Syllabus
1. Fundamental concepts, conservation laws - notion of continuum, representative elementary volume (how much is 264 and why to know that); - quantities, their flux and production, and what do divergence and various integrals say about them (divide and conquer); - deformation as a change of geometry, length, angle and volume; Lagrange and Euler description; - velocity, acceleration and conservation of mass; material time-derivative and continuity equation; - balance of momentum and of angular momentum; forces, traction vector and stress tensor (from Newton to Cauchy); - laws of thermodynamics, conservation of energy and a few words about entropy (energy conserved but not stored);
2. Phenomenology of materials, constitutive relations - elasticity, viscosity, plasticity; - stress-strain curves, mechanical analogues; - Newtonian fluid (neither blood, nor ketchup, Kevlar, starch); - viscometer, rheometer and Poiseuile, Couette and other gentlemen; - elastic deformation, Hooke's law, and Hookean and related materials; - plastic materials and their strength.
3. More on constitutive relations - determinism, objectivity and thermodynamical compatibility (three pillars of the constitutive relations?); - objective quantities and how to find them, objectivity tests, simple materials; - incompressibility as a kinematic constraint; - homogeneous, isotropic or both? and the material symmetries to sum up; - how the theory helps with the experiments (and how nicely it restrains us);
4. More on fluids - Euler fluid and two Newtonian ones: Stokes and Navier-Stokes fluid; - incompressibility and pressure; - self-similarity and non-dimensional description, Reynolds number; - laminar and turbulent flow, flow around a ball;
5. Mathematical tools (on practicals, through the whole course) - calculus of vectors and tensors, scalar product, norm; - scalar-, vector- and tensor fields; - partial derivatives, gradient, divergence and rotation; - curve- and surface integrals, divergence theorem; - differential- and partial differential equations, initial value- and boundary value problems.
Annotation
An introduction into the ``language'' of continuum mechanics, its concepts and notions and how they are built up, piled up and bent. The language whose grammar was founded in 18th century by Bernoulli, Euler, d'Alambert,
Lagrange and others; and in which the ``continuum'' is discussed by mathematicians, nature scientists, physicists and engineers, in basic research as well as in countless applications, from the flow in rivers, motion of soil or rock, or magma, as far as air, blood or stars themselves.
The lectures will be a condensed exposition of basic physical principles and their mathematical description, the practicals will supplement the mathematical tools. An effort will be made, instead of learning a loads of equations, to reveal natural relations and laws behind the processes (an behind the equations as well). Particular applications addressed by other courses in Applied geology will serve as examples.