Nucleation barriers for the cubic-to-tetragonal phase transformation

Hans Knüpfer, Robert V. Kohn, Felix Otto

Research output: Contribution to journalArticlepeer-review


We are interested in the phase transformation from austenite to martensite. This transformation is typically accompanied by the generation and growth of small inclusions of martensite. We consider a model from geometrically linear elasticity with sharp energy penalization for phase boundaries. Focusing on a cubic-to-tetragonal phase transformation, we show that the minimal energy for an inclusion of martensite scales like $\max \{ V^{2/3}, V^{9/11} \}$ in terms of the volume V. Moreover, our arguments illustrate the importance of self-accommodation for achieving the minimal scaling of the energy. The analysis is based on Fourier representation of the elastic energy.

Original languageEnglish (US)
Pages (from-to)867-904
Number of pages38
JournalCommunications on Pure and Applied Mathematics
Issue number6
StatePublished - Jun 2013

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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