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2003 | 1 | 4 | 670-689

Tytuł artykułu

On quasistatic inelastic models of gradient type with convex composite constitutive equations

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EN

Abstrakty

EN
This article defines and presents the mathematical analysis of a new class of models from the theory of inelastic deformations of metals. This new class, containing so called convex composite models, enlarges the class containing monotone models of gradient type defined in [1]. This paper starts to establish the existence theory for models from this new class; we restrict our investigations to the coercive and linear self-controlling case.

Wydawca

Czasopismo

Rocznik

Tom

1

Numer

4

Strony

670-689

Opis fizyczny

Daty

wydano
2003-12-01
online
2003-12-01

Bibliografia

  • [1] H.-D. Alber: Materials with memory, Lecture Notes in Math., Vol. 1682, Springer, Berlin Heidelberg New York, 1998.
  • [2] H.-D. Alber and K. Chełmiński: “Quasistatic problems in viscoplasticity theory I: Models with linear hardening”, A part of the monograph: I. Gohberg et al.: Operator theoretical methods and applications to mathematical physics. The Erhard Meister memorial volume, Birkhäuser, Basel, in print.
  • [3] G. Anzellotti and S. Luckhaus: “Dynamical evolution of elasto-perfectly plastic bodies”, Appl. Math. Optim., Vol. 15, (1987), pp. 121–140. http://dx.doi.org/10.1007/BF01442650
  • [4] J.P. Aubin and A. Cellina: Differential inclusions. Springer, Berlin Heidelberg New York, 1984.
  • [5] M. Brokate: “Elastoplastic constitutive laws of nonlinear kinematic hardening type”, Technical Report 97-14, Berichtsreihe des Mathematischen Seminars, Kiel, 1997.
  • [6] K. Chełmiński: “Coercive limits for a subclass of monotone constitutive equations in the theory of inelastic material behaviour of metals”, Mat. Stos., Vol. 40, (1997), pp. 41–81.
  • [7] K. Chełmiński: “On self-controlling models in the theory of inelastic material behaviour of metals”, Contin. Mech. Thermodyn., Vol. 10, (1998), pp. 121–133. http://dx.doi.org/10.1007/s001610050085
  • [8] K. Chełmiński: “Global existence of weak-type solutions for models of monotone type in the theory of inelastic deformations”, Math. Meth. Appl. Sci., Vol. 25, (2002), pp. 1195–1230. http://dx.doi.org/10.1002/mma.336
  • [9] K. Chełmiński: “Coercive approximation of viscoplasticity and plasticity”, Asymptotic Analysis, Vol. 26, (2001), pp. 105–133.
  • [10] K. Chełmiński: “On noncoercive models in the theory of inelastic deformations with internal variables”, ZAMM, Vol. 81, Suppl. 3, (2001), pp. 595–596.
  • [11] K. Chełmiński: “On quasistatic models in the theory of inelastic deformations”, Proceedings in Applied Mathematics, Vol. 1, (2002), pp. 401–402. http://dx.doi.org/10.1002/1617-7061(200203)1:1<401::AID-PAMM401>3.0.CO;2-Z
  • [12] K. Chełmiński and P. Gwiazda: “Monotonicity of operators of viscoplastic response: application to the model of Bodner-Partom”, Bull. Polish Acad. Sci.: Tech. Sci., Vol. 47, (1999), pp. 191–208.
  • [13] K. Chełmiński and P. Gwiazda: “Nonhomogeneous initial-boundary value problems for coercive and self-controlling models of monotone type”, Contin. Mech. Thermodyn., Vol. 12, (2000), pp. 217–234. http://dx.doi.org/10.1007/s001610050136
  • [14] K. Chełmiński and Z. Naniewicz: “Coercive limits for constitutive equations of monotone-gradient type”, Nonlinear Anal., Vol. 48, (2002), pp. 1197–1214. http://dx.doi.org/10.1016/S0362-546X(01)00096-7
  • [15] F.H. Clarke: Optimization and nonsmooth analysis, CMR Université de Montréal, Montréal, 1989.
  • [16] S. Guillaume: “Subdifferential evolution inclusion in nonconvex analysis”, Positivity, Vol. 4, (2000), pp. 357–395. http://dx.doi.org/10.1023/A:1009821417484
  • [17] P. Gwiazda: “Non-homogeneous boundary value problem for the Chan-Bodner-Linholm model”, Math. Methods Appl. Sci., Vol. 23:11, (2000), pp. 1011–1022. http://dx.doi.org/10.1002/1099-1476(20000725)23:11<1011::AID-MMA148>3.0.CO;2-#
  • [18] B. Halphen and Nguyen Quoc Son: “Sur les matèriaux standards généralisés”, J. Méc., Vol. 14, (1975), pp. 39–63.
  • [19] P.-M. Suquet: “Evolution problems for a class of dissipative materials”, Quart. Appl. Math., Vol. 38, (1980), pp. 391–414.
  • [20] R. Temam: “A generalized Norton-Hoff model and the Prandtl-Reuss law of plasticity”, Arch. Rational Mech. Anal., Vol. 95, (1986), pp. 137–183. http://dx.doi.org/10.1007/BF00281085

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Bibliografia

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bwmeta1.element.doi-10_2478_BF02475187
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