1. Course Outline & Descriptions

Continuum Mechanics studies motions of continuum materials. In this course, I will cover fluids, elasticity, and plasticity. It is designed for graduate students to have a global picture of continuum mechanics from the perspectives of classical field theory and differential geometry. I will take three approaches : Newton, Lagrange, and Hamilton, both in Lagrangian and Eulerian coordinate frames of references. Thus, variational principles of fluid mechanics and solid mechanics, Hamiltonian Fluid Mechanics, Hamiltonian Elasticity will be studied. 

Contents
• Thermodynamics of gases
• Newtonian Formulation of Fluid Mechanics
• Lagrangian Formulation of Fluid Mechanics
• Hamiltonian Fluid Mechanics
• Geometric Fluid Mechanics (option)
• Kinematics of Elasticity
• Strain and Stress
• Variational Formulation of Elasticity
• Geometric Elasticity (option)
• Thermoelasticity
• Plasticity

Goal

To provide students a global picture of continuum mechanics from the perspectives of classical field theory and differential geometry. It is designed for graduate students to do research on fluid dynamics, nonlinear elasticity or plasticity, either in mathematical analysis or computation.

Keywords
Thermodynamics, compressible/incompressible fluid dynamics, large deformation elasticity, strain, stress, least action principle, vorticity, symmetry, tensor, differential forms.

Prerequisites
Linear Algebra, Multi-variable Calculus (or Vector Calculus),
Differential Equations, Some differential geometry (if possible).

Textbook
I-Liang Chern, Fundamentals of Continuum Mechanics

References
•C. Truesdell, W. Noll, The Nonlinear Field Theory for Mechanics (2003)
•J. Marsden, T. Hughes, Mathematical Foundation of Elasticity.

2. Lecture Note

https://drive.google.com/file/d/1E-LKE8WzJSc4XC02Ljda-IobE7ShfNji/view?usp=drive_link

3. Grading

(40%) Participation

(60 %) A report and an oral presentation.

4. Credit

3

5. Course Number/ ID

No.: NCTS 5054 (三校聯盟之學生於課程網選課適用)

ID: V41 U5100