# Overview of Modules

Description and external links of compulsory and elective modules
[Photo: University of Stuttgart]

## Compulsory Modules - 1st Semester

 Lecturer Prof. Dr.-Ing. Holger Steeb Content Continuum-mechanical 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: Vector and Tensor Algebra: symbols, spaces, products, specific tensors and definitions  Vector and Tensor Analysis: functions of scalar-, vector- and tensor-valued variables, integral theorem (e. g., after Gauss or Stokes Foundations of Continuum Mechanics: kinematics and deformation, forces and stress concepts; Cauchy’s lemma and theorem, Cauchy, Kirchhoff and Piola-Kirchhoff stress tensors Fundamental Balance Laws: master balance, axiomatic balance relations of mechanics (mass balance, momentum and angular momentum balances) Related Balance Laws and Concepts: balance of mechanical energy, stress power and the concept of conjugate variables, d’Alembert’s principle and the principle of virtual work Numerical Aspects of Continuum Mechanics: strong and weak formulation of the boundary value problem The Closure Problem of Mechanics: finite elasticity of solid mechanics (as an example), linearization of the field equations ECTS points 6

 Lecturer Prof. Dr.-Ing. Marc-André Keip Content This core course focuses on the theory and numerics of material models. Important classes of material models are investigated both for the one-dimensional and the three-dimensional context. Introduction to discrete and continuous modeling of materials (microstructures, homogenization techniques and multi-scale approaches) Fundamental theoretical concepts (basic rheology, classification of the phenomeno- logical material response, elements of continuum thermodynamics) Fundamental numerical concepts (discretization techniques for evolution systems, linearization techniques, and iterative solution of nonlinear systems) Linear and nonlinear elasticity, damage mechanics, viscoelasticity (linear and nonlinear models, stress update algorithms and consistent linearization) Rate-independent plasticity (theoretical formulations, return mapping schemes, incremental variational formulations, consistent elastic-plastic tangent moduli)Viscoplasticity (classical approaches and overstress models) Material stability, failure analysis (nonlocal modes, discrete failure mechanisms) 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. direct stiffness method isoparametric concept variational formulation of finite elements, mixed variational principles, shape functions, approximation spaces and mathematical convergence requirements finite elements for trusses, beams, plates and solids locking, reduced integration, mixed and hybrid finite element methods modelling in structural mechanic, mathematical model and numerical model (discretization) interpretation of numerical results ECTS points 6

 Lecturer Content Discretization Methods :  The lecture deals with the numerical treatment of differential equations which arise from different mechanical and thermodynamical problems. Contents are:  deduction of differential equations based on the principles of mechanics and thermodynamics and their classification  the Finite Difference Method  the method of weighted residuals: method of subdomains, collocation method, least squares method, and Galerkin's method  the Finite Element Method  different time integration schemes  convergence and stability Introduction to Scientific Programming: part I: layout of a computer  von Neumann architecture  design of modern microprocessors, memory hierarchy , parallelism  programming languages  part II: algorithms and data structures  complexity, Bachmann-Landau notation  example sorting algorithms (sub-topic: recursion) arrays,lists, hashtables, trees (binary, KD, Quadtree, Octree), Heap  graphs (exemplary algorithms Cuthill McKee, Dijkstra)  part III: numerics  number representation intager and floating point  rounding and rounding errors  condition and stability  matrices and linear mappings (demonstrative meaning, effect on geometric objects)  solving of linear systems of equations (Gaussian elimination, LU- decomposition, Pivoting, Cholesky decomposition)  polynomial interpolation (different bases and algorithms: Lagrange, Newton, Aitken-Neville, divided differences, error estimation, condition)  spline interpolation & parametric curves (Beacute;zier) ECTS points 6

 Lecturer Prof. Dr.-Ing. Prof. E.h. Peter Eberhard Content Formulation of the optimization problem: optimization criteria, scalar optimization problem, multicriteria optimization Sensitivity Analysis: Numerical differentiation, semianalytical methods, automatic differentiation Unconstrained parameter optimization: theoretical basics, strategies, Quasi-Newton methods, stochastic methods Constrained parameter optimization: theoretical basics, strategies, Lagrange-Newton methods ECTS points 6

