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Hysteresis operators

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Phase Transitions and Hysteresis

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References

  1. Brokate, M.: Optimale Steuerung von gewöhnlichen Differentialgleichungen mit Nichtlinearitäten vom Hysteresis-Typ, Lang 1987. In German; English translation in: Automation and Remote Control 52 (1991), 1639–1681, and 53 (1992), 1–33.

    Google Scholar 

  2. Brokate, M.: Some BV properties of the Preisach hysteresis operator, Applicable Analysis 32 (1989), 229–252.

    Article  MathSciNet  MATH  Google Scholar 

  3. Brokate, M., Visintin, A.: Properties of the Preisach model for hysteresis, J. Reine Angew. Math. 402 (1989), 1–40.

    MathSciNet  MATH  Google Scholar 

  4. Brokate, M.: On a characterization of the Preisach model for hysteresis, Rend. Sem. Mat. Padova 83 (1990), 153–163.

    MathSciNet  MATH  Google Scholar 

  5. Brokate, M.: On the moving Preisach model, Math. Methods Appl. Sci. 15 (1992), 145–157.

    Article  MathSciNet  MATH  Google Scholar 

  6. Brokate, M., Dreßler, K., Krejčí, P.: On the Mróz model, submitted.

    Google Scholar 

  7. Chu, C.C.: A three-dimensional model of anisotropic hardening in metals and its application to the analysis of sheet metal formability, J. Mech. Phys. Solids 32 (1984), 197–212.

    Article  Google Scholar 

  8. Chu, C.C.: The analysis of multiaxial cyclic problems with an anisotropic hardening model, Int. J. Solids Structures 23 (1987), 567–579.

    Google Scholar 

  9. Clormann, U.H., Seeger, T.: RAINFLOW-HCM: Ein Zählverfahren für Betriebsfestigkeitsnachweise auf werkstoffmechanischer Grundlage, Stahlbau 55 (1986), 65–71. (in German).

    Google Scholar 

  10. Damlamian, A., Visintin, A.: Une généralization vectorielle du modèle de Preisach pour l’hystérésis, C. R. Acad. Sci. Paris, Série I, 297 (1983), 437–440.

    MathSciNet  MATH  Google Scholar 

  11. Della Torre, E.: Effect of interaction on the magnetization of single domain particles, IEEE Trans. Audio Electroacoustics AU 14 (1966), 86–93.

    Article  Google Scholar 

  12. Dreßler, K., Krüger, W.: The optimal stochastic reconstruction of loading histories from a rainflow matrix, submitted.

    Google Scholar 

  13. Everett, D.H.: A general approach to hysteresis. Part 1 (with Whitton, W.I.); Part 2: Development of the domain theory (with Smith, F.W.); Part 3: A formal treatment of the independent domain model of hysteresis; Part 4: An alternative formulation of the domain model, Trans. Faraday Soc. 48 (1952), 749–757; 50 (1954), 187–197; 50 (1954), 1077–1096; 51 (1955), 1551–1557.

    Article  Google Scholar 

  14. Fuchs, H.O., Stephens, R.I.: Metal fatigue in engineering, Wiley 1980.

    Google Scholar 

  15. Hilpert, M.: On uniqueness for evolution problems with hysteresis, in: Mathematical models for phase change problems (ed. J.F. Rodrigues), Birkhäuser 1989, 377–388.

    Google Scholar 

  16. Ishlinskii, A.Yu.: Some applications of statistical methods to describing deformations of bodies, Izv. AN SSSR, Techn.Ser., no. 9(1944), 580–590. (In Russian.)

    Google Scholar 

  17. Krasnosel’skii, M.A., Pokrovskii, A.V.: Systems with hysteresis, Springer 1989. Russian edition: Nauka 1983.

    Google Scholar 

  18. Krejčí, P.: Hysteresis and periodic solutions to semilinear and quasilinear wave equations, Math. Z. 193 (1986), 247–264.

    Article  MathSciNet  MATH  Google Scholar 

  19. Krejčí, P.: Existence and large time behaviour of solutions to equations with hysteresis, Preprint no. 21, Institute of Math., Czechoslovakian Academy of Science, 1986.

    Google Scholar 

  20. Krejčí, P.: A monotonicity method for solving hyperbolic problems with hysteresis, Apl. Mat 33 (1988), 197–203.

    MathSciNet  MATH  Google Scholar 

  21. Krejčí, P.: On Maxwell equations with the Preisach hysteresis operator: The one-dimensional time-periodic case, Apl. Mat. 34 (1989), 364–374.

