Venue: Rm 440, Astro-Math. Bldg.

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. Course 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 Keywords Thermodynamics, compressible/incompressible fluid dynamics, large deformation elasticity, strain, stress, least action principle, vorticity, symmetry, tensor, and differential forms. Lecture Note: https://drive.google.com/file/d/1E-LKE8WzJSc4XC02Ljda-IobE7ShfNji/view?usp=drive_link

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.

Participation (40%), An oral presentation with a report (60%)

Textbook: I-Liang Chern, Fundamentals of Continuum Mechanics (available on http://www.math.ntu.edu.tw/~chern/) References: ‧ C.Truesdell,W.Noll, TheNonlinearFieldTheoryforMechanics(2003) ‧ J. Marsden, T. Hughes, Mathematical Foundation of Elasticity.