Continuum Mechanics

1. Kinematics of deformable media (velocity field of a fluid / continuity equation)

2. Hydrodynamics (stress tensor and viscosity / fundamental equations: Euler & Navier-Stokes / Bernoulli equation / Aerofoil theory / viscosity and Reynolds number / high Reynolds numbers and turbulence / small Reynolds numbers / waves / tsunamis)

3. Elasticity (stress tensor / energy balance / linear theory of elasticity: Hooke’s law / elastic waves / thin plates)

After successful completion of the module the students are able

1.  to know the meaning of the conservation quantities, balance equations and velocity fields, to understand the correlations and to calculate the descriptive quantities for simple systems
2.  to know the basics of the dynamics of liquids
3.  to describe the difference between laminar and turbulent flow, to know the conditions for the occurrence of both flow types and to calculate the relevant quantities.
4.  to know the basics of the deformation theory of elastic media and to understand and describe the formation and propagation of waves.
5.  to know the phenomena occurring in the reduction of extended media to one or two dimensions.

No preconditions in addition to the requirements for the Master’s program in Physics.

The modul consists of a lecture and exercise classes.

The lecture is designed for the presentation of the subject, usually by blackboard or beamer presentation. The focus resides on theoretical foundations of the field, presentation of methods and simple, illustrative examples. Command of basic methods is deepened and practised through homework problem sheets, which cover important aspects of the field. The homework problems should develop the analytic skills of the students and their ability to perform calculations. The homework problems are discussed by the students themselves under the supervision of a tutor in order to develop the skills to explain a physics problem logically.

scriptum of lecture, exercise sheets, internet site associated with lecture, video of the lecture

* D.J. Acheson, Elementary fluid dynamics, Clarendon Press
* H. Stephani & G. Kluge, Theoretische Mechanik, Spektrum Akademischer Verlag
* Lai, Introduction to Continuum Mechanics, Butterworth-Heinemann
* Landau/Lifshitz, Theory of Elasticity (Theoretical Physics 7), Butterworth-Heinemann Ltd

There will be a written exam of 90 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using calculation problems and comprehension questions.

For example an assignment in the exam might be:

• Consider a 2D incompressible flow v = (v_x , v_y) with v_x = y^2/x. Determine the second (y) component of the velocity field.
• Consider the strain tensor ε_11 = c_1 r_1 (r_12 + r_22), ε_22 = (1/3) c_2 r_13, ε_12 = c_3 r_12 r_2, where c_1, c_2, c_3 are const. For which c_1, c_2, c_3 does this present a valid deformation state?
• Define the Reynolds number and give an interpretation.

Participation in the exercise classes is strongly recommended since the exercises prepare for the problems of the exam and rehearse the specific competencies.

There will be a bonus (one intermediate stepping of "0,3" to the better grade) on passed module exams (4,3 is not upgraded to 4,0). The bonus is applicable to the exam period directly following the lecture period (not to the exam repetition) and subject to the condition that the student passes the mid-term of achieving of at least 50% of the points in the homework problems