Continuum mechanics

Description

This course provides an introduction into the fundamentals of continuum mechanics, which describes the movement of matter under force on a length scale that is sufficiently large as to use continuous variables. Therefore continuum mechanics is an example of a classical field theory, like electrodynamics. There are two main fields, the stress field (stress = force per area, cause of the deformation) and the deformation field (the effect of the applied stresses). Continuum mechanics is very important for soft matter physics and materials science; it is also relevant in biophysics, especially for cell and tissue mechanics, where it is often augmented by the concept of active stresses.

We will discuss both linear and non-linear elasticity theory as well as viscoelasticity and active stresses. The following subjects will be discussed:

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
15. active stress
16. finite element method (FEM), weak formulation

The course is designed for physics students in advanced bachelor and beginning master semesters (students from other disciplines are also welcome). It will be given in English. A basic understanding of physics and differential equations is sufficient to attend. The course takes place every Wednesday from 11.15 - 12.45 pm in room 106 at Philosophenweg 12. Every second week on Wednesday afternoons the solutions to the exercises will be discussed in a tutorial. If you attend the course and solve more than 60 percent of the exercises, you earn 4 credit points. A script is available from earlier versions of this course.

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