
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 PhDstudents. 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 nonlinear 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, KelvinVoigt model
 complex modulus
 stress and strain tensors
 Lagrangian versus Eulerian coordinates
 geometrical and material nonlinearities
 linear elasticity theory
 rods and plates
 contact problems
 nonlinear elasticity theory, neoHookean 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, McGrawHill 1970
 David Boal, Mechanics of the Cell, Cambridge University Press 2002
FEMsoftware
 Matlab
 Matlab finite element package mlfem_nac from Oomens book
 Comsol multiphysics
 Abaqus
 Ansys
 Adina
 Deal II
 Dune