Modeling and simulation of martensitic phase transitions with a triple point

A framework for modeling complicated 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 (orthoI) and monoclinic phases are stable. After presenting a simple two-dimensional framework to deal with this symmetry breaking, an explicit energy is 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), since the class of functions considered here is strictly larger. Finite Element simulations with the energy constructed here investigate the pattern formation in Zirconia at the triple point.