Phase-field methods in materials science and engineering

This comprehensive and self-contained, one-stop source discusses phase-field methodology in a fundamental way, explaining advanced numerical techniques for solving phase-field and related continuum-field models. It also presents numerical techniques used to simulate various phenomena in a detailed, step-by-step way, such that readers can carry out their own code developments. Features many examples of how the methods explained can be used in materials science and engineering applications.

PART I: Phase Transformation in Materials Science; 1. Introduction to Phase transformations and microstructure formation in materials science; 2. An example: Solidification of pure materials; 3. Phase Transformations and Phenomenology of Landau; 4. Phase field model for solidification in pure materials; 5. Phase Transformations in binary alloys; 6. Phase-field models of phase transformations in binary alloys; 7. Applications to microstructure growth in binary alloys; 8. Connection between phase-field and sharp-interface parameters; PART II: Elastic and Plastic Effects in Phase Transformations; 1. Review of Mechanics of Materials; 2. Overview of Modeling and Simulation Techniques in Mechanics; 3. Phase-field Models; 4. Applications: Effects of Elastic Stress on Thin Film Growth and Phase Transformations; PART III: Modeling Atomic Scale Systems using the Phase-Field Method; 1. Phase field Modeling of Periodic Systems; 2. Modeling Crystals with Phase Fields; 3. Applications; PART IV: Numerical Solution Methods for simulating Phase-Field Models; 1. Introduction to Numerical Methods for PDEs -; Space Discretization; 2. Iterative Methods for sparse Linear Systems; 3. Numerical Methods f…