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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.
Czasopismo
Rocznik
Tom
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