 Lecturer Content Metals: Fundamentals of dislocation theory Plastic deformation of metals Possibilities of strengthening Influences on behaviour of material   Concrete: Properties of concrete The behaviour of concrete under compressive loading The behaviour of concrete under tensile loading Time dependent behaviour Special concretes   Soils: Stresses in soils Stiffness of soils Strength of soils ECTS points 6

## Elective Modules - 2nd Semester

 Lecturer Prof. Dr.-Ing. habil. Manfred Bischoff Description The course covers variational formulations, various locking phenomena and alternative formulations for finite elements and advanced discretiza-tion schemes. variational formulation of finite elements, mixed variational principles  geometrical and material locking effects in structural and solid mechanics hybrid-mixed and enhanced assumed strain finite element for-mulations, reduced integration and stabilization, DSG method, u-p formulations patch test, stability, convergence linear and non-linear analyses locking effects and their avoidance in advanced discretization schemes, like isogeometric analysis ECTS points 6

 Lecturer Prof. Dr.-Ing. 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: multibody-dynamics, non-smooth dynamics, nonlinear-dynamics, 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 limit-cycle 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), zero-moment 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 3

 Lecturer Dr.-Ing. Philipp Weißgraeber Aim of the lecture Provide overview of fracture mechanics Show link between fracture mechanics, strength of materials and damage mechanics Create interest in the diverse world of fracture phenomena Scope of the lecture Dynamic crack branching Anticrack initiation Crack pattern analysis Mixed mode crack growth and among others ECTS points 3

### Video Description

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 Lecturer Prof. Dr.-Ing. Marc-André 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 three-dimensional material models at small strains, micro-mechanically-based 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, rate-independent and rate-dependent plasticity, micromechanically-based models of plasticity for crystalline solids, introduction to homogenization methods and micro-to-macro 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:   Thermodynamics of a general internal variable formulation of inelasticity at small strains Linear and nonlinear elasticity (isotopic spectral forms, anisotropic models based on structural tensors) Finite Element implementation of nonlinear elasticity Viscoelasticity (linear and nonlinear models, stress update algorithms and consistent linearization) Rate-independent and rate-dependent plasticity (theoretical formulations, stress update algorithms and local variational formulations, consistent linearization) Micromechanically-based models of plasticity for crystalline solids Introduction to homogenization methods and micro-to-macro transitions General internal variable formulation of inelasticity at large strains Approaches to the modelling and numerics finite elasticity and finite viscoelasticity ECTS points 6

 Lecturer Prof. Dr.-Ing. Rainer Helmig Content Discretization methods: Knowledge of the common methods (finite differences, finite elements, finite volume) and the differences between them Advantages and disadvantages and of the methods and thus of their applicability Derivation of the various methods Use and choice of the correct boundary conditions for the various methods Time discretization: Knowledge of the various possibilities Assessment of stability, computational effort, precision Courant number, CFL criterion Transport equation: Various discretisation possibilities Physical background Stabiity criteria of the methods (Peclet number) Choice of a grid Overview of discretazation techniques on the basis of the stationary groundwater equation: Finite differences Finite volume (integral finite differences) Finite elements Time discretisation on the basis of the instationary groundwater equation: Explicit and implicit methods Discretisation of the transport equation: Central difference methods Upwinding Introduction to stability analysis, convergence Clarification of concepts: model, simulation Derivation of the finite element method Application of the finite element method to the stationary groundwater equation Setting-up of a simulation programme for modeling groundwater: Programme requirements Programming individual routines Fundamentals of programming in C: Control structures Functions Arrays Debugging Visualisation of the simulation results ECTS points 6

 Lecturer Prof. Dr.-Ing. habil. Manfred Bischoff Content The course covers the theory of non-linear structural mechanics and corresponding discretization methods and algorithms with a focus on the finite element methods. basic principles, phenomena and concepts of structural mechanics non-linear strain measures and stress measures large deformations, stability problems methods and algorithms of non-linear structural mechanics iteration methods and path following techniques stability analysis, buckling problems ECTS points 6

 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: Nonlinear vector fields and flows Stability and bifurcations Lie brackets and commutativity of flows Manifolds, vector fields on manifolds and integrability Center manifolds and advanced stability theory Applications in Control, Mechanics and Optimization Extremum Seeking Control ECTS points 6

 Lecturer Prof. Dr.-Ing. 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 set-valued functions are introduced. The second part of the course discusses set-valued 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

