Ecole d’été régionale franco-roumaine en mathématiques appliquées, Sinaia, 2 - 11 Juillet 2017

Modélisation par champs des phases de la déformations des cristaux

Phase field method is based on the Ginzburg-Landau theory of phase transitions. In this theory, a continuous function, so-called order parameter, has been introduced to describe the equilibrium thermo-dynamical properties of a system that undergoes a phase transition. In this course, we will apply this theory to describe solid-to-solid phase transformations, as observed in martensitic materials, where crystallographic relation between different solid phases has to be taken into account in order to reproduce properly the elastic interactions. Secondly, we will present a theory that goes beyond the classical Landau theory in order to study the coupling between phase transition and plasticity using GL(2,Z) group symmetry.