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Atomistische Modellierung von Materialien
Atomistic Modeling of Materials

Modul MW2109

Dieses Modul wird durch Professur für Kontinuumsmechanik (Prof. Koutsourelakis) bereitgestellt.

Diese Modulbeschreibung enthält neben den eigentlichen Beschreibungen der Inhalte, Lernergebnisse, Lehr- und Lernmethoden und Prüfungsformen auch Verweise auf die aktuellen Lehrveranstaltungen und Termine für die Modulprüfung in den jeweiligen Abschnitten.


MW2109 ist ein Semestermodul in Englisch auf Master-Niveau das im Wintersemester angeboten wird.

Die Gültigkeit des Moduls ist von WS 2013/4 bis SS 2017.

GesamtaufwandPräsenzveranstaltungenUmfang (ECTS)
150 h 45 h 5 CP

Inhalte, Lernergebnisse und Voraussetzungen


The course provides an introduction to theoretical and computational aspects in the atomistic modeling and simulation of materials. It is intended for engineering students interested in statistical mechanics, in the constitutive behavior of materials from first principles and multiscale simulations. It includes a review of continuum models of material deformation and basic concepts of statistical mechanics such as phase functions, time averages, canonical distributions, and ensemble averages. Furthermore, we discuss connections between thermodynamical (continuum) and statistical mechanical (atomistic) descriptions. The most important component involves the theory and application of atomistic simulations to model, understand, and predict the properties of real materials. This includes the use of various potentials, errors and accuracy of quantitative predictions under different thermodynamic ensembles, Monte Carlo sampling and molecular dynamics simulations, and free energy computations.


Traditional engineering curriculum on materials has focused on continuum theories and models. Recent developments in computing capabilities as well as mathematical modeling have enabled the simulation of materials at the level of atoms and molecules. Such descriptions provide unparalleled insight to a variety of physical processes such as material failure and enable constitutive modeling of material behavior from first-principles. Furthermore they provide a unifying framework for treating interdisciplinary problems in bio/chemical/electronic/structural materials. Finally the predictive power of atomistic modeling enables the design and optimization of new materials with improved properties tailored for specific applications.

The most important objective is to introduce the connections between thermodynamical (continuum) descriptions that students have been exposed to in several other modules, with statistical mechanical (atomistic) descriptions. Specific topics include crystal elasticity (harmonic and quasi-harmonic approximations to crystals), constitutive laws for crystalline solids and free-energy computations. The course will enable the critical use and evaluation of computational atomistic simulation tools and discuss avenues for enabling coupling with continuum models and performing multiscale simulations.


Mathematical foundations (calculus, partial/ordinary differential equations), Continuum mechanics, Numerical analysis (linear algebra, solution of ODEs), Probability

Lehrveranstaltungen, Lern- und Lehrmethoden und Literaturhinweise

Lern- und Lehrmethoden

The learning outcomes of this module will be developed based on several coordinated teaching components. The lecture is supported when necessary by animation and demonstration of computing tools. Additionally the course includes practice examples to deepen the course content. Methods required for finishing the problems will be presented. Furthermore, there will be homework for personal study at home. Tutors are available to answer questions of students.


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Lecture slides and several readings from various sources will be provided throughout the semester


Beschreibung der Prüfungs- und Studienleistungen

There will be an exam at the end of the course.


Eine Wiederholungsmöglichkeit wird im Folgesemester angeboten.

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