Unconventional phase field simulations of transforming materials with evolving microstructures

Transforming materials with evolving microstructures is one of the most important classes of smart materials that have many potential technological applications, and an unconventional phase field approach based on the characteristic functions of transforming variants has been developed to simulate the formation and evolution of their microstructures. This approach is advantageous in its explicit material symmetry and energy well structure, minimal number of material coefficients, and easiness in coupling multiple physical processes and order parameters, and has been applied successfully to study the microstructures and macroscopic properties of shape memory alloys, ferroelectrics, ferromagnetic shape memory alloys, and multiferroic magnetoelectric crystals and films with increased complexity. In this topical review, the formulation of this unconventional phase field approach will be introduced in details, and its applications to various transforming materials will be discussed. Some examples of specific microstructures will also be presented.