. – New York: Macmillan.
  • [19] Hill R. (1966): Generalized constitutive relations for incremental deformation of metal crystals by multislip. – J. Mech. Phys. Solids, No.14, pp.95-102.
  • [20] Hill R. and Rice J.R. (1972): Constitutive analysis of elastic-plastic crystals at arbitrary strain. – J. Mech. Phys. Solids, No.20, pp.401-413.
  • [21] Asaro R.J. and Rice J.R. (1977): Strain localization in ductile single crystals. – J. Mech. Phys. Solids, No.25, pp.309-338.
  • [22] Asaro R.J. (1979): Geometrical effects in the inhomogeneous deformation of ductile single crystals. – Acta Metallurgica, No.27, pp.445-453.
  • [23] Sansour C. and Bocko J. (2003): On the numerical implications of multiplicative inelasticity with an anisotropic elastic constitutive law. – Int. J. Num. Meth. Engrg., vol.5, No.14, pp.2131-2160.
  • [24] Holzapfel G.A. (2001): Nonlinear Solid Mechanics. A Continuum Approach for Engineering. – Chichester: John Wiley and Sons Ltd.
  • [25] Bonet J. and Wood R.D. (2008): Nonlinear Continuum Mechanics for Finite Element Analysis. 2nd ed. – Cambridge: Cambridge University Press.
  • [26] Spencer A.J.M. (1980): Continuum Mechanics. – New York: Longman.
  • [27] Borisenko A.I. and Tarapov I.E. (1978): Vector and Tensor Analysis with Applications. – New York: Dover.
  • [28] Maugin G.A. (2015): The saga of internal variables of state in continuum thermo-mechanics. – Research Communications, No.69, pp.79-86.
  • [29] Écsi L. and Élesztős P. (2012): Moving toward a more realistic material model of a ductile material with failure mode transition. – Mat.-Wiss. U. Werkstofftech., vol.5, No.43, pp.379-387.
  • [30] Müller W. (1996): Beitrag zur Charakterisierung von Blechwerkstoffen unter Merachsiger Beamspruchung. – Berlin-Heidelberg: Springer Verlag.
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-b25bf1b3-d939-496c-b8da-5ee4537270ad
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