Numerical Simulation of Phase Transformations in Shape Memory Alloy Thin Films

  • Debiprosad Roy Mahapatra
  • Roderick V. N. Melnik
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3992)


A unified variational framework and finite element simulations of phase transformation dynamics in shape memory alloy thin films are reported in this paper. The computational model is based on an approach which combines the lattice based kinetics involving the order variables and non-equilibrium thermodynamics. Algorithmic and computational issues are discussed. Numerical results on phase nucleation under mechanical loading are reported.


Shape Memory Alloy Order Variable Free Energy Density Martensitic Variant Variational Framework 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Ball, J.M., Carstensen, C.: Compatibility conditions for microstructures and the austenite-martensite transition. Mater. Sci. and Eng. A 273, 231–236 (1999)CrossRefGoogle Scholar
  2. 2.
    Bhattacharya, K.: Microstructure of Martensite. Oxford University Press, Oxford (2003)MATHGoogle Scholar
  3. 3.
    Belik, P., Luskin, M.: Computational modeling of softening in a structural phase transformation. Multiscale Model. Simul. 3(4), 764–781 (2005)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Abeyaratne, R., Chu, C., James, R.D.: Kinetics of materials with wiggly energies: The evolution of twinning microstructure in a Cu-Al-Ni shape memory alloys. Phil. Mag. 73A, 457–496 (1996)Google Scholar
  5. 5.
    Artemev, A., Wang, Y., Khachaturyan, A.G.: Three-dimensional phase field model and simulation of martensitic transformation in multilayer systems under applied stresses. Acta Mater. 48, 2503–2518 (2000)CrossRefGoogle Scholar
  6. 6.
    Ichitsubo, T., Tanaka, K., Koiwa, M., Yamazaki, Y.: Kinetics of cubic to tetragonal transformation under external field by the time-dependent Ginzburg-Landau approach. Phy. Rev. B 62, 5435 (2000)CrossRefGoogle Scholar
  7. 7.
    Auricchio, F., Petrini, L.: A three-dimensional model describing stress-temperature induced solid phase transformations: solution algorithm and boundary value problems. Int. J. Numer. Meth. Engng. 61, 807–836 (2004)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Levitas, V.I., Preston, D.L.: Three-dimensional Landau theory for multivariant stress-induced martensitic phase transformations. I. Austenite \(\leftrightarrow\) martensite. Phys. Rev. B 66, 134–206 (2002)Google Scholar
  9. 9.
    Levitas, V.I., Preston, D.L., Lee, D.W.: Three-dimensional Landau theory for multivariant stress-induced martensitic phase transformations. III. Alternative potentials, critical nuclei, kink solutions, and dislocation theory. Phys. Rev. B 68, 134–201 (2003)CrossRefGoogle Scholar
  10. 10.
    Mahapatra, D.R., Melnik, R.V.N.: A dynamic model for phase transformations in 3D samples of shape memory alloys. In: Sunderam, V.S., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds.) ICCS 2005. LNCS, vol. 3516, pp. 25–32. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  11. 11.
    Roy Mahapatra, D., Melnik, R.V.N.: Finite element approach to modelling evolution of 3D shape memory materials, Math. Computers Simul (September 2005) (submitted)Google Scholar
  12. 12.
    Falk, F., Kanopka, P.: Three-dimensional Landau theory describing the martensitic phase transformation of shape-memory alloys. J. Phys.: Condens. Matter 2, 61–77 (1990)CrossRefGoogle Scholar
  13. 13.
    Boyd, J.G., Lagoudas, D.C.: A thermodynamical constitutive constitutive model for shape memory materials. Part I. the monolithic shape memory alloy. Int. J. Plasticity 12(6), 805–842 (1996)MATHCrossRefGoogle Scholar
  14. 14.
    Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Springer, Heidelberg (1997)Google Scholar
  15. 15.
    Boullay, P., Schryvers, D., Ball, J.M.: Nanostructures at martensite macrotwin interfaces in Ni65Al35. Acta Mater. 51, 1421–1436 (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Debiprosad Roy Mahapatra
    • 1
  • Roderick V. N. Melnik
    • 1
  1. 1.Mathematical Modelling and Computational SciencesWilfrid Laurier UniversityWaterlooCanada

Personalised recommendations