    MathSciNet  MATH  Google Scholar 

  22. Krejčí, P., Lovicar, V.: Continuity of hysteresis operators in Sobolev spaces, Apl. Mat. 35, 60–66.

    Google Scholar 

  23. Krejčí, P.: Hysteresis memory preserving operators, Applications of Math. 36 (1991), 305–326.

    MathSciNet  MATH  Google Scholar 

  24. Krejčí, P.: Vector hysteresis models, European J. Appl. Math. 2 (1991), 281–292.

    Article  MathSciNet  MATH  Google Scholar 

  25. Krejčí, P.: Global behaviour of solutions to the wave equations with hysteresis, submitted.

    Google Scholar 

  26. Krüger, W., Scheutzow, M., Beste, A., Petersen, J.: Markov-und Rainflowrekon-struktion stochastischer Beanspruchungszeitfunktionen, VDI-Report, series 18, no. 22, 1985. (In German.)

    Google Scholar 

  27. Macki, J.W., Nistri, P., Zecca, P.: Mathematical models for hysteresis, SIAM Review 35 (1993), 94–123.

    Article  MathSciNet  MATH  Google Scholar 

  28. Madelung, E.: Über Magnetisierung durch schnellverlaufende Ströme und die Wirkungsweise des Rutherford-Marconischen Magnetdetektors, Ann. Phys. 17 (1905), 861–890. (In German.)

    Article  Google Scholar 

  29. Masing, G.: Eigenspannungen und Verfestigung bei Messing, in: Proc. 2nd Int. Congress of Appl. Mech., 1926, 332–335. (In German.)

    Google Scholar 

  30. Mayergoyz, I.D.: Mathematical models of hysteresis, Springer 1991.

    Google Scholar 

  31. Miner, M.A.: Cumulative damage in fatigue, J. Appl. Mech. 12 (1945), A 159–A 164.

    Google Scholar 

  32. Murakami, Y. (ed.): The rainflow method in fatigue, Butterworth & Heinemann, Oxford 1992.

    Google Scholar 

  33. Mróz, Z.: On the description of anisotropic workhardening, J. Mech. Phys. Solids 15 (1967), 163–175.

    Article  Google Scholar 

  34. Prandtl, L.: Ein Gedankenmodell zur kinetischen Theorie der festen Körper, ZAMM 8 (1928), 85–106. (In German).

    Article  MATH  Google Scholar 

  35. Preisach, F.: Über die magnetische Nachwirkung, Z. Physik 94 (1935), 277–302. (In German.)

    Article  Google Scholar 

  36. Rychlik, I.: A new definition of the rainflow cycle counting method, Int. J. Fatigue 9 (1987), 119–121.

    Article  Google Scholar 

  37. Rychlik, I.: Rainflow cycles in Gaussian loads, Fatigue Fract. Engng. Mater. Struct. 15 (1992), 57–72.

    Article  Google Scholar 

  38. Rychlik, I.: Note on cycle counts in irregular loads, Fatigue Fract. Engng. Mater. Struct. (to appear)

    Google Scholar 

  39. Saunders, P.T.: An introduction to catastrophe theory, Cambridge University Press 1980.

    Google Scholar 

  40. Seidman, T.I.: Switching systems and periodicity, in: Nonlinear semigroups, partial differential equations and attractors, LN Math. 1394 (1989), 199–210.

    Google Scholar 

  41. Seidman, T.I.: Switching systems I, Control Cybernet. 19 (1990), 63–92.

    MathSciNet  MATH  Google Scholar 

  42. Visintin, A.: A model for hysteresis of distributed systems, Ann. Mat. Pura Appl. 131 (1982), 203–231.

    Article  MathSciNet  MATH  Google Scholar 

  43. Visintin, A.: On the Preisach model for hysteresis, Nonlinear Anal. 9 (1984), 977–996.

    Article  MathSciNet  MATH  Google Scholar 

  44. Visintin, A.: Rheological models and hysteresis effects, Rend. Sem. Matem. Univ. Padova 77 (1987), 213–243.

    MathSciNet  MATH  Google Scholar 

  45. Visintin, A.: Mathematical models of hysteresis, in: Topics in nonsmooth mechanics (eds. J.J. Moreau, P.D. Panagiotopoulos, G. Strang), Birkhäuser 1988, 295–326.

    Google Scholar 

  46. Visintin, A.: Differential models of hysteresis, to appear.

    Google Scholar 

  47. Zeeman, E.C.: Catastrophe theory, Scientific American 234 (1976), 65–83. In expanded form in: Catastrophe theory, Addison-Wesley 1977.

    Article  Google Scholar 

  48. Zeidler, E.: Nonlinear functional analysis and its applications, vol. II B, Springer 1990.

    Google Scholar 

  49. Ziegler, H.: An introduction to thermomechanics, 2nd edition, North Holland 1983.

    Google Scholar 

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Brokate, M. (1994). Hysteresis operators. In: Visintin, A. (eds) Phase Transitions and Hysteresis. Lecture Notes in Mathematics, vol 1584. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073394

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  • DOI: https://doi.org/10.1007/BFb0073394

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