Finite Element Simulation in Material Science

This lecture aims at introducing the fundamentals of the finite element method (FEM) and its application in solving various problems closely relevant to material sciences, e.g., the elastic fields and driving force of different types of defects in an arbitrary domain, and chemomechanical problems. The open-source FE package MOOSE will be introduced and utilized for FE simulations. The outline of the course is as follows: Part I: Theory (Recap): a. Continuum Mechanics Basis (linear elasticity) b. Chemomechanical basis (two-way-coupled) c. Mechanics of Defects in Solids d. Configurational force Part II: FEM basis. a. Weak form construction of PDEs (pure mechanics, chemomechanics, driving force) b. Finite elements: element types, shape functions, interpolation, numerical integration, stiffness matrix and residual assembling. c. Numerical methods for solving linear/nonlinear FE equations d. Postprocessing Part III: Implementation and Applications a. Mechanical and chemomechanical problems without defects b. Mechanical problems with defects: Point defects; (0D) Dislocations; (1D) Cracks (Interface, surface); (2D) Inclusions, pores; (3D) Configurational driving force; If time permits, chemomechanical problems with defects.