Phase-field modeling of solidification: Formulation Equilibrium profile and parameters Allen-Cahn evolution equation. Sharp-interface modeling of solidification: Interfacial structure, Energy and entropy (im)balances Stefan equation Generalized Gibbs-Thomson equation, stability of a solidification front. Thermomechanical modeling of the solid-solid phase transformation in 3D: Mechanical, energy and entropy (im)balances in the presence of a surface of discontinuity Entropy production at the interphase kinetic relation. Review of classical thermodynamics: First and second laws, thermodynamic potentials Minimum principles First order phase transition. Mechanical modeling of the solid-solid phase transformation in 1D: Mechanics of bars and stability of equilibria The Ericksen's bar Phase boundary motion and dissipation Driving force and kinetic relation Resulting macroscopic stress-strain response. We address existing models for the evolution of the microstructure in phase transitions problems. Furthermore, phase transition between phases and was found at a pressure and temperature of 0.35 GPa and 400 K, respectively. The switching observed at the macroscale results from the nucelation and growth of domains of polarization. At the macroscale, this transformation is responsible for two exotic behaviors, namely, pseudoelasticity and shape memory effect.įerroelectric switching, whereby the spontaneous electric polarization of ferroelectric materials is reversed by the application of an electric field. Shape memory alloys are materials whose crystallographic-structure changes under mechanical or thermal loading. Solid-solid phase transitions, a prominent example of which is the martensitic transformation in shape memory alloys. We aim at understanding how the solidification front propagates, how it its subject to instabilities (e.g., formation snowflakes). Solidification, where the solid phase of a material grows at the expense of its liquid phase through the propagation of the solid/liquid interface. Phase transitions are observed whenever the potential energy density of a system is a non-convex function of one of its state variables.
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