2D Model Material

  • Oliver Kastner
Part of the Springer Series in Materials Science book series (SSMATERIALS, volume 163)


In this chapter we present MD simulations of martensitic phase transformations in 2D Lennard–Jones (L–J) crystals. A binary L–J potential is used to describe a square-to-hexagonal transformation by shear-and-shuffle processes. The model material is capable of the complex thermo-mechanical coupling present in SMA—pseudo-plasticity, pseudo-elasticity and the shape memory effect [1, 2].


Critical Load Ground State Energy Shape Memory Effect Transformation Strain Martensite Variant 
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  1. 1.
    O. Kastner, Molecular dynamics of a 2D model of the shape memory effect. Part II: thermodynamics of a small system. Continuum Mech. Therm. 18(1–2), 63–81 (2006)Google Scholar
  2. 2.
    O. Kastner, G. Eggeler, Molecular dynamics simulations of the shape memory effect in a chain of Lennard-Jones crystals. MMMS 6(1), 78–91 (2010)Google Scholar
  3. 3.
    O. Kastner, Molecular dynamics of a 2D model of the shape memory effect. Part I: model and simulations. Continuum Mech. Therm. 15(5), 487–502 (2003)Google Scholar
  4. 4.
    U. Pinsook, G.J. Ackland, Simulation of martensitic microstructural evolution in zirconium. Phys. Rev. B 58(17), 11252 (1998)Google Scholar
  5. 5.
    U. Pinsook, G.J. Ackland, Atomistic simulation of shear in a martensitic twinned microstructure. Phys. Rev. B 62(9), 5427–5434 (2000)Google Scholar
  6. 6.
    T. Suzuki, M. Shimono, A simple model for martensitic transformations. J. Phy. IV France 112, 129–132 (2003)CrossRefGoogle Scholar
  7. 7.
    X.D. Ding, T. Suzuki, X.B. Ren, J. Sun, K. Otsuka, Precursors to stress-induced martensitic transformations and associated superelasticity: molecular dynamics simulations and an analytical theory. Phys. Rev. B 74, 104–111 (2006)Google Scholar
  8. 8.
    F.E. Hildebrand, R. Abeyaratne, An atomistic investigation of the kinetics of detwinning. J. Mech. Phys. Solids 56(4), 1296–1319 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    R.S. Elliott, J.A. Shaw, N. Triantafyllidis, Stability of thermally-induced martensitic transformations in bi-atomic crystals. J. Mech. Phys. Solids 50, 2463–2493 (2002)MathSciNetADSzbMATHCrossRefGoogle Scholar
  10. 10.
    M. Born, K. Huang, Dynamical Theory of Crystal Lattices. International Series of Monographs on Physics (Oxford University Press, New York, 1954)Google Scholar
  11. 11.
    D.C. Swift, G.J. Ackland, A. Hauer, G.A. Kyrala, First principles equations of state for simulations of shock waves. Phys. Rev. B 64, 214107 (2001)ADSCrossRefGoogle Scholar
  12. 12.
    J. Solyom, Fundamentals of the Physics of Solids, Volume 1: Structure and Dynamics (Springer, Berlin, 2007)Google Scholar
  13. 13.
    E.A. Mastny, J.J. de Pablo, Melting line of the Lennard-Jones system. J. Chem. Phys. 127, 104504 (2007)Google Scholar
  14. 14.
    I. Müller, P. Villaggio, A model for an elastic-plastic body. Arch. Rational. Mech. Anal. 65(1), 25–46 (1977)MathSciNetADSzbMATHCrossRefGoogle Scholar
  15. 15.
    G. Puglisi, L. Truskinovsky, Mechanics of a discrete chain with bi-stable elements. J. Mech. Phys. Solids 48(1), 1–27 (January 2000)MathSciNetADSzbMATHCrossRefGoogle Scholar
  16. 16.
    I. Müller, A model for a body with shape-memory. Arch. Ration. Mech. An. 70, 61–77 (1979)zbMATHCrossRefGoogle Scholar
  17. 17.
    R. Abeyaratne, J. Knowles, A continuum model of a thermoelastic solid capable of undergoing phase transitions. J. Mech. Phys. Solids 41, 541–571 (1993)MathSciNetADSzbMATHCrossRefGoogle Scholar
  18. 18.
    A. Vainchtein, T. Healey, P. Rosakis, L. Truskinovsky, The role of the spinodal region in one-dimensional martensitic phase transitions. Phys. D 115(1–2), 29–48 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    I. Müller, S. Seelecke, Thermodynamic aspects of shape memory alloys. Math. Comput. Model. 34, 1307–1355 (2001)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Oliver Kastner
    • 1
  1. 1.Faculty of Mechanical Engineering, Institute for MaterialsRuhr University BochumBochumGermany

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