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.
Features many examples of how the methods explained can be used in materials science and engineering applications.
Table of Contents
PART I: Phase Transformation in Materials Science1. 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 for PDEs -
Time Marching Schemes
4. Discretization of the Diffusion Equation
5. Discretization of Advection Diffusion Equations
6. Introduction to the Message Passing Interface (MPI)
7. Solved MPI Examples
