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NE 795 607 Phase Field Modeling in Moose

NE 795 607 Phase Field Modeling in Moose

April 1, 2025

3 Credit Hours

Modeling and simulation of microstructural evolution during phase transformation in solids; spinodal decomposition, nucleation, ordering, solidification, grain growth, fracture and crack propagation, multiphase flows, and vesicle dynamics; primary focus on finite-element and phase-field methods and the utilization of advanced, open-source software MOOSE to implement them.

Prerequisites

No specific prerequisites are required, but courses in materials and some modeling skills are preferred.

Course Objectives

  • Derive the phase-field Allen-Cahn and Cahn-Hilliard equations, along with their weak formulations for the finite element method.
  • Implement numerical solutions for phase-field models using the open-source MOOSE framework.
  • Verify and validate the models through analytical relationships or experimental observations.
  • Formulate and construct kinetic-based models for far-from-equilibrium systems (e.g., chemical, biological, and irradiation-driven processes).
  • Develop phase-field models for mechanics-related problems, including multiphase flows and fracture mechanics.
  • Summarize and communicate the results of modeling and simulation projects in a standard article format.

Course Outline

  • Introduction, overview
  • Basics of finite element methods
  • Tutorials on MOOSE framework
  • Introduction to thermodynamics and kinetics of materials
  • Concept of phase-field method and evolution equations
  • Phase-field models of phase-transitions in materials
  • Phase-field models of spinodal decomposition
  • Multiple-order parameters phase-field models
  • Phase-field fracture models
  • Phase-field models in multiphase flows
  • Phase-field models of vesicle dynamics

Course Requirements

50% Homework and 50% Final Project.

Textbook

• Provatas, N., & Elder, K. (2010). Phase-Field Methods in Materials Science and Engineering.
• Janssens, K., et al. (2007). Computational Materials Engineering: An Introduction to Microstructure Evolution. Elsevier.
• Biner, S. B. (2017). Programming Phase-Field Modeling. Springer Cham.
• Chen, L.-Q. (2023). Thermodynamic Equilibrium and Stability of Materials.

Software Requirements

MOOSE Framework (https://mooseframework.inl.gov).

Created: 04/01/2025