Wellposedness of kinematic hardening models in elastoplasticity
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 32 (1998) no. 2, p. 177-209
@article{M2AN_1998__32_2_177_0,
     author = {Brokate, Martin and Krej\v c\'\i , Pavel},
     title = {Wellposedness of kinematic hardening models in elastoplasticity},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {Dunod},
     volume = {32},
     number = {2},
     year = {1998},
     pages = {177-209},
     zbl = {0902.73031},
     mrnumber = {1622607},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1998__32_2_177_0}
}
Brokate, Martin; Krejčí, Pavel. Wellposedness of kinematic hardening models in elastoplasticity. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 32 (1998) no. 2, pp. 177-209. http://www.numdam.org/item/M2AN_1998__32_2_177_0/

[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. | 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 pre05376857

[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. | 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. | Numdam | MR 904623 | Zbl 0633.73001

38] A. Visintin, 1994, Differential models of hysteresis, Springer-Verlag, Berlin. | MR 1329094 | Zbl 0820.35004