Multiscale bifurcation and stability of multilattices

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A lattice-level model is developed for active materials, such as shape memory alloys, that undergo martensitic phase transformations. The model is investigated using equilibrium path following and bifurcation techniques. It is shown that a multiscale stability criterion is essential for correctly interpreting the stability of crystal equilibrium configurations under both thermal- and stress-loading conditions. A two-stage temperature-induced phase transformation is predicted from a cubic B2 phase to an orthorhombic Cmmm phase to a final orthorhombic B19 phase. Under stress-loading conditions, martensitic transformations from the B2 austenite phase to a number of possible martensite phases are identified. These include reconstructive transformations to B11, B33, and C2/m structures and proper transformation to a C2/m monoclinic phase which displays characteristic tension-compression asymmetry. The prediction of both temperature-induced and stress-induced proper martensitic transformations indicates the likelihood that the current model will exhibit shape memory behavior.

Original languageEnglish (US)
Pages (from-to)143-157
Number of pages15
JournalJournal of Computer-Aided Materials Design
Issue numberSUPPL. 1
StatePublished - Dec 2007

Bibliographical note

Funding Information:
Acknowledgements The author would like to acknowledge valuable discussions with Professors John A. Shaw and Nicolas Triantafyllidis. This work was supported by: National Science Foundation grant CMS 0409084 (Dr. Ken Chong, Program Director), the University of Minnesota Supercomputing Institute, and by the U.S. Army High Performance Computing Research Center under the auspices of the U.S. Department of the Army, Army Research Laboratory cooperative agreement No. DAAD 191-01-2-0014.


  • Bifurcation
  • Cauchy-Born kinematics
  • Martensitic transformation
  • Multiscale stability
  • Phonon stability
  • Shape memory alloys


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