Stability of microstructures for some martensitic transformations

Y. Efendiev, M. Luskin

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We analyze the stability of laminated microstructure for martensitic crystals that undergo cubic to trigonal, orthorhombic to triclinic, and trigonal to monoclinic transformations. We show that the microstructure is unique and stable for all laminates except when the lattice parameters satisfy certain identities.

Original languageEnglish (US)
Pages (from-to)1289-1305
Number of pages17
JournalMathematical and Computer Modelling
Issue number12-13
StatePublished - Nov 5 2001

Bibliographical note

Funding Information:
We have developed an analysis to determine what quantities remain stable for deformations of low energy that satisfy boundary conditions compatible with a simple laminate \[4,6-9\]. We have used this analysis to study the orthorhombic to monoclinic transformation (two-well) \[6\], the cubic to tetragonal transformation (three-well) \[7\],t he cubic to orthorhombic transformation (six-well) \[8\], and the tetragonal to monoclinic transformation (four-well) \[9\]. The analysis of the stability of microstructures becomes more difficult for transformations with a larger number of variants (or for transformations with a greater change of symmetry) because the existence of the additional energy-minimizing variants gives the crystal more freedom to deform without This work was supported in part by NSF DMS 95-05077, by AFOSR F49620-98-1-0433, by ARO DAAG55-98-1-0335, by the Institute for Mathematics and Its Applications, and by the Minnesota Supercomputer Institute.


  • Error estimate
  • Finite element
  • Martensitic transformation
  • Microstructure
  • Nonconvex variational problem
  • Simple laminate
  • Volume fraction
  • Young measure


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