Content
 Compulsory Modules
 Elective Modules
Links for further information about the modules
 List of modules in C@mpus
All the COMMAS modules and modules from other study programs which can be taken by students, and the actual informations about modules can be found here  Curriculum
Structure of the program, modules and additional information can be found here  Examination Regulations
The examination regulations for the COMMAS program can be found here. As these documents are official documents, they are only in German  Module Handbook
The Module Handbook of the COMMAS program can be download as pdffile following this link. It contains further information about the modules and their examinations  Institutes and Lecturers
Additional information on some of the associated institutes and lecturers
Compulsory Modules
Lecturer  Prof. Dr.Ing. Holger Steeb 
Content 
Continuummechanical knowledge is the fundamental basis for the computation of deformation processes of solid materials. Based on the methods of tensor calculus, the lecture offers the following content:

ECTS points  6 
Lecturer  Jun.Prof. Dr.Ing. MarcAndré Keip 
Content 
This core course focuses on the theory and numerics of material models. Important classes of material models are investigated both for the onedimensional and the threedimensional context.

ECTS points  6 
Lecturer  Prof. Dr.Ing. habil. Manfred Bischoff 
Content  The module combines fundamental topics of structural mechanics and finite element theory in their respective context.

ECTS points  6 
Lecturer  
Content 
Discretization Methods : The lecture deals with the numerical treatment of differential equations
Introduction to Scientific Programming: part I: layout of a computer
part II: algorithms and data structures
part III: numerics

ECTS points  6 
Lecturer  Prof. Dr.Ing. Prof. E.h. Peter Eberhard 
Content 

ECTS points  6 
Lecturer  
Content 
Metals:
Concrete:

ECTS points  6 
Elective Modules  2nd Semester
Lecturer  Jun.Prof. Dr.Ing. MarcAndré Keip 
Content 
The course Micromechanics of Materials and Homogenization Method advances the topics of the core course Computational Mechanics of Materials. It is structured into the parts computational mechanics of threedimensional material models at small strains, micromechanicallybased material models, homogenization methods and computational mechanics of solid materials at large strains. Basic contents are thermodynamics of a general internal variable formulation of inelasticity at small strains, linear and nonlinear elasticity, finite element implementation of nonlinear elasticity, viscoelasticity, rateindependent and ratedependent plasticity, micromechanicallybased models of plasticity for crystalline solids, introduction to homogenization methods and microtomacro transitions, a general internal variable formulation of inelasticity at large strains, approaches to the modeling and numerics of finite elasticity and finite viscoelasticity. The following topics will be covered:

ECTS points  6 
Lecturer  Prof. Dr.Ing. habil. Manfred Bischoff 
Content 
The course covers the theory of nonlinear structural mechanics and

ECTS points  6 
Lecturer  Prof. Dr.Ing. habil. Joško Ožbolt 
Content 
The most frequently used models and procedures for modelling of concrete and reinforced structures will be discussed. The main difficulties related to the modelling of quasibrittle materials, such as concrete, will be pointed out and possible solutions discussed. The contents of the course is as follows:

External Link  Numerical Modelling of Soils and Concrete Structures [68790] 
ECTS points 
Lecturer  Prof. Dr.Ing. Christian Ebenbauer 
Content 
This course provides an introduction to intrinsically nonlinear phenomena in dynamical systems. The main focus of this course is on differential geometric methods. Applications will include problems from nonlinear control, optimization and mechanics. Some of the topics covered in this course are:

ECTS points  6 
Lecturer  Prof. Dr.Ing. Rainer Helmig 
Content 
Discretization methods:
Time discretization:
Transport equation:
Choice of a grid
Time discretisation on the basis of the instationary groundwater equation:
Discretisation of the transport equation:
Introduction to stability analysis, convergence
Fundamentals of programming in C:
Visualisation of the simulation results 
ECTS points  6 
Lecturer  
Content 
The ultimate goal of the lecture to foster the understanding of general inelastic material behavior with regard to the theoretical modeling and the numerical treatment based on selected model problems. For example, the selected material models under consideration may cover (i) micromechanically motivated approaches to inelastic material response such as crystal plasticity or (ii) purely phenomenological formulations of an inelastic material response such as viscoelasticity. Contents:

External Link  
ECTS points  6 
Lecturer  
Content 
The lecture provides an indepth perspective on the formulation and algorithmic implementation of material models for the description of physically and geometrically nonlinear deformation and failure mechanisms of solids. Material models of elasticity, viscoelasticity, plasticity as well as damage and fracture at finite deformations are covered in the course. This also includes nonmechanical effects such as thermomechanical or electromechanical coupling. In addition to continuum mechanical models, discrete modeling approaches on different space and time scales are presented, and fundmental concepts of multiscale models and mathematical homogenization techniques are addressed. The lecture covers theoretical and numerical aspects in a integrated sense. For example, modelspecific algorithms for time integration, global solvers for coupled nonlinear field equations as well as different finite element formulations for the spatial discretization of nonlinear material models and discontinuities are considered. Many of the presented developments and methods are current topics in research. A specification and orientation of this broad subject based on the interests of the audience is possible. Contents:

