Stored energy functions for phase transitions in crystals

Johannes Zimmer

Research output: Contribution to journalArticle

14 Citations (Scopus)
146 Downloads (Pure)

Abstract

A method is presented to construct nonconvex free energies that are invariant under a symmetry group. Algebraic and geometric methods are used to determine invariant functions with the right location of minimizers. The methods are illustrated for symmetry-breaking martensitic phase transformations. Computer algebra is used to compute a basis of the corresponding class of invariant functions. Several phase transitions, such as cubic-to-orthorhombic, are discussed. An explicit example of an energy for the cubic-to-tetragonal phase transition is given.
Original languageEnglish
Pages (from-to)191-212
Number of pages22
JournalArchive for Rational Mechanics and Analysis
Volume172
Issue number2
Early online date11 Feb 2004
DOIs
Publication statusPublished - May 2004

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