Stored energy functions for phase transitions in crystals

Reference:

Zimmer, J., 2004. Stored energy functions for phase transitions in crystals. Archive for Rational Mechanics and Analysis, 172 (2), pp. 191-212.

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Official URL:

http://dx.doi.org/10.1007/s00205-003-0286-1

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.

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