Course materials for CIVL 5830 (Advanced Mechanics of Materials) instructed by Tianju Xue at HKUST in Spring 2026.
This graduate-level course provides an introduction to continuum mechanics and its applications. Lectures 1–10 cover standard continuum mechanics: mathematical preliminaries (tensor algebra); kinematics of finite deformation (deformation gradient, stretch, rotation); strain measures (Green-Lagrange, Euler-Almansi); rate of strain (velocity gradient, stretching, spin); stress measures (Cauchy, Piola-Kirchhoff); balance principles (mass, momentum, energy); first and second laws of thermodynamics; variational principles (Euler-Lagrange equation); objectivity (material frame indifference); and constitutive theories encompassing hyperelasticity and viscoelasticity. Lectures 11–13 then focus on three selected topics: fracture mechanics, presented from the energy approach and the stress intensity factor approach, along with their equivalence and the J‑integral; stability of structures, using energy methods; and homogenization, covering asymptotic homogenization and self‑consistent methods.
Let me know if you find any mistake or have any comments/suggestions (cetxue@ust.hk).
For educational purposes.
© [2026] [Tianju Xue]. All course materials licensed under [CC BY-NC 4.0].