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

Krzysztof Chełmiński

Open Mathematics (2003)

  • Volume: 1, Issue: 4, page 670-689
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Krzysztof Chełmiński. "On quasistatic inelastic models of gradient type with convex composite constitutive equations." Open Mathematics 1.4 (2003): 670-689. <http://eudml.org/doc/268798>.

@article{KrzysztofChełmiński2003,
abstract = {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.},
author = {Krzysztof Chełmiński},
journal = {Open Mathematics},
keywords = {35Q72; 73E60; 73F99},
language = {eng},
number = {4},
pages = {670-689},
title = {On quasistatic inelastic models of gradient type with convex composite constitutive equations},
url = {http://eudml.org/doc/268798},
volume = {1},
year = {2003},
}

TY - JOUR
AU - Krzysztof Chełmiński
TI - On quasistatic inelastic models of gradient type with convex composite constitutive equations
JO - Open Mathematics
PY - 2003
VL - 1
IS - 4
SP - 670
EP - 689
AB - 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.
LA - eng
KW - 35Q72; 73E60; 73F99
UR - http://eudml.org/doc/268798
ER -

References

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  1. [1] H.-D. Alber: Materials with memory, Lecture Notes in Math., Vol. 1682, Springer, Berlin Heidelberg New York, 1998. 
  2. [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. [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 Zbl0616.73047
  4. [4] J.P. Aubin and A. Cellina: Differential inclusions. Springer, Berlin Heidelberg New York, 1984. 
  5. [5] M. Brokate: “Elastoplastic constitutive laws of nonlinear kinematic hardening type”, Technical Report 97-14, Berichtsreihe des Mathematischen Seminars, Kiel, 1997. 
  6. [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. Zbl1071.74582
  7. [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 Zbl0911.73023
  8. [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 Zbl1099.74029
  9. [9] K. Chełmiński: “Coercive approximation of viscoplasticity and plasticity”, Asymptotic Analysis, Vol. 26, (2001), pp. 105–133. Zbl1013.74010
  10. [10] K. Chełmiński: “On noncoercive models in the theory of inelastic deformations with internal variables”, ZAMM, Vol. 81, Suppl. 3, (2001), pp. 595–596. Zbl1051.74548
  11. [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 Zbl05296956
  12. [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. Zbl0987.74019
  13. [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 Zbl1003.74033
  14. [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 Zbl1056.35146
  15. [15] F.H. Clarke: Optimization and nonsmooth analysis, CMR Université de Montréal, Montréal, 1989. Zbl0727.90045
  16. [16] S. Guillaume: “Subdifferential evolution inclusion in nonconvex analysis”, Positivity, Vol. 4, (2000), pp. 357–395. http://dx.doi.org/10.1023/A:1009821417484 Zbl0968.35068
  17. [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-# Zbl0976.35090
  18. [18] B. Halphen and Nguyen Quoc Son: “Sur les matèriaux standards généralisés”, J. Méc., Vol. 14, (1975), pp. 39–63. Zbl0308.73017
  19. [19] P.-M. Suquet: “Evolution problems for a class of dissipative materials”, Quart. Appl. Math., Vol. 38, (1980), pp. 391–414. Zbl0501.73030
  20. [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 Zbl0615.73035

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