Finite element analysis of microstructure for the cubic to tetragonal transformation

B. O. Li, Mitchell Luskin

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


Martensitic crystals which can undergo a cubic to tetragonal phase transformation have a nonconvex energy density with three symmetry-related, rotationally invariant energy wells. We give estimates for the numerical approximation of a first-order laminate for such martensitic crystals. We give bounds for the L2 convergence of directional derivatives in the "twin" plane, for the L2 convergence of the deformation, for the weak convergence of the deformation gradient, for the convergence of the microstructure, and for the convergence of nonlinear integrals of the deformation gradient.

Original languageEnglish (US)
Pages (from-to)376-392
Number of pages17
JournalSIAM Journal on Numerical Analysis
Issue number1
StatePublished - 1998


  • Error estimate
  • Finite element
  • Martensitic transformation
  • Microstructure
  • Nonconvex variational problem


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