Stored energy functions for phase transitions in crystals

Johannes Zimmer

doi:10.1007/s00205-003-0286-1

Stored energy functions for phase transitions in crystals

Johannes Zimmer

Department of Mathematical Sciences

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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 language	English
Pages (from-to)	191-212
Number of pages	22
Journal	Archive for Rational Mechanics and Analysis
Volume	172
Issue number	2
Early online date	11 Feb 2004
DOIs	https://doi.org/10.1007/s00205-003-0286-1
Publication status	Published - May 2004

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ID number: ISI:000220995400002

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10.1007/s00205-003-0286-1

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This is the pre-peer reviewed version of the following article: Zimmer, J. (2004). Stored energy functions for phase transitions in crystals. Archive for Rational Mechanics and Analysis, 172(2), 191-212. 10.1007/s00205-003-0286-1, which has been published in final form at http://dx.doi.org/10.1007/s00205-003-0286-1. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving."
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Cite this

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AB - 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.

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Stored energy functions for phase transitions in crystals

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