Thermomechanical lattice instability and phase field theory of martensitic phase transformations, twinning and dislocations at large strains

Using the second law of thermodynamics, a criterion for the instability of a crystal lattice with respect to a change in order parameters is derived for finite strains and lattice rotations. An explicit relation for lattice rotation is derived. A Gibbs (Landau) potential describing martensitic phase transformations, twinning, and dislocation nucleation is derived for a prescribed nonsymmetric nominal stress tensor and small elastic strain, but finite transformation strain and rotations. The equilibrium and transformation conditions are obtained. Martensitic phase transformations in NiAl, BN and C are analyzed and the importance of finite-strain corrections is demonstrated.