Kinetics of lattice phase transitions<br/><br/><br/><br/>

Saturday, November 6, 2004 - 3:30pm - 4:00pm
EE/CS 3-180
Understanding the origin of energy dissipation and the associated kinetics of phase boundaries remains an important open problem in modeling lattice phase transitions in martensites. Following the pioneering work of Ericksen [1975], it has become common to model these materials by an up-down-up stress-strain relation in the framework of continuum elasticity theory. The corresponding dynamic problem changes type and is ill-posed; however, it may be regularized by prescribing an additional kinetic relation between the driving force and the velocity of a phase boundary. This relation is usually either postulated or derived from a phenomenological model accounting for dispersive and dissipative effects.

In this talk we will describe how one can avoid introducing additional phenomenological parameters and instead obtain a kinetic relation by replacing the continuum model with its natural discrete analog. We consider a lattice model of martensitic phase transition which takes into account long-range interactions of an arbitrary range. Although the model is Hamiltonian at the microscale, it generates a nontrivial macroscopic kinetic relation. The apparent dissipation is due to the induced radiation of lattice waves carrying energy away from the front.

This is joint work with Lev Truskinovsky (Ecole Polytechnique, France).