The Γ-convergence of a sharp interface thin film model with nonconvex elastic energy

Pavel Bělík, Mitchell Luskin

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We give results for the Γ-limit of a scaled elastic energy of a film as the thickness h > 0 converges to zero. The elastic energy density models materials with multiple phases or variants and is thus nonconvex. The model includes an interfacial energy that allows sharp interfaces between the phases and variants and is proportional to the total variation of the deformation gradient.

Original languageEnglish (US)
Pages (from-to)414-433
Number of pages20
JournalSIAM Journal on Mathematical Analysis
Volume38
Issue number2
DOIs
StatePublished - 2006

Keywords

  • Bounded variation
  • Martensite
  • Surface energy
  • Thin film
  • Γ-convergence

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