Finite Element Simulation for Material Science

Overview

The lecture covers the fundamentals of the finite element methods and its application in material science. Specifically, the focus is on strong and weak forms of linear elasticity and heat conduction problems. Finite element formulations as well as its implementation for linear elasticity and heat conduction problems will be discussed.

• Review of Basics of tensor calculus, Linear algebra, Continuum mechanics (kinematics) and Material mechanics (Hook’s law)
• Weak form construction for 1D bar and “truss-based” FE problem
• Learning about the Galerkin approach for a general solid and construction of the weak form for a general PDE
• Finite element (1): concept of Shape functions and discretised version of the weak form
• Finite element (2): construction of residual vector and Stiffness matrix
• Finite element (3): learning about numerical integration and post-processing.
• Multiphysics problems: focusing on a simple thermo-mechanical problem (Strong form + Weak form)
• Thermo-mechanical problem (finite element discretization)
• Discussions towards nonlinear FE (simple plasticity model)
• If time permits: Multi-scaling and Machine learning in FE

Literature

• T. I. Zohdi and P. Wriggers, An Introduction to Computational Micromechanics. Springer, 2010.
• Zienkiewicz OC, Taylor RL, Zhu JZ. The finite element method: its basis and fundamentals. Elsevier; 2005.
• Jacob, Fish, and Belytschko Ted. A first course in finite elements. Wiley, 2007.
• Lecture notes on FE by Prof. Carlos A. Felippa: https://quickfem.com/wp-content/uploads/

Teacher: Dr.-Ing. Shahed Rezaei; Dr. Behnam Sobhaniaragh