Hysteresis in the shape memory alloys


  • Stefania Donescu
  • Ligia Munteanu
  • Iulian Girip


hysteresis operator, shape memory alloys, exponential evolution law, feedforward control


This paper discusses the hysteretic behaviour of a shape memory strip under uniaxial tension. The generalized play hysteresis operator is coupled with the exponential evolution law of 1D constitutive model of the shape memory material. The model considers two phase transformations: conversion of austenite into single-variant martensite and conversion of single-variant martensite into austenite. This paper also discusses the modeling and feedforward control for the strip hysteresis for some unstable cases. For these cases, the generalized play operator is analyzed in connection with the feedforward control. Results show that hysteresis can be reduced to less than 20% when applying the feedforward control.


KRANOSELSKII, M.A., POKROVSKII, A.V., Systems with Hysteresis, Springer, Berlin, 1989 (in Russian, Nauka, Moscow, 1983).

BROKATE, M., SPREKELS, J., Hysteresis and Phase Transitions, Springer, Berlin, 1996.

KRE?Í, P., Convexity, Hysteresis and Dissipation in Hyperbolic Equations, Gakkotosho, Tokyo, 1997.

VISINTIN, A., Differential Models of Hysteresis, Springer-Verlag, Berlin, 1995.

VISINTIN, A., Quasi-linear hyperbolic equations with hysteresis, Ann. Inst. H. Poincaré (C) Nonlinear Analysis, 19, 4, pp. 451-476, 2002.

VISINTIN, A., Hysteresis and semigroups, in: Models of Hysteresis (ed. A. Visintin), Longman, Harlow, pp. 192-206, 1993.

BERTOTTI, G., MAYERGOYZ, I. (eds.), The Science of Hysteresis, Elsevier, Amsterdam, 2006.

MAYERGOYZ, I.D., Mathematical Models of Hysteresis and Their Applications, Elsevier, Amsterdam, 2003.

BERTOTTI, G., Hysteresis in Magnetism, Academic Press, Boston, 1998.

PENROD, L., TALLEY, D., FROYD, J., CASO, R., LAGOUDAS, D., KOHUTEK, T., Integrating smart materials into a firt-year engineering curriculum: A case study, 32nd ASEE/IEEE Frontiers in Education Conference, Session Fb3, pp. 1-26, Boston, MA, November 6-9, 2002.

OTSUKA, K., REN, X., Recent developments in the research of shape memory alloys, Intermetallics, 7, pp. 511-528, 1999.

MIHAILESCU, M., CHIROIU, V., Advanced mechanics on shells and intelligent structures, Editura Academiei, Bucharest, 2004.

KUCZMA, M.S., MIELKE, A., STEIN, E., Modelling of hysteresis in two-phase systems, PolishJapanese Workshop Testing and Modelling the behaviour of shape memory alloys within the 32nd Solid Mechanics Conference, Zakopane, Poland, September 1-5, 1998.

IONESCU, M.F., MUNTEANU, L., CHIROIU, V., On the KdV equation with hysteresis, World Journal of Mechanics (WJM), Scientific Research Publishing, Inc. USA, 1, 1, pp. 1-5, 2011.

VISINTIN, A., Homogenization of some models of hysteresis, Physica B, 403, pp. 245-249, 2008.

VISINTIN, A., Mathematical models of hysteresis (Chap. 1), in: The Science of Hysteresis (eds. G. Bertotti, I. Mayergoyz), Elsevier, 2006, pp. 1-123.

KOPFOVÁ, J., Nonlinear semigroup methods in problems with hysteresis, Discrete and Continuous Dynamical Systems (Supplement), pp. 580-589, 2007.

TRUESDELL, C., NOLL, W., The nonlinear field theories of mechanics, Springer-Verlag, Berlin, 1992.

LUBLINER, J., TAYLOR, R.L., AURICCHIO, F., A new model of generalized plasticity and its numerical implementation, Int. J. of Solids and Structures, 30, 22, pp. 3171-3184, 1993.



Most read articles by the same author(s)

1 2 3 > >>