EXISTENCE OF SOLITARY WAVES IN MARTENSITIC ALLOYS

Starting from a discrete lattice model, we investigate the dynamics of nonlinear waves that are supposed to represent domain walls. We consider an atomic chain, of which each particle represents a crystal plane. Motion is allowed in the longitudinal direction as well as in the transverse one, since transverse deformation are large; this modelling can account for the change in volume. The nonlinear equations of motion yield solitary wave solutions of several types. Kink solutions represent domain walls either between austenite and martensite or between two martensite variants. They move only when an external force is applied and they obey a Rankine-Hugoniot equation. Pulse solutions correspond to a matrix of austenite or martensite containing a moving sheet of the other phase. The presence of longitudinal deformation and its coupling with transverse deformation strongly affects the stability of the various excitations.