ECTS points  6 
Lecturer  Dr. techn. Andreas Langer 
Content 
Topcis:
Goal:

ECTS points  6 
Lecturer  Prof. Dr. Remy 
Description  The overarching goal of this class is to provide students with an overview of the current state of the art in the field of dynamics and control of legged (robotic) systems. To achieve this goal, the course will use and apply a large number of key theoretical principles of mechanical dynamics, including: multibodydynamics, nonsmooth dynamics, nonlineardynamics, limit cycles, orbital stability, continuation, and bifurcations. Using these concepts, students will learn about different gaits, the effects of scaling, modeling of legged systems, simple models of locomotion, passive dynamics, and limitcycle locomotion. For students, this will provide a unique opportunity to experience how their theoretical dynamics knowledge can be put into practice. In addition, the class will cover a broad range of different control strategies for legged robots, including: Raibert’s controller (best known from Boston Dynamics’ Big Dog), control based on inverse kinematics (used in Little Dog), zeromoment point control (used in the Honda Asimo), capture points (used in the IHMC bipeds), virtual model control (used in RAMone), hybrid zero dynamics (used in Cassie Blue), as well as optimal control through multiple shooting and direct collocation. 
ECTS points  6 
Lecturer  Prof. Dr. Leine 
Description 
The course Nonsmooth Dynamics is concerned with the mathematical description and numerical simulation of mechanical systems with unilateral constraints. Nonsmooth mechanical systems are characterized by jumps in the velocities or accelerations of the bodies in contact. Examples are systems with impact and friction. Mathematical concepts from convex and nonsmooth analysis, which are essential for the description of nonsmooth systems, are discussed in the first part of the course. Topics such as convex sets and functions, the subdifferential and setvalued functions are introduced. The second part of the course discusses setvalued force laws. Special attention is paid to Coulomb friction, both in the planar and spatial case, and to Newtonian impact laws. The third part of the course is concerned with nonsmooth dynamical systems. Numerical methods for the simulation of nonsmooth systems are explained and illustrated with example problems. 
ECTS points  6 
Elective Modules  3rd Semester
Lecturer  Prof. Dr.Ing. Christian Ebenbauer 
Content 
In many practical control problems it is desired to optimize a given cost functional while satisfying constraints involving dynamical systems. These kind of problems typically fall into the area of optimal control, a centerpiece of modern control theory. This course gives an introduction to the theory and application of optimal control for linear and nonlinear systems. Topics covered in the course are:
The course is intended to students having visited SGRT/ERT lectures. 
ECTS points  6 
Lecturer  Prof. Dr.Ing. habil. Manfred Bischoff 
Content 
The course covers design and analysis of shells, membrane and shell theory as well as mathematical and computational models for analysis of shells. The theoretical contents is supplemented and exemplified with applications of commercial finite element software.

ECTS points  6 
Lecturer  Dr.Ing Pascal Ziegler 
Content 
The first part of the lecture communicates the fundamentals of vehicle dynamics via selected contributions in research. In doing so, the mechanical modeling and the mathematical description are concerned with vehicle systems for ground transportation that contain vehicle superstructures, support and guidance systems and tracks. In the second part, occupant protection systems in vehicles are introduced from industrial practice such as airbags and belt restraint systems, with all steps from modeling via simulation to experimental verification being treated. Part I of the lecture is based on a modularization of the vehicle substructures with standardized interfaces: vehicle superstructures, support and guidance systems and track descriptions are the elements of complete vehicletracksystems, which are supplemented by assessment criteria for the human vibrational feeling. The theoretical methods are clarified by examples of simple longitudinal, lateral and vertical motions. Part II of the lecture gives attention to the fundamentals of occupant protection systems and the modeling of airbags and belt systems in a full vehicle. The experiments from subsystem testing towards crash tests are introduced. They are followed by the design of restraint systems. The excursion to TRW Automotive in Alfdorf delivers insight into the industrial practice. 
ECTS points  3 
Lecturer  Dr.Ing. Albrecht Eiber 
Content 

