Syllabus
1. Geometry of deformation, Eulerian and Lagrangian frames, displacement, strain tensor.
2. Material and spatial time derivative. Reynolds transport theorem.
3. Body and surface forces. Stress tensor.
4. Conservation laws in global and local scale, continuity and momentum equations.
5. Constitutive relationships. Elastic, viscous and plastic deformation.
6. Law of energy conservation. Entropy. Dissipation of mechanical energy. Thermal convection.
7. Mathematically correct formulation of continuum mechanics problems. Boundary conditions.
8. Pre-stressed media, thermal stresses, phase transitions.
9. Thin shell approximation of basic equations, membranes, shallow water approximation.
10. Applications: flow of oceans and atmosphere, sub-solidus flow of rocks and ices, viscoelastic liquids etc.
11. Numerical methods to solve the continuum mechanics problems.
12. Unsolved questions and open problems in continuum mechanics theory.
Annotation
Continuum mechanics is a theoretical ground for solving many problems of basic and applied research. The lecture provides the basics of the continuum mechanics theory and describes practical applications of its use.