Thermodynamic variational principle, its connections to the phenomenological laws and its applications to the derivation of microstructural models

Understanding microstructural evolution occupies a central position in the discipline of materials science and engineering. As stated by Carter et al., microstructural evolution involves complex, coupled, and often nonlinear processes even the description of the dynamics for isolated microstructural evolution processes can be quite complicated. It would be desirable to enrich the microstructural evolution theory by introducing a powerful mathematical tool, which could enable describing and predicting the rich intertwining phenomena such as diffusive or displacive phase transformation, grain growth, generation, or annihilation of defects (vacancy, dislocations, etc.) in a straightforward manner. There have been continuing efforts along this front, and I will restrict myself to the issues in the development and application of the thermodynamic variational principle. Although being reviewed by various authors recently, we hope to redraw attentions to some valuable papers and provide our understanding and viewpoints. It is our opinion that the most appealing feature about the principle is the nature that it could give approximate solutions with tunable accuracy. The other feature is its role as a basic principle in deriving the new models. It is hoped that this paper could promote the development and application of the variational principle even further in materials science.