ECTS points  3 
Lecturer  Prof. Dr.Ing. Holger Steeb 
Content 
Fundamental knowledge of nonlinear continuum thermodynamics is a crucial prerequisite for the description of large deformations of arbitrary materials with nonlinear constitutive laws. The lecture provides a systematic representation of nonlinear continuum mechanics and the basics of thermodynamics (energy balance, entropy inequality). Proceeding from the fundamental principles of constitutive theory and the 2nd law of thermodynamics, the procedure for the derivation of thermodynamic consistent and admissible material models is described. All methods are exemplarily applied for the description of a nonlinear deformable, thermoelastic solid. Moreover, some aspects of the numerical treatment of nonlinear processes in space and time are discussed. In particular, the lecture comprises the following topics:

ECTS points  6 
Lecturer  Prof. Oliver Röhrle, PhD 
Content  Biological processes can be modelled within a continuummechanical framework which leads to the study of continuum biomechanics. The lecture focuses on modelling the mechanical response of soft biological tissues using the principles of continuum biomechanics. Basic concepts of the Theory of Porous Media are introduced which are then applied to the modelling of the intervertebral disc that is selected as an example problem. Principles of material modelling are examined and selected tissues with different mechanical characteristics are modelled accordingly. The lecture covers the following topics: Introduction and motivation.

ECTS points  6 
Lecturer  
Content 
Erdbeben führen als unvermeidbare und derzeit nur schwer vorhersagbare Naturkatastrophen zu schwerwiegenden Folgen in den betroffenen Gebieten. Die Vorlesung gibt eine Einführung in die Technik des erdbebensicheren Bauens in theoretischen und konstruktiven Belangen. Insbesondere soll der Blick für den erdbebengerechten Entwurf von Hochbauten geschärft werden. Der Inhalt der Veranstaltung gliedert sich hierbei wie folgt:

ECTS points  6 
Lecturer  apl. Prof. Dr.Ing. Michael Hanss 
Content 

ECTS points  6 
Lecturer  apl. Prof. Dr.Ing. Holger Class 
Content 
The lecture deals with flow in natural hydrosystems with particular emphasis on groundwater / seepage flow and on flow in surface water / open channels. Groundwater hydraulics includes flow in confined, semiconfined and unconfined groundwater aquifers, wells, pumping tests and other hydraulic investigation methods for exploring groundwater aquifers. In addition, questions concerning regional groundwater management (z.B. recharge, unsaturated zone, saltwater intrusion) are discussed. Using the example of groundwater flow, fundamentals of CFD (Computational Fluid Dynamics) are explained, particularly the numerical discretisation techniques finite volume und finite difference. The hydraulics of surface water deals with shallow water equations / Saint Venant equations, unstationary channel flow, turbulence und layered systems. Calculation methods such as the methods of characteisitcs are explained. The contents are:

ECTS points  6 
Lecturer  Prof. Dr.Ing. Rainer Helmig 
Content 
Using complex models in engineering practice requires wellfounded knowledge of the characteristics of discretisation techniques as well as of the capabilities and limitations of numerical models, taking into account the respective concepts implemented and the underlying model assumptions. The contents are:
Numerical solution of the multiphase flow equation
Multicomponent systems
Application examples:

ECTS points  6 
Lecturer  Prof. Dr.Ing. MarcAndré Keip 
Content 
The modeling approaches are rooted in micromechanics, mostly phenomenological, and build on the framework of continuum mechanics and the thermodynamicallyconsistent formulation of constitutive equations as taught in earlier courses. This framework, which accounts for thermomechanical coupling, is extended, where necessary, to include electric and magnetic coupling effects. The lecture covers the following topics:

ECTS points  6 
Lecturer  Dr.Ing. Felix Fritzen 
Content 
Motivation 
ECTS points  6 
Lecturer  Jun.Prof. Dr.Ing. MarcAndré Keip 
Content 
The knowledge of continuum mechanics and continuum thermodynamics is the fundamental requirement for the theoretical and algorithmic understanding of geometrically and physically nonlinear deformation, failure and transport processes in solids consisting of metallic, polymer or geological materials. This course offers a presentation of fundamental concepts of continuum mechanics and constitutive theory at finite elastic and inelastic strains. The chosen formulation accentuates geometrical aspects based on the modern terminology of differential geometry, which also includes the description of multifield theories with thermo and electromechanical coupling. Algorithmic aspects of the computer implementation of nonlinear continuum mechanics models are covered in parallel to the theoretical description. Contents:

ECTS points  6 
Lecturer  Dr.Ing. Malte von Scheven 
Content 

ECTS points  6 
Lecturer  Prof. Dr. rer. nat. Dr. h.c. Siegfried Schmauder 
Content  Computational Materials Science The theoretical foundations of Monte Carlo (MC), Molecular Dynamics (MD) and other advanced simulation techniques with respect to atomistic phenomena in computational materials science, such as, e.g., precipitation strengthening in steels. Another focus is put on dislocation theory including the dislocation dynamics and the applications for the understanding of the local deformation processes in metallic materials. FiniteElementmethods, crystal plasticity and damage mechanical modelling are further essential topics in this course. 
ECTS points  6 
Lecturer  Prof. Dr. Christian Holm 
Content  Simulation Methods in Physics 1 (2 SWS Lecture + 2 SWS Tutorials in Winter Term)

