Free Access
Issue
ESAIM: M2AN
Volume 32, Number 2, 1998
Page(s) 177 - 209
DOI https://doi.org/10.1051/m2an/1998320201771
Published online 27 January 2017
  1. P. J. ARMSTRONG and C. O. FREDERICK, 1966, A mathematical representation of the multiaxial Bauschinger effect, C.E.G.B., Report RD/B/N 731.
  2. A. F. BOWER, 1989, Cyclic hardening properties of hard-drawn copper and rail steel, J. Mech. Phys. Solids, 37, pp. 455-470.
  3. H. BRÉZIS, 1972, Problèmes unilatéraux, J. Math. Pures et Appl., 51, pp. 1-168. [MR: 428137] [Zbl: 0237.35001]
  4. M. BROKATE, K. DRESSLER, and P. KREJČÍ, 1996, On the Mróz model, Eur. J. Appl. Math., 7, pp. 473-497. [MR: 1419644] [Zbl: 0857.73028]
  5. M. BROKATE, K. DRESSLER and P. KREJČÍ, 1996, Rainflow counting and energy dissipation for hysteresis models in elastoplasticity, Eur. J. Mech. A/Solds, 15, pp. 705-737. [MR: 1412202] [Zbl: 0863.73022]
  6. M. BROKATE and J. SPREKELS, 1996, Hysteresis and phase transitions, Springer, New York. [MR: 1411908] [Zbl: 0951.74002]
  7. J.-L. CHABOCHE, 1989, Constitutive equations for cyclic plasticity and cyclic viscoplasticity, Int. J. Plasticity, 5, pp. 247-302. [Zbl: 0695.73001]
  8. J.-L. CHABOCHE, 1991, On some modifications of kinematic hardening to improve the description of ratchetting effects, Int. J. Plasticity, 7, pp. 661-678.
  9. J.-.L. CHABOCHE, 1994, Modeling of ratchetting: evaluation of various approaches, Eur. J. Mech., A/Solids, 13, pp. 501-518.
  10. C. C. CHU, 1984, A three dimensional model of anisotropic hardening in metals and its application to the analysis of sheet metal formability, J. Mech. Phys. Solids, 32, pp. 197-212.
  11. C. C. CHU, 1987, The analysis of multiaxial cyclic problems with an anisotropic hardening model, Int. J. Solids Structures, 23, pp. 567-579.
  12. G. DUVAUT and J. L. LIONS, 1976, Inequalities in mechanics and physics, Springer-Verlag, Berlin. French edition Dunod, Paris 1972. [MR: 521262] [Zbl: 0331.35002]
  13. K. GRÖGER, 1979, Initial value problems for elastoplastic and elasto-viscoplastic systems, in : Nonlinear Analysis, Function Spaces and Applications, eds. S. Fuclc and A Kufner, Teubner, Leipzig, pp. 95-127. [EuDML: 220893] [MR: 578911] [Zbl: 0442.73037]
  14. B. HALPHEN and Q. S. NGUYEN, 1975, Sur les matériaux standard généralises, J. de Mécanique, 14, pp. 39-63. [MR: 416177] [Zbl: 0308.73017]
  15. B. HALPHEN, 1976, L'accomodation des structures élastoplastiques à écrouissage cinématique, C. R. Acad. Sc. Paris, 283, pp. 799-802. [MR: 436712] [Zbl: 0357.73035]
  16. Y. JIANG and H. SEHITOGLU, 1994, Cyclic ratchetting of 1070 steel under multiaxial stress states, Int. J. Plasticity, 10, pp. 579-608. [MR: 1336972]
  17. Y. JIANG and H. SEHITOGLU, 1994, Multiaxial cyclic ratchetting under multiple step loading, Int. J. Plasticity, 10, pp. 849-870.
