Ruprecht Karls Universität Heidelberg

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

  1. scalar elasticity
  2. material laws and constitutive equations
  3. viscoelasticity
  4. Hookean solid, Newtonian fluid, Maxwell model, Kelvin-Voigt model
  5. complex modulus
  6. stress and strain tensors
  7. Lagrangian versus Eulerian coordinates
  8. geometrical and material non-linearities
  9. linear elasticity theory
  10. rods and plates
  11. contact problems
  12. non-linear elasticity theory, neo-Hookean solid
  13. fracture and plasticity
  14. thermoelasticity
After solid mechanics, we will briefly discuss hydrodynamics. We then will turn to modern applications of continuum mechanics, in particular to the questions of how to deal with growth and active stresses in biological systems. Finally we will also cover numerical approaches to continuum mechanics, namely the finite element method (FEM) and its implementation in commercial and open source code.

Material for the course


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


Groups at Heidelberg working with continuum mechanics