 Lecturer Dr. techn. Andreas Langer Content Topcis: Different types of differential equations (ordinary differential equations, partial differential equations) Existence of (unique) solution Algorithms for solving differential equations Theoretical analysis of numerical schemes Implementation of numerical schemes within MATLAB Goal: knowledge about the theory of ordinary and partial differential equations overview about numerical solution methods for these problems ability to link a given problem and the appropriate method ability to program solution methods in MATLAB ECTS points 6
 Lecturer Univ.-Prof. Dr.-Ing. habil. Christian Moormann Content The lecture's goal is to improve understanding of general soil behaviour and its numerical treatment. The course will cover the fundamentals of elasticity and plasticity, as well as more advanced constitutive models used not only in typical industrial applications but also in research. The course will not only provide a theoretical framework for the constitutive laws, but will also demonstrate their implementation in a simple Finite Element software written in FORTRAN. In addition to the lectures, tutorials on the commercial finite element software Plaxis™ will be provided. Candidates will be expected to work independently to simulate geotechnical structures and present their findings in a 10-minute presentation. The course will cover the following topics: Introduction to Plasticity Different yield criterions used in soil mechanics : Drucker-Prager, Matsuoka-Nakai, etc., Modified Cam Clay model Hardening soil model Hypoplastic soil model Programming of constitutive laws in Fortran Simulating geotechnical structures using Plaxis™ External Link Numerical Modelling of Soils and Concrete Structures  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: Introduction to inelastic material behavior Micromechanical structure of solids Kinematics of inelastic deformations at finite strains Foundations of continuum-based material modeling for selected problems, e.g. finite crystal plasticity and viscoelasticity Integration algorithms of evolution systems, stress-update algorithms and consistent linearization of updating schemes External Link Selected Topics in the Theories of Plasticity and Viscoelasticity  from Chair of Material Theory Selected Topics in the Theories of Plasticity and Viscoelasticity  from Chair of Continuum Mechanics ECTS points 6
 Lecturer Content The lecture provides an in-depth 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, visco-elasticity, plasticity as well as damage and fracture at finite deformations are covered in the course. This also includes non-mechanical 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 multi-scale models and mathematical homogenization techniques are addressed. The lecture covers theoretical and numerical aspects in a integrated sense. For example, model-specific 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: Direct variational methods of finite elasticity and uniqueness Anisotropic finite elasticity and isotropic tensor functions Damage models and elements of fracture mechanics Finite elasto-visco-plasticity of metals and polymers Discrete models: particle methods and dislocation dynamics Multi-scale models and numerical homogenization techniques Material instabilities, phase transitions and microstructures ECTS points 6

 Lecturer Jun.-Prof., Ph.D. Carina Bringedal Description The course covers examples of multiscale models, in particular from porous media, together with analytical and numerical multiscale methods to simplify and simulate such models. The course is structured into three parts; first part is on multiscale models, where the focus is to describe their multiscale characteristics. The second part is on (analytical) multiscale methods, where matched asymptotic expansions and averaging techniques such as volume averaging and homogenization are covered. The theoretical justification of homogenization through two-scale convergence is also included. The third part is on multiscale numerical methods, where discretization methods such as multiscale finite element methods and finite volume methods are covered, and the idea behind heterogeneous multiscale methods is described. The course is mathematically oriented, but the main part of the content is covered through applying these methods to examples, including implementing multiscale discretizations. The following topics will be covered:    • Multiscale models in porous media    • Phase-field models    • Averaging techniques    • Homogenization Ansatz    • Use of asymptotic expansions    • Two-scale convergence    • Multiscale FEM    • Multiscale FV    • Heterogeneous multiscale methods    • Adaptive two-scale methods ECTS points 6

## Elective Modules - 3rd Semester

 Lecturer Dr.-Ing. Albrecht Eiber Content Inhalte der Vorlesung sind: Einführung, Problemstellung, Aufgaben; Modelle und Modellbildungsverfahren (Gewebe, Muskeln, Knochen); Sensorik; Motorik; Messverfahren (zur Parameteridentifikation und Diagnose); Simulation von Bewegungsabläufen sowie natürlicher und pathologischer Funktionen; Rekonstruktion gestörter Funktionen (Gelenke, Körperteile); Beispiel: das natürliche, pathologische und rekonstruierte Gehör (siehe auch unten im Abschnitt Inhalt der Vorlesung ). ECTS points 3

