Globally stable quasistatic evolution in plasticity with softening

Networks and Heterogeneous Media

Volumn 3, Issue 3, 2008, Pages 567-614

  Dal Maso, G ^a   DeSimone, A ^a   Mora, M G ^a   Morini, M ^a  

^a SISSA   (Italy)

Author keywords

Incremental problems; Plasticity with softening; Prandtl Reuss plasticity; Quasistatic evolution; Rate independent processes; Relaxation; Shear bands; Young measures

Indexed keywords

SHEAR BANDS;

INCREMENTAL PROBLEMS; QUASI-STATIC EVOLUTION; RATE-INDEPENDENT PROCESS; RELAXATION; YOUNG MEASURE;

COMPUTER APPLICATIONS;

EID: 56849088495     PISSN: 15561801     EISSN: 1556181X     Source Type: Journal    
DOI: 10.3934/nhm.2008.3.567     Document Type: Article

References (19)

1. G. Anzellotti and M. Giaquinta, On the existence of the field of stresses and displacements for an elasto-perfectly plastic body in static equilibrium, J. Math. Pures Appl., 61 (1982), 219-244.
2. H. Brézis, "Opérateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert," North-Holland, Amsterdam-London; American Elsevier, New York, 1973.
3. G. Dal Maso, A. DeSimone and M. G. Mora, Quasistatic evolution problems for linearly elastic - perfectly plastic materials, Arch. Ration. Mech. Anal., 180 (2006), 237-291.
4. G. Dal Maso, A. DeSimone, M. G. Mora and M. Morini, Time-dependent systems of generalized Young measures, Netw. Heterog. Media, 2 (2007), 1-36.
5. G. Dal Maso, A. DeSimone, M. G. Mora and M. Morini, A vanishing viscosity approach to quasistatic evolution in plasticity with softening, Arch. Ration. Mech. Anal., to appear.
6. C. Goffman and J. Serrin, Sublinear functions of measures and variational integrals, Duke Math. J., 31 (1964), 159-178.
7. W. Han and B. D. Reddy, "Plasticity. Mathematical Theory and Numerical Analysis," Springer Verlag, Berlin, 1999.
8. R. Hill, "The Mathematical Theory of Plasticity," Clarendon Press, Oxford, 1950.
9. L. M. Kachanov, "Fundamentals of the Theory of Plasticity," Dover, 2004.
10. J. Lubliner, "Plasticity Theory," Macmillan Publishing Company, New York, 1990.
11. S. Luckhaus and L. Modica, The Gibbs-Thompson relation tuithin the gradient theory of phase transitions, Arch. Ration. Mech. Anal., 107 (1989), 71-83.
12. J. B. Martin, "Plasticity, Fundamentals and General Results," MIT Press, Cambridge, 1975.
13. N. G. Meyers and J. Serrin, H=W, Proc. Nat. Acad. Sci. U.S.A., 51 (1964), 1055-1056.
14. A. Mielke, Evolution of rate-independent systems, in "Evolutionary Equations. Vol. II.", (eds. C.M. Dafermos and E. Feireisl), Handbook of Differential Equations, 461-559, Elsevier/ North-Holland, Amsterdam, 2005.
15. A. Mieike and M. Ortiz, A class of minimum prtnetples for characterizzng the trajectories and the relaxation of dissipative systems, ESAIM Control Optim. CaIc. Var., to appear.
16. A. Mielke, T. Roubícek and U. Stefanelli, I-limits and relaxations for rate-independent evolutionary problems, Calc. Var. Partial Differential Equations, 31 (2008), 387-416.
17. Yu. G. Reshetnyak, Weak convergence of completely additive vector functions on a set, Siberian Math. J., 9 (1968), 1039-1045.
18. R. T. Rockafellar, "Convex Analysis," Princeton University Press, Princeton, 1970.
19. R. Temam, "Mathematical Problems in Plasticity," Gauthier-Villars, Paris, 1985. Translation of "Problèmes mathématiques en plasticité," Gauthier-Villars, Paris, 1983.