Local and global regularity in time dependent viscoplasticity

IUTAM Bookseries

Volumn 11, Issue , 2008, Pages 363-372

  Alber, Hans Dieter ^a   Nesenenko, Sergiy ^a  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Difference quotient technique; Interpolation; Maximalmonotone operator; Melan prager model; Regularity; Viscoplasticity

Indexed keywords

CONSTITUTIVE EQUATIONS; INITIAL VALUE PROBLEMS; INTERPOLATION; VISCOPLASTICITY;

DIFFERENCE QUOTIENT TECHNIQUES; GENERALIZED STANDARD MATERIALS; INELASTIC MATERIALS; INITIAL-BOUNDARY VALUE PROBLEMS; KINEMATIC HARDENING; MAXIMALMONOTONE OPERATOR; MELAN-PRAGER MODELS; REGULARITY;

PLASTICITY;

EID: 70349144293     PISSN: 18753507     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-1-4020-9090-5_33     Document Type: Conference Paper

References (28)

1. H.-D. Alber (1998) Materials with Memory- Initial-Boundary Value Problems for Constitutive Equations with Internal Variables. Lecture Notes in Mathematics, Vol. 1682, Springer, Berlin.
2. H.-D. Alber, K. Chełmínski (2004) Quasistatic problems in viscoplasticity theory. I. Models with linear hardening. In: I. Gohberg, A.F. dos Santos, F.O. Speck, F.S. Teixeira, W.Wendland (Eds.), Operator Theoretical Methods and Applications to Mathematical Physics, Vol. 147. Birkhäuser, Basel.
3. H.-D. Alber, K. Chełmínski (2007) Math. Models Meth. Appl. Sci. 17(2): 189-213.
4. H.-D. Alber, S. Nesenenko (2008) Submitted.
5. 1 regularity. In: J.L. Lions (Ed.), Boundary Value Problems for Partial Differential Equations and Applications, Res. Notes Appl. Math., Vol. 29, Paris.
6. A. Bensoussan, J. Frehse (1996) Comment. Math. Univ. Carolinae 37(2): 285-304.
7. A. Bensoussan, J. Frehse (2002) Regularity Results for Nonlinear Elliptic Systems and Applications, Applied Mathematical Sciences, Vol. 151. Springer, Berlin.
8. V.I. Burenkov (1998) Sobolev Spaces on Domains, Teubner-Texte zur Mathematik, Vol. 137. Teubner, Stuttgart/Leipzig.
9. C. Carstensen, S. Müller (2002) SIAM J. Math. Anal. 34(2): 495-509.
10. A. Demyanov (2007) Regularity of the stresses in Prandtl-Reuss perfect plasticity. Preprint, SISSA Trieste http://hdl.handle.net/1963/1963.
11. M. Fuchs, G. Seregin (2000) Variational Methods for Problems from Plasticity Theory and for Generalized Newtonian Fluids, Lecture Notes in Mathematics, Vol. 1749. Springer, New York.
12. B. Halphen, Nguyen Quoc Son (1975) Sur les matériaux standards généralisés. J. Méc. 14: 39-63.
13. D. Knees (2004) Regularity results for quasilinear elliptic systems of power-law growth in nonsmooth domains. Boundary, transmission and crack problems. PhD thesis, Stuttgart.
14. D. Knees (2006) Math. Methods. Appl. Sci. 29: 1363-1391.
15. J. Lemaitre, J.-L. Chaboche (1990) Mechanics of Solid Materials. Cambridge University Press, Cambridge.
16. J. Lubliner (1990) Plasticity Theory. Macmillan, New York.
17. P. Neff, D. Knees (2008) SIAM J. Math. Anal., to appear.
18. S. Nesenenko (2006) Homogenization and regularity in viscoplasticity. PhD Thesis, Darmstadt, Germany.
19. S. Nesenenko (2007) SIAM J. Math. Anal. 39(1): 236-262.
20. L. Prandtl (1925) Spannungsverteilung in plastischen Körpern. In Proc. Int. Congr. Appl. Mech. Delft 1924: 43-54 (Gesammelte Abhandlungen. Springer, Berlin (1961), 133-148).
21. S.I. Repin (1996) Math. Models Meth. Appl. Sci. 6(5): 587-604.
22. A. Reuss (1930) Z. Angew. Math. Mech. 10: 266-274.
23. G.A. Seregin (1987) Differents. Uravn. 23: 1981-1991.
24. G.A. Seregin (1987), English translation in Differential Equations 23, (1987), 1349-1358
25. G.A. Seregin (1988) A local Caccioppoli-type estimate for extremals of variational problems in Hencky plasticity. In: Some Applications of Functional Analysis to Problems of Mathematical Physics. Novosibirsk, pp. 127-138 [in Russian].
26. G.A. Seregin (1990) Algebra Analiz 2: 121-140.
27. G.A. Seregin (1999) J. Math. Sci. 93(5): 779-783.
28. E. Showalter (1997) Monotone Operators in Banach Spaces and Nonlinear Partial Differential Equations. Math. Surveys Monogr., Vol. 49, AMS, Providence.