  18. Y. JIANG and H. SEHITOGLU, 1996, Comments on the Mroz multiple surface type plasticity models, Int. J. Solids Structures, to appear. [Zbl: 0900.73153]
  19. C. JOHNSON, 1978, On plasticity with hardening, J. Math. Anal. Appl. 62, pp. 325-336. [MR: 489198] [Zbl: 0373.73049]
  20. M. KAMLAH, M. KORZEŃ and CH. TSAKMAKIS, 1997, Uniaxial ratchetting in rate-independent plasticity laws, Acta Mechanica, 120, pp. 173-198. [MR: 1436472] [Zbl: 0907.73027]
  21. M. A. KRASNOSEL'SKII and A. V. POKROVSKII, 1989, Systems with hysteresis, Springer Verlag, Berlin Russian edition: Nauka, Moscow, 1983. [MR: 742931]
  22. P. KREJČÍ, 1991, Vector hysteresis models, Euro. Jnl of Applied Mathematics, 2, pp. 281-292. [MR: 1123144] [Zbl: 0754.73015]
  23. P. KREJČÍ, 1996, Hysteresis, convexity and dissipation in hyperbolic equations, Gakkotosho, Tokyo. [MR: 2466538] [Zbl: 1187.35003]
  24. J. LEMAITRE and J.-L. CHABOCHE, 1990, Mechanics of solid materials, Cambridge University Press, Cambridge 1990. French édition Dunod, Paris, 1985. [Zbl: 0743.73002]
  25. J.-L. LIONS, 1969, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris. [MR: 259693] [Zbl: 0189.40603]
  26. G. A. MAUGIN, 1992, The thermomechanics of plasticity and fracture, Cambridge University Press, Cambridge, 1992. [MR: 1173212] [Zbl: 0753.73001]
  27. E. MELAN, 1938, Zur Plastizität des räumlichen Kontinuums, Ingenieur-Archiv, 9, 116-126. [Zbl: 64.0840.01] [JFM: 64.0840.01]
  28. J. C. MOOSBRUGGER and D. L. McDOWELL, 1989, On a class of kinematic hardening rules for nonproportional cyclic plasticity, J. Eng. Mat. Techn., 111, pp. 87-98.
  29. Z. MRÓZ, 1967, On the description of anisotropic workhardening, J. Mech. Phys. Solids, 15, pp. 163-175.
  30. J. NEČS and I. HLAVÁČEK, 1981, Mathematical theory of elastic and elastoplastic bodies : An introduction, Elsevier, Amsterdam. [Zbl: 0448.73009]
  31. Q. S. NGUYEN, 1977, On the elastic plastic initial-boundary value problem and its numerical integration, Int. J. Numer. Int. J. Numer. Meth. Engng., 11, pp. 817, 832. [MR: 446041] [Zbl: 0366.73034]
  32. P. D. PANAGIOTOPOULOS, Inequality problems in mechanics and applications, Burkhauser, Basel. [Zbl: 0579.73014]
  33. W. PRAGER, 1949, Recent developments in the mathematical theory of plasticity, J. Appl. Phys., 20, pp. 235-241. [MR: 28760] [Zbl: 0034.26605]
  34. L. PRANDTL, 1928, Ein Gedankenmodell zur kinetischen Theorie der festen Körper, ZAMM, 8, pp. 85-106. [JFM: 54.0847.04]
  35. R. TEMAM, 1985, Mathematical problems in plasticity, Gauthier-Villars, Paris. [MR: 711964]
  36. CH. TSAKMAKIS, 1987, Über inkrementelle Materialgleichungen zur Beschreibung groβer inelastischer Deformationen, Fortschritt-Berichte VDI Reihe 18, Nr. 36, VDI-Verlag, Düsseldorf.
  37. A. VISINTIN, 1987, Rheological models and hysteresis effects, Rend. Sem. Matem. Univ. Padova, 77, pp. 213-243. [EuDML: 108064] [MR: 904623] [Zbl: 0633.73001]
  38. 38] A. VISINTIN, 1994, Differential models of hysteresis, Springer-Verlag, Berlin. [MR: 1329094] [Zbl: 0820.35004]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you