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Existence and uniqueness of a problem in thermo-elasto-plasticity with phase transitions in TRIP steels under mixed boundary conditions

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Języki publikacji
EN
Abstrakty
EN
In this paper a complex model describing thermo-elasto-plasticity, phase transitions (PT) and transformation-induced plasticity (TRIP) is studied. The main objective is the analysis of the corresponding initial and boundary value problem (IBVP) considering linearized thermo-elastic dissipation and a viscosity-like regularization.
Wydawca
Rocznik
Strony
87--98
Opis fizyczny
Bibliogr. 29 poz.
Twórcy
autor
  • Bremen Institute of Mechanical Engineering, University of Bremen, Am Biologischen Garten 2, 28359 Bremen, Germany
Bibliografia
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  • [4] S. Boettcher, Modelling, analysis and simulation of thermo-elasto-plasticity with phase transitions in steel , Ph.D. thesis, Universität Bremen, 2012.
  • [5] S. Boettcher, Über eine mathematische Aufgabe zum Materialverhalten von Stahl mit Phasenumwandlungen und Umwandlungsplastizität , ZeTeM Reports, Universität Bremen, 2012.
  • [6] S. Boettcher, M. Böhm and M. Wolff, Well-posedness of a thermo-elasto-plastic problem with phase transitions in TRIP steels under mixed boundary conditions, ZAMM Z. Angew. Math. Mech. 95 (2015), no. 12, 1461-1476.
  • [7] E. Bonetti and G. Bonfanti, Existence and uniqueness of the solution to a 3D thermoviscoelastic system, Electron. J. Differential Equations 2003 (2003), 1-15.
  • [8] E. Bonetti and G. Bonfanti, Asymptotic analysis for vanishing acceleration in a thermoviscoelastic system, Abstr. Appl. Anal. 2 (2005), 150-202.
  • [9] H. Brézis, Operateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert , Math. Stud. 5, North-Holland, Amsterdam, 1973.
  • [10] K. Chelminski, D. Hömberg and D. Kern, On a thermomechanical model of phase transitions in steel, Adv. Math. Sci. Appl. 18 (2008), 119-140.
  • [11] K. Chelminski and R. Racke, Mathematical analysis of thermoplasticity with linear kinematic Hardening, J. Appl. Anal. 12 (2006), 37-57.
  • [12] G. Duvant and J. L. Lions, Inequalities in Mechanics and Physics , Grundlehren Math. Wiss. 219, Springer, Berlin, 1976.
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  • [17] I. Hüßler, Mathematische Untersuchungen eines gekoppelten Systems von ODE und PDE zur Modellierung von Phasenumwandlungen im Stahl , Diploma Thesis, Universität Bremen, 2007.
  • [18] P. Kaminski, Nonlinear problems in inelastic deformation theory, ZAMM Z. Angew. Math. Mech. 88 (2008), 267-282.
  • [19] D. Kern, Analysis and numerics for a thermomechanical phase transition model in steel Ph.D. thesis, TU Berlin, 2011.
  • [20] J. L. Lions and E. Magenes, Non-Homogenous Boundary Value Problems and Applications 1, Grundlehren Math. Wiss. 183, Springer, Berlin, 1973.
  • [21] R. Mahnken, M. Wolff, A. Schneidt and M. Böhm, Multi-phase transformations at large strains - Thermodynamic framework and simulation, Int. J. Plast. 39 (2012), 1-26.
  • [22] L. Panizzi, On a mathematical model for case hardening of steel Ph.D. thesis, TU Berlin/Scuola Normale Superiore di Pisa, 2010.
  • [23] R. E. Showalter, Monotone Operators in Banach Spaces and Nonlinear Partial Differential Equations , Math. Surveys Monogr. 49, American Mathematical Society, Providence, 1997.
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  • [25] M. Wolff, M. Böhm and S. Boettcher, Phase transformation in steel in the multi-phase case - general modelling and parameter identification , ZeTeM Reports, Universität Bremen, 2007.
  • [26] M. Wolff, M. Böhm, M. Dalgic and I. Hüßler, Evaluation of models for TRIP and stress-dependent transformation behaviour for the martensitic transformation of the steel 100Cr6, Comput. Mat. Sci. 43 (2008), 108-114.
  • [27] M. Wolff, M. Böhm and D. Helm, Material behaviour of steel - Modeling of complex phenomena and thermodynamic consistency, Int. J. Plast. 24 (2008), 746-774.
  • [28] M. Wolff, M. Böhm, R. Mahnken and B. Suhr, Implementation of an algorithm for general material behavior of steel taking interaction of plasticity and transformation-induced plasticity into account, Int. J. Numer. Meth. Engng. 87 (2011), 1183-1206.
  • [29] E. Zeidler, Linear Monotone Operators , Nonlinear Functional Analysis and its Applications II/A, Springer, New York, 1990.
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-5e4afb4e-0391-43ac-9e4c-4197389a42df
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