Continuum Mechanics
Module PH1007
This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.
Module version of WS 2018/9 (current)
There are historic module descriptions of this module. A module description is valid until replaced by a newer one.
available module versions  

WS 2018/9  WS 2017/8  WS 2015/6  WS 2014/5 
Basic Information
PH1007 is a semester module in English language at Master’s level which is offered in winter semester.
This Module is included in the following catalogues within the study programs in physics.
 Theory courses for Biophysics
 Theory courses for Applied and Engineering Physics
 Complementary catalogue of special courses for condensed matter physics
 Complementary catalogue of special courses for nuclear, particle, and astrophysics
 Specialization Modules in EliteMaster Program Theoretical and Mathematical Physics (TMP)
If not stated otherwise for export to a nonphysics program the student workload is given in the following table.
Total workload  Contact hours  Credits (ECTS) 

300 h  90 h  10 CP 
Responsible coordinator of the module PH1007 is Martin Zacharias.
Content, Learning Outcome and Preconditions
Content

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

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

Elasticity (stress tensor / energy balance / linear theory of elasticity: Hooke’s law / elastic waves / thin plates)
Learning Outcome
After successful completion of the module the students are able
 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
 to know the basics of the dynamics of liquids
 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.
 to know the basics of the deformation theory of elastic media and to understand and describe the formation and propagation of waves.
 to know the phenomena occurring in the reduction of extended media to one or two dimensions.
Preconditions
No preconditions in addition to the requirements for the Master’s program in Physics.
Courses, Learning and Teaching Methods and Literature
Courses and Schedule
Type  SWS  Title  Lecturer(s)  Dates 

VO  4  Continuum Mechanics  Zacharias, M. 
Mon, 14:00–16:00, PH HS2 Tue, 08:30–10:00, PH HS2 
UE  2  Exercise to Continuum Mechanics 
Responsible/Coordination: Zacharias, M. 
dates in groups 
Learning and Teaching Methods
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.
Media
scriptum of lecture, exercise sheets, internet site associated with lecture, video of the lecture
Literature
* D.J. Acheson, Elementary fluid dynamics, Clarendon Press
* H. Stephani & G. Kluge, Theoretische Mechanik, Spektrum Akademischer Verlag
* Landau/Lifshitz, Theory of Elasticity (Theoretical Physics 7), ButterworthHeinemann Ltd
Module Exam
Description of exams and course work
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.
Exam Repetition
The exam may be repeated at the end of the semester.