Course description
This course introduces the theory of wave propagation and stability in elastic media, with emphasis on nonlinear elasticity and incremental formulations. After reviewing the fundamentals of linear and nonlinear elasticity, we will develop the mathematical tools needed to analyse wave motion, incremental deformations, and bifurcation phenomena in elastic continua, with applications to solids and soft materials. The course is designed to be accessible to Ph.D. students with a background in applied mathematics, mechanics, or related fields. No prior course in solid mechanics is required: the essential concepts of continuum and solid mechanics will be briefly reviewed at the beginning of the course.
Course topics
The course organization is flexible to meet the necessities and curiosity of students. Topics include
- Fundamentals of linear and nonlinear elasticity
- Wave propagation in linear elastic media
- Theory of incremental elastic deformations
- Incremental boundary value problems in simple geometries
- Stroh/Hamiltonian formulation of the incremental equations and impedance matrix method
- Numerical algorithms for bifurcation problems in nonlinear elasticity
Bibliography
- R. W. Ogden, Non-Linear Elastic Deformations, Dover Publications, 1997.
- D. Bigoni, Nonlinear Solid Mechanics: Bifurcation Theory and Material Instability, Cambridge University Press, Cambridge, 2012.
- M. Destrade, “Incremental Equations for Soft Fibrous Materials”, in L. Dorfmann, R. W. Ogden (eds.),Nonlinear Mechanics of Soft Fibrous Materials, CISM Courses and Lectures, vol. 559, Springer, Vienna, 2015.
- R. Seydel, Practical Bifurcation and Stability Analysis, Springer, 2010
Schedule
All lectures will take place in room 134.
- Mon 23 Feb 2026, 14:00–16:00
- Wed 25 Feb 2026, 14:00–16:00
- Mon 02 Mar 2026, 14:00–16:00
- Wed 04 Mar 2026, 14:00–16:00
- Mon 09 Mar 2026, 14:00–16:00
- Wed 11 Mar 2026, 14:00–16:00
- Mon 16 Mar 2026, 14:00–16:00
- Wed 18 Mar 2026, 14:00–16:00
- Mon 23 Mar 2026, 14:00–16:00
- Wed 25 Mar 2026, 14:00–16:00
- Fri 27 Mar 2026, 11:00–13:00
- Mon 30 Mar 2026, 14:00–16:00
- Fri 10 Apr 2026, 11:00–13:00
- Mon 13 Apr 2026, 14:00–16:00
- Wed 15 Apr 2026, 14:00–16:00