Nonlinear dynamics and stability of microstructures in a lattice model for ferroelastic materials (Q1905572)

The author investigates a two-dimensional lattice model describing nonlinear dynamics of elastic domains and interfaces in ferroelastic materials undergoing a first-order phase transition characterized by a shear deformation. Special attention is devoted to an instability mechanism of a moving strain band that produces localized domains. An asymptotic model for the long term evolution of this nonlinear structure is given. Based on the above, the author then studies the motion of two perpendicular strain bands, taking into account the applied forces and dissipative effects. The results are interpreted as a microtwinning in crystalline alloys. A numerical simulation on the microscopic system is also provided, and the results are interpreted as a coexistence of elliptical ferroelastic domains with homogeneous planar domains along perpendicular directions. Finally, potential extensions of the model are pointed out.