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Tytuł artykułu

Approximation of the Norton–Hoff plasticity model with isotropic hardening through Cosserat plasticity

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Języki publikacji
EN
Abstrakty
EN
In this paper the regularizing properties of Cosserat elasto-plastic models in a geometrically linear setting are investigated. For vanishing Cosserat effects it is shown that the Norton–Hoff model with isotropic hardening is approximated by the model with microrotations.
Rocznik
Strony
37--54
Opis fizyczny
Bibliogr. 22 poz., rys.
Twórcy
autor
  • Department of Mathematics and Information Sciences Warsaw University of Technology Koszykowa 75, 00-661 Warsaw, Poland
Bibliografia
  • 1. E. Cosserat, F. Cosserat, Théorie des corps déformables, Librairie Scientifique A. Hermann et Fils, Paris, 1909.
  • 2. P. Neff, K. Chełmiński, Infinitesimal elastic-plastic Cosserat micropolar theory. Modeling and global existence in the rate-independent case, Proc. Roy. Soc. Edinburgh A, 135, 5, 1017–1039, 2005.
  • 3. F.H. Norton, The Creep of Steel at High Temperatures, McGraw-Hill Company, London, 1929.
  • 4. A. Bensoussan, J. Frehse, Asymptotic behaviour of the time dependent Norton–Hoff law in plasticity theory and H1-regularity, Comment. Math. Univ. Carolin., 37, 2, 285–304, 1996.
  • 5. R. Temam, A generalized Norton–Hoff model and the Prandtl–Reuss law of plasticity, Arch. Rational Mech. Anal., 95, 137–183, 1986.
  • 6. K. Chełmiński, Coercive limits for a subclass of monotone constitutive equations in the theory of inelastic material behaviour of metals, Mat. Stos., 40, 41–81, 1997.
  • 7. D.H. Alber, Materials with Memory: Initial-Boundary Value Problems for Constitutive Equations with Internal Variables, Springer, Berlin, 1998.
  • 8. P. Neff, K. Chełmiński, A note on approximation of Prandtl-Reuss plasticity through Cosserat plasticity, Quart. Appl. Math., 66, 2, 351–357, 2008.
  • 9. K. Chełmiński, P. Neff, H1 loc-stress and strain regularity in Cosserat plasticity, ZAMM Z. Angew. Math. Mech., 89, 4, 257–266, 2009.
  • 10. P. Neff, K. Chełmiński, W. Müller, C. Wieners, Numerical solution method for an infinitesimal elastic-plastic Cosserat model, Math. Models Methods Appl. Sci., 17, 1211–1239, 2007.
  • 11. P. Neff, K. Chełmiński, Well-posedness of dynamic Cosserat plasticity, Appl. Math. Optimization, 56, 19–35, 2007.
  • 12. K. Chełmiński, P. Neff, S. Owczarek, Poroplasticity with Cosserat effects, ZAMM Z. Angew. Math. Mech., 92, 6, 462–478, 2012.
  • 13. J. Jeong, P. Neff, Existence, uniqueness and stability in linear Cosserat elasticity for weakest curvature conditions, Math. Mech. Solids, 15, 1, 78–95, 2010.
  • 14. J. Jeong, H. Ramézani, I. Münch, P. Neff, A numerical study for linear isotropic Cosserat elasticity with conformally invariant curvature, ZAMM Z. Angew. Math. Mech., 89, 7, 552–569, 2009.
  • 15. P. Neff, K.-I. Hong, J. Jeong, The Reissner-Mindlin plate is the Γ-limit of Cosserat elasticity, Math. Models Methods Appl. Sci., 20, 9, 1553–1590, 2010.
  • 16. P. Neff, J. Jeong, A new paradigm: the linear isotropic Cosserat model with conformally invariant curvature energy, ZAMM Z. Angew. Math. Mech., 89, 2, 107–122, 2009.
  • 17. P. Neff, J. Jeong, I. Münch, H. Ramézani, Linear Cosserat elasticity, conformal curvature and bounded stiffness [in:] G. A. Maugin, V. A. Metrikine [eds.], Mechanics of Generalized Continua. One hundred years after the Cosserats, Adv. Mech. Math., 21, 55–63, 2010.
  • 18. L.C. Evans, Partial Differential Equations, American Mathematical Society, Providence, 1998.
  • 19. R. Temam, Navier–Stokes Equations: Theory and Numerical Analysis, North-Holland, Amsterdam, 1984.
  • 20. P.D. Lax, Functional Analysis, Wiley-Interscience, New York, 2002.
  • 21. W. Rudin, Functional Analysis, McGraw-Hill Book Company, New York, 1973.
  • 22. J.P. Aubin, A. Cellina, Differential Inclusions. Set-valued Maps and Viability Theory, Springer, Berlin, 1984.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-632140f9-9240-48f4-9126-23c251cd2eab
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