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

References

[1] H. D. Alber and K. Chelminski, Quasistatic problems in viscoplasticity theory, preprint (2002). Search in Google Scholar

[2] V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff, Leyden, 1976. 10.1007/978-94-010-1537-0Search in Google Scholar

[3] S. Bartels and T. Roubíček, Thermoviscoplasticity at small strains, ZAMM Z. Angew. Math. Mech. 88 (2008), 735–754. 10.1002/zamm.200800042Search in Google Scholar

[4] S. Boettcher, Modelling, analysis and simulation of thermo-elasto-plasticity with phase transitions in steel, Ph.D. thesis, Universität Bremen, 2012. Search in Google Scholar

[5] S. Boettcher, Über eine mathematische Aufgabe zum Materialverhalten von Stahl mit Phasenumwandlungen und Umwandlungsplastizität, ZeTeM Reports, Universität Bremen, 2012. Search in Google Scholar

[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. 10.1002/zamm.201300287Search in Google Scholar

[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. Search in Google Scholar

[8] E. Bonetti and G. Bonfanti, Asymptotic analysis for vanishing acceleration in a thermoviscoelastic system, Abstr. Appl. Anal. 2 (2005), 150–202. 10.1155/AAA.2005.105Search in Google Scholar

[9] H. Brézis, Operateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, Math. Stud. 5, North-Holland, Amsterdam, 1973. Search in Google Scholar

[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. Search in Google Scholar

[11] K. Chelminski and R. Racke, Mathematical analysis of thermoplasticity with linear kinematic Hardening, J. Appl. Anal. 12 (2006), 37–57. 10.1515/JAA.2006.37Search in Google Scholar

[12] G. Duvant and J. L. Lions, Inequalities in Mechanics and Physics, Grundlehren Math. Wiss. 219, Springer, Berlin, 1976. 10.1007/978-3-642-66165-5Search in Google Scholar

[13] A. Fasano and M. Primicerio, An analysis of phase transition models, European J. Appl. Math. 7 (1996), 439–451. 10.1017/S0956792500002485Search in Google Scholar

[14] D. Hömberg, A mathematical model for the phase transitions in eutectoid carbon steel, IMA J. Appl. Math. 54 (1995), 31–57. 10.1093/imamat/54.1.31Search in Google Scholar

[15] D. Hömberg, Irreversible phase transitions in steel, Math. Methods Appl. Sci. 20 (1997), 59–77. 10.1002/(SICI)1099-1476(19970110)20:1<59::AID-MMA849>3.0.CO;2-ZSearch in Google Scholar

[16] D. Hömberg and A. Khludnev, A thermoelastic contact problem with a phase transition, IMA J. Appl. Math. 71 (2006), 479–495. 10.1093/imamat/hxl003Search in Google Scholar

[17] I. Hüßler, Mathematische Untersuchungen eines gekoppelten Systems von ODE und PDE zur Modellierung von Phasenumwandlungen im Stahl, Diploma Thesis, Universität Bremen, 2007. Search in Google Scholar

[18] P. Kaminski, Nonlinear problems in inelastic deformation theory, ZAMM Z. Angew. Math. Mech. 88 (2008), 267–282. 10.1002/zamm.200700120Search in Google Scholar

[19] D. Kern, Analysis and numerics for a thermomechanical phase transition model in steel Ph.D. thesis, TU Berlin, 2011. Search in Google Scholar

[20] J. L. Lions and E. Magenes, Non–Homogenous Boundary Value Problems and Applications 1, Grundlehren Math. Wiss. 183, Springer, Berlin, 1973. 10.1007/978-3-642-65393-3Search in Google Scholar

[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. 10.1016/j.ijplas.2012.05.009Search in Google Scholar

[22] L. Panizzi, On a mathematical model for case hardening of steel Ph.D. thesis, TU Berlin/Scuola Normale Superiore di Pisa, 2010. Search in Google Scholar

[23] R. E. Showalter, Monotone Operators in Banach Spaces and Nonlinear Partial Differential Equations, Math. Surveys Monogr. 49, American Mathematical Society, Providence, 1997. Search in Google Scholar

[24] J. Wloka, Partial Differential Equations, Cambridge University Press, Cambridge, 1987. 10.1017/CBO9781139171755Search in Google Scholar

[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. Search in Google Scholar

[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. 10.1016/j.commatsci.2007.07.040Search in Google Scholar

[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. 10.1016/j.ijplas.2007.07.005Search in Google Scholar

[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. 10.1002/nme.3154Search in Google Scholar

[29] E. Zeidler, Linear Monotone Operators, Nonlinear Functional Analysis and its Applications II/A, Springer, New York, 1990. 10.1007/978-1-4612-0981-2Search in Google Scholar