Generalized continua and phase-field models : application to crystal plasticity
Résumé
Three continuum field theories are presented that account for the size-dependent behaviour of materials. The micromorphic medium is endowed with microdeformation degrees of freedom that describe the rotation and distortion of a triad of microstructural directions, like crystallographic lattice directions. It is a very general framework that can be specialized to strain gradient plasticity theory dedicated to the modelling of plastic events in metals and alloys. Both frameworks are developed here in the special case of crystal plasticity as a complete example of transition from micro-physical phenomena to continuum macro-modelling. Finally the phase field method is introduced in this landscape as a continuum modelling approach to the motion of phase boundaries and interfaces driven by thermodynamics and mechanics.