This is a 60-hours introductory course on continuum mechanics and its applications. The aim is to provide first year students with a solid understanding of the fundamental principles of the subject. Topics covered by the course will include but are not limited to: i) reminders on tensor algebra and calculus; ii) kinematics of deformable bodies (deformation, motion, material and spatial description of relevant fields); iii) balance laws of continuum mechanics (conservation of mass, balance of linear and angular momentum, and their consequences); iv) constitutive assumptions and invariance of material response under a change in observer; v) continuum thermodynamics (energy balance, entropy imbalance, Clausius-Duhem inequality, Helmholtz free energy, Coleman-Noll procedure); vi) selected topics in fluid mechanics, solid mechanics, and on the mechanics of biological systems and active materials.
Books:
- M. Gurtin, Introduction to Continuum Mechanics, Academic Press, 1981
- M. Gurtin, L. Anand, and E. Fried, The Mechanics and Thermodynamics of Continua, Cambridge UP, 2010
- D. Bigoni, Nonlinear Solid Mechanics, Bifurcation Theory and Material Instability, Cambridge UP, 2012
- P. Podio-Guidugli, Continuum Thermodynamics, Springer, 2019