On Rigidity for the Four-Well Problem Arising in the Cubic-to-Trigonal Phase Transformation

Angkana Rüland, Theresa M. Simon

Research output: Contribution to journalArticlepeer-review

Abstract

We classify all exactly stress-free solutions to the cubic-to-trigonal phase transformation within the geometrically linearized theory of elasticity, showing that only simple laminates and crossing-twin structures can occur. In particular, we prove that although this transformation is closely related to the cubic-to-orthorhombic phase transformation, all its solutions are rigid. The argument relies on a combination of the Saint-Venant compatibility conditions together with the underlying nonlinear relations and non-convexity conditions satisfied by the strain components.

Original languageEnglish (US)
Pages (from-to)455-475
Number of pages21
JournalJournal of Elasticity
Volume153
Issue number3
DOIs
StatePublished - Apr 2023
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Materials Science
  • Mechanics of Materials
  • Mechanical Engineering

Keywords

  • Cubic-to-trigonal phase transformation
  • Geometrically linearized theory
  • Rigidity
  • Shape-memory alloy
  • Structure result

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