Stability of microstructure for tetragonal to monoclinic martensitic transformations

Pavel Bělík, Mitchell Luskin

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

We give an analysis of the stability and uniqueness of the simply laminated microstructure for all three tetragonal to monoclinic martensitic transformations. The energy density for tetragonal to monoclinic transformations has four rotationally invariant wells since the transformation has four variants. One of these tetragonal to monoclinic martensitic transformations corresponds to the shearing of the rectangular side, one corresponds to the shearing of the square base, and one corresponds to the shearing of the plane orthogonal to a diagonal in the square base. We show that the simply laminated microstructure is stable except for a class of special material parameters. In each case that the microstructure is stable, we derive error estimates for the finite element approximation.

Original languageEnglish (US)
Pages (from-to)663-685
Number of pages23
JournalMathematical Modelling and Numerical Analysis
Volume34
Issue number3
DOIs
StatePublished - 2000

Keywords

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

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