  A thermodynamically consistent multiphase phase-field approach for stress and
temperature-induced martensitic phase transformation at the nanoscale and under
large strains is developed. A total of N independent order parameters are
considered for materials with N variants, where one of the order parameters
describes A <-> M transformations and the remaining N-1 independent order
parameters describe the transformations between the variants. A
non-contradictory gradient energy is used within the free energy of the system
to account for the energies of the interfaces. In addition, a non-contradictory
kinetic relationships for the rate of the order parameters versus thermodynamic
driving forces is suggested. As a result, a system of consistent coupled
Ginzburg-Landau equations for the order parameters are derived. The
crystallographic solution for twins within twins is presented for the cubic to
tetragonal transformations. A 3D complex twins within twins microstructure is
simulated using the developed phase-field approach and a large-strain-based
nonlinear finite element method. A comparative study between the
crystallographic solution and the simulation result is presented.