 Lecturer Dr.-Ing. Anton Tkachuk Content Introduction to kinematics of contact, Signorini conditions Weak and strong forms of a contact problem Spatial discretization Global and local contact search Global solution algorithms: active set and complementarity algorithms Treatment of contact for explicit time integration Treatment of contact for implicit time integration Mesh tying techniques ECTS points 6

 Lecturer Prof. Dr. C. David 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 off-the-shelf software for design or analysis. ECTS points 6

 Lecturer Prof. Dr. rer. nat. Dr. h.c. Siegfried Schmauder Content 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. Finite-Element-methods, crystal plasticity and damage mechanical modelling are further essential topics in this course. 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. Historical overview of shell theory Geometrical basics and load carrying behavior Shell models, Prerequisites and assumptions Membrane theory, basic equations and analytical solutions for shells of revolution Computation of stress resultants and displacements Bending theory, analytical solutions for cylindrical shells Computational models for shells with arbitrary geometry, shear deformable (Reissenr/Mindlin) shell finite elements Non-linear analysis and stability Application of shell elements using commercial codes ECTS points 6

 Lecturer Prof. Oliver Röhrle, PhD Content Biological processes can be modelled within a continuum-mechanical 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.  Biological tissue as a porous medium: the intervertebral disc as a porous medium, basic concepts and fundamental equations of the Theory of Porous Media. Material modelling: basic concepts and principles of material modelling, material symmetry, symmetry groups, invariants. Strain energy functions for selected material types: mechanical characteristics of soft tissues, rubber-like materials, Fung-type material laws, passive and active behaviour of the heart muscle. Student presentations on recent research studies related to the modelling of biological tissues. ECTS points 6

 Lecturer Prof. Dr.-Ing. Felix Fritzen Content MotivationData is omnipresent in engineering and science. The processing of field data and simulation results is an essential tool in knowledge building. In recent years the focus on data-oriented modeling an simulation has gained significant momentum and it has led to the establishment of this discipline as a field in its own right.ScopeThe course teaches basic elements in data acquisition, preparation, analysis, visualization and data-based/-assisted modeling. The content is particularly designed for the use in engineering and in science (mathematics, physics, chemistry). A part of the lecture is designated to the construction of data-driven surrogate models using kernel interpolation and regression and artificial neural networks.Selected topicsdenoising • filtering • statistical characterization • image processing • dimensionality reduction • Fourier Transform • Kernel interpolation and regression • introduction to artificial neural networks 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, semi-confined 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: Potential flow and groundwater flow Computational Fluid Dynamics Shallow water equations for surface water Charakteristikenmethode Examples from civil and environmental engineering ECTS points 6

 Lecturer apl. Prof. Dr.-Ing. Michael Hanss Content Fundamentals of Fuzzy theory Fuzzy logic Fuzzy systems Fuzzy control Fuzzy arithmetic Fuzzy cluster analysis ECTS points 6

 Lecturer Prof. Dr.-Ing. Marc-André 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 multi-field 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: Tensor algebra and -analysis on manifold Differential geometry of finite deformations Balance principles of nonlinear continuum thermodynamics Phenomenological material theory at finite strains Uniqueness of boundary value problems and stability theory ECTS points 6

 Lecturer Dr.-Ing. Malte von Scheven Content principal structure of a finite element code pre- and post-processing, software engineering in the context of finite element programs integration of element stiffness matrices and load vectors, implementation of boundary conditions assembly of stiffness matrices solution of linear systems of equations storage formats for sparse matrices ECTS points 6

 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: Motivation and introduction of the problem Nonlinear continuum mechanics: kinematics, transport theorems, nonlinear deformation and strain measures in absolute and convective notation Stress tensors of Cauchy, Kirchhoff, Piola-Kirchhoff, Biot,Mandel and Green-Naghdi Mechanical balance relations: balances of mass, linear momentum and angular momentum Thermodynamic balance relations: energy balance and entropy inequality (1st and 2nd law of thermodynamics) Elements of classical thermodynamics: internal energy and caloric state variables, thermodynamic potentials, Legendre transformations Thermodynamic materials theory: thermodynamic principles and process variables, material symmetry Thermoelastic solid: evaluation of the entropy principle, isotropy, the coupled problem of thermomechanics, thermoelasticity in nominal form, energy and entropy elasticity Numerical aspects: weak form of the boundary-value problem, time integration of coupled problems, linearization of the field equations, stability criteria ECTS points 6

