106
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

phase transition and hysteresis analysis for shape memory alloys applications

Pages 300-309 | Received 28 Sep 2001, Published online: 14 Oct 2010

References

  • Auchenbach , M. and Muller , I. 1985 . Simulation of material behaviour of alloys with shape memory . Archives of Mechanics , 35 : 537 – 585 .
  • Bekker , A. and Brinson , L.C. 1997 . Temperature‐induced phase transformation in a shape memory alloy: phase diagram based kinetics approach . J. Mech. Phys. Solids , 45 (6) : 949 – 988 .
  • Bruno , A.D. 1998 . Normal forms . Mathematics and Computer in Simulation , 45 : 413 – 427 .
  • Carr , J. 1981 . Applications of Center Manifold Theory , N.Y. : Springer‐Verlag .
  • Chow , S.‐N. , Liu , W. and Yi , Y. 2000 . Center manifold for invariant sets . J. of Differential Equations , 168 : 355 – 385 .
  • Golden , J.M. 2001 . Consequences of non‐uniqueness in the free energy of materials with memory . Int.J.of Eng. Science , 39 : 53 – 70 .
  • Govindjee , S. and Hall , G.J. 2000 . A computational model for shape memory alloys . Int.J.of Solids and Structures , 37 : 735 – 760 .
  • Hoffmann , K.‐H. and Zou , J. 1995 . Finite element approximations of Landau‐Ginzburg's equation model for structural phase transitions in shape memory alloys . M2 AN , 29 : 629 – 655 .
  • Hsu , L. , Min , L.J. and Favretto , L. 2001 . A recursive approach to compute normal forms . Journal of Sound and Vibration , 243 (5) : 909 – 927 .
  • Krejci , P. , Sprekels , J. and Zhang , S.M. 2001 . Asymptotic behaviour for a phase‐field system with hysteresis . J. of Differential Equations , 175 : 88 – 107 .
  • Lagoudas , D.C. 1997 . Modeling of the thermomechanical response of active laminates with SMA strips using the layerwise finite element method . J.of Intell. Mater. Syst. and Struct. , 8 : 476 – 488 .
  • Mane , R. 1977 . Persistent manifolds are normally hyperbolic . Trans. Amer. Math. Soc. , 246 : 261 – 283 .
  • Melnik , R.V.N. , Roberts , A.J. and Thomas , K.A. 1999 . Modelling dynamics of shape‐memory‐alloys via computer algebra . Proceedings of SPIE . 1999 . Vol. 3667 , pp. 290 – 301 .
  • Melnik , R.V.N. , Roberts , A.J. and Thomas , K.A. 2000 . Computing dynamics of copper‐based SMA via center manifold reduction of 3D models . Computational Materials Science , 18 : 255 – 268 .
  • Niezgodka , M. and Sprekels , J. 1991 . Convergent numerical approximations of the thermomechanical phase transitions in SMA . Numer. Math. , 58 : 759 – 778 .
  • Patoor , E. 2000 . Stress‐induced martensitic transformation in polycrystalline alloys . ZAMM, Suppl , 2 ( 80 ) : 443 – 444 .
  • Pliss , V.A. and Sell , G.R. 1998 . Approximation dynamics and the stability of invariant sets . J. of Differential Equations , 149 : 1 – 51 .
  • Pliss , V.A. and Sell , G.R. 2001 . Perturbations of normally hyperbolic manifolds with applications to the Navier‐Stokes equations . J. of Differential Equations , 169 : 396 – 492 .
  • Roberts , A.J. 1997 . Low‐dimensional modelling of dynamics via computer algebra . Computer Physics Communications , 100 : 215 – 230 .
  • Roberts , A.J. 2000 . Computer algebra derives initial conditions for low‐dimensional dynamical models . Comp. Phys. Commun. , 126 : 187 – 206 .
  • Sprekels , J. 1990 . Shape memory alloys: mathematical models for a class of first order solid‐solid phase transitions in metals . Control and Cybernetics , 19 : 287 – 308 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.