Modeling and simulation of martensitic phase transitions with a triple point

P W Dondl, J Zimmer

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A framework for modeling complex global energy landscapes in a piecewise manner is presented. Specifically, a class of strain-dependent energy functions is derived for the triple point of Zirconia (ZrO2), where tetragonal, orthorhombic (orthol) and monoclinic phases are stable. A simple two-dimensional framework is presented to deal with this symmetry breaking. An explicit energy is then fitted to the available elastic moduli of Zirconia in this two-dimensional setting. First, we use the orbit space method to deal with symmetry constraints in an easy way. Second, we introduce a modular (piecewise) approach to reproduce or model elastic moduli, energy barriers and other characteristics independently of each other in a sequence of local steps. This allows for more general results than the classical Landau theory (understood in the sense that the energy is a polynomial of invariant polynomials). The class of functions considered here is strictly larger. Finite-element simulations for the energy constructed here demonstrate the pattern formation in Zirconia at the triple point. (C) 2004 Elsevier Ltd. All rights reserved.
Original languageEnglish
Pages (from-to)2057-2077
Number of pages21
JournalJournal of the Mechanics and Physics of Solids
Issue number9
Early online date20 May 2004
Publication statusPublished - Sept 2004


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