 Lecturer Prof. 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:   Motivation: necessity for model order reduction in numerical studies; properties of parameterized mechanical systems (with examples) Continuum mechanical foundations: Heat conduction (stationary; instationary), Discrete mechanical systems (spring-mass-systems) elasto statics matrix algebra (eigenproblems/SVD, ...); formal definitions of function spaces substructuring techniques definition of local and global measures of the approximation error proper orthogonal decomposition (POD) reduced basis methods for linear time invariant problems (LTI) reduced basis methods for linear time dependent problems introduction to model order reduction of nonlinear systems numerical aspects of model order reduction for nonlinear problems ECTS points 6

 Lecturer Prof. Dr.-Ing. Marc-André Keip Content The modeling approaches are rooted in micromechanics, mostly phenomenological, and build on the framework of continuum mechanics and the thermodynamically-consistent 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: Introduction to continuum mechanics and basic modeling concepts Numerical solution of partial differential equations with the Finite Element Method in one dimension Maxwell Theory (electro-magnetism) Modeling of electro-mechanically coupled materials Modeling of magneto-mechanically coupled materials ECTS points 6

 Lecturer Prof. Dr.-Ing. Rainer Helmig Content Using complex models in engineering practice requires well-founded 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:  Theory of multiphase flow in porous media Derivation of the differential equations Constitutive relations Numerical solution of the multiphase flow equation Box method Linearisation Time discretisation Multicomponent systems Thermodynamic fundamentals and non-isothermal processes Application examples: Thermal remediation techniques CO2 storage in geological formations Water/ oxygen transport in gas diffusion layers of fuel cells 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, stick-slip vibrations, post-buckling behaviour of frames and nonlinear control techniques. Exercises and examples during the course include: hunting motion of railway vehicles, forced oscillation of a nonlinear mass-spring 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. 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: Nonlinear programming approach Dynamic programming Model predictive control Pontryagin maximum principle Applications The course is intended to students having visited SGRT/ERT lectures. 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: Erdbebenentstehung, seismische Grundlagen (Plattentektonik, seismische Wellen, Erdbebenskalen), Erdbebenfolgen und Erdbebenbeanspruchung Schwingungen mit einem Freiheitsgrad, freie ungedämpfte und gedämpfte Schwingung, erzwungene Schwingungen, Resonanz, Faltungsintegral Schwingungen mit mehreren Freiheitsgraden, modale Koordinaten, Modalanalyse Antwortspektren der Relativverschiebung, Relativgeschwindigkeit und Absolutbeschleunigung, Bemessungsgrundlagen nach DIN 4149 bzw. EC 8 Bauliche Aspekte, erdbebengerechter Entwurf, typische Schadensmuster, konstruktive Manahmen für erdbebensicheres Bauen (Grundriss, Aufriss, Gründung,Massenverteilung) Modellbildung, Ersatzstabmodell, Modell der starren Stockwerksscheiben Zeitverlaufsverfahren, numerische Integration der Schwingungsdifferential- gleichungen, Newmark-Verfahren Ausblick: weitere Methoden zur Erdbebensimulation ECTS points 6

 Lecturer Prof. Dr. Christian Holm Content Simulation Methods in Physics 1 (2 SWS Lecture + 2 SWS Tutorials in Winter Term)  History of Computers Finite-Element-Method Molecular Dynamics (MD) Integrators Different Ensembles: Thermostats, Barostats Observables Simulation of quantum mechanical problems Solving the Schrödinger equation Lattice models, Lattice gauge theory Monte-Carlo-Simulations (MC) Spin Systems, Critical Phenomena, Finite Size Scaling Statistical Errors, Autocorrelation 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: thermo-mechanical couplings, electro-mechanical couplings, chemical-mechanical 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 non-linear nature of the system of equations to be solved, special element formulations are presented. Motivation and overview Introduction to the Theory of Porous Media (TPM) Development of thermodynamically consistent material equations Continuum mechanical treatment Example: fluid-saturated porous solid Preparation of the coupled model equations for numerical implementation Verification of the model concept with sample calculation 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 vehicle-track-systems, 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

## 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: Cluster Methods Discretization of Newtonian mechanics Molecular dynamics: linked lists, parallelization Lattice Boltzmann Advanced simulation methods Partial differential equations: Schrödinger equation ECTS points 6