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Lecture course Continuum mechanics summer term 2013
This course is addressed to master students in physics, but it is also open for advanced bachelor and PhD-students. It provides an introduction into the fundamentals of continuum mechanics, which describes the movement of matter under force on a scale that is sufficiently large as to use continuous variables. Therefore continuum mechanics is an example of a classical field theory, like electrodynamics.
The course takes place every Monday from 2.15 - 3.45 pm in Philosophenweg 12, room 106 (next to the grosser Hoersaal). Weakly exercises are distributed on the day of the lecture and solutions have to be handed in one week later. The tutorial takes place every Monday after the lecture (same room, tutor Irina Surovtsova). To get the full four credit points, you have to solve at least 50 percent of the exercises.
The main part of the course will be concerned with solid mechanics, roughly on the level of the books of Landau and Lifschitz (linear elasticity theory) as well as Howell, Kozyreff and Ockendon (which also includes non-linear elasticity theory). For viscoelasticity, the book by Oomens, Brekelmans and Baaijens is recommended.
Major subjects in this part will be
- scalar elasticity
- material laws and constitutive equations
- viscoelasticity
- Hookean solid, Newtonian fluid, Maxwell model, Kelvin-Voigt model
- complex modulus
- stress and strain tensors
- Lagrangian versus Eulerian coordinates
- geometrical and material non-linearities
- linear elasticity theory
- rods and plates
- contact problems
- non-linear elasticity theory, neo-Hookean solid
- fracture and plasticity
- thermoelasticity
Material for the course
Exercises
- 1st set of exercises April 22
- 2nd set of exercises April 29
- 3rd set of exercises May 6
- 4th set of exercises May 13
- 5th set of exercises May 27
- 6th set of exercises June 3
- 7th set of exercises June 10
- 8th set of exercises June 17
- 9th set of exercises June 24
- 10th and last set of exercises July 1
Recommended literature
- Landau and Lifschitz, Elasticity Theory, volume VII of the series on theoretical physics, Akademie Verlag 1991
- Howell, Kozyreff and Ockendon, Applied Solid Mechanics, Cambridge Texts in Applied Mathematics 2009
- Oomens, Brekelmans and Baaijens, Biomechanics: Concepts and Computation, Cambridge Texts in Biomedical Engineering 2009
- Gerhard A Holzapfel, Nonlinear solid mechanics, John Wiley 2000
- Basile Audoly and Yves Pomeau, Elasticity and Geometry: From Hair Curls to the Nonlinear Response of Shells, Oxford UP 2010
- AEH Love, A treatise on the mathematical theory of elasticity, CUP 1927
- Timoshenko and Goodier, Theory of Elasticity, McGraw-Hill 1970
- David Boal, Mechanics of the Cell, Cambridge University Press 2002
FEM-software
- Matlab
- Matlab finite element package mlfem_nac from Oomens book
- Comsol multiphysics
- Abaqus
- Ansys
- Adina
- Deal II
- Dune