ECTS points  6 
Lecturer  Dr.Ing. Anton Tkachuk 
Content 

ECTS points  6 
Lecturer  Dr.Ing. Dipl.Math. techn. Felix Fritzen 
Content  The lecture gives an introduction to model order reduction, more specifically for methods aiming at a reduction of linear function spaces by using a reduced basis. The course is partitioned as follows:

ECTS points  6 
Lecturer  Prof. Dr. Remy 
Description  This course covers the description of kinematics and dynamics of multibody systems as they are typical for applications in robotics, mechatronics, and biomechanics. The course provides the theoretical background to describe such systems in a precise mathematical way, while it also pays attention to an intuitive physical understanding of the underlying dynamics. It discusses the tools and methods necessary to create the governing differential equations analytically and it covers a range of computational algorithms that do so in a numerically efficient way. Special attention is paid to the handling of closed loops, collisions, and variying structure. As part of the exercises accompanying this course, the students will implement their own multibody dynamics engine in MATLAB, using advanced programming techniques that include recursive formulations and object oriented programming. The gained knoweldege will enable a creative approach to the design and control of robotic systems. It will enable the students to debug their own solutions more intuitively and understand what is going on when using offtheshelf software for design or analysis. 
ECTS points  6 
Lecturer  Prof. Dr. Leine 
Description  This lecture is intended for graduate and PhD students from engineering sciences and physics who are interested in the behaviour of nonlinear dynamical systems. The course makes the student familiar with nonlinear phenomena such as limit cylces, quasiperiodicity, bifurcations and chaos. These nonlinear phenomena occur in for instance biological, economical, celestial and electrical systems but only mechanical multibody systems will be taken as examples. With the theory explained in the course one is able to understand flutter instability of wings, stickslip vibrations, postbuckling behaviour of frames and nonlinear control techniques. Exercises and examples during the course include: hunting motion of railway vehicles, forced oscillation of a nonlinear massspring system, instability of the Watt steam governor and symmetric and asymmetric buckling. Engineering practice as well as the standard engineering curriculum often does not exceed a linear analysis of nonlinear systems. The course pays special attention to indicate the limitations of a linear analysis. The aim of the course is to give the student a basic knowledge and understanding of nonlinear system behaviour and to provide analysis tools to analyze nonlinear dynamical systems. 
ECTS points  6 
Lecturer  Prof. Dr.Ing. Tim Ricken 
Description 
In addition to purely mechanical questions, the Finite Element Method (FEM) can also be used to address more complex questions with coupled field equations. Examples include: thermomechanical couplings, electromechanical couplings, chemicalmechanical couplings or combinations thereof. The treatment of these problems requires the development of coupled material equations, which do not contradict the thermodynamic principles. Furthermore, the system of equations may be extended by an additional process variable, e.g. the temperature, the electric field or a chemical state variable, which negatively influence the numerical solution properties in the context of the finite element approximation. For a stable solution of coupled problems using the finite element method, it is necessary to formulate thermodynamically consistent material equations, to develop advanced finite element formulations and to use suitable numerical solution methods. The lecture will be complemented with computer pool exercises. 
ECTS points  6 
Lecturer  Prof. Dr.Ing. Tim Ricken 
Description 
As a conceptual approach for the treatment of discrete multicomponent materials, the Theory of Porous Media (TPM) is presented. The conceptual procedure for the development of thermodynamically consistent material equations is discussed. The resulting system of equations is solved numerically using the finite element method (FEM). Due to the mostly strongly coupled and nonlinear nature of the system of equations to be solved, special element formulations are presented.

ECTS points  6 
Elective Modules  4th Semester
Lecturer  Prof. Dr.Ing. Rainer Helmig 
Content  The lecture deals with the heat and mass budget of natural and technical systems. This includes transport processes in lakes, rivers and groundwater, heat and mass transfer processes between compartments as well as between various phases (sorption, dissolution), conversion of matter in aquatic systems and the quantitative description of these processes. In addition to classical single fluid phase systems, multiphase flow and transport processes in porous media will be considered. On the basis of a comparison of single and multiphase flow systems, the various model concepts will be discussed and assessed. In the accompanying exercises, example problems present applications, extend the lecture material and help prepare for the exam. Computer exercises improve the grasp of the problems and give insight into the practical application of what has been learned. 
ECTS points  6 
Lecturer  JP. Dr. Maria Fyta 
Content 
Contents:

ECTS points  6 