## Module Handbook

• Dynamischer Default-Fachbereich geändert auf MV

## Notes on the module handbook of the department Mechanical and Process Engineering

Die hier dargestellten veröffentlichten Studiengang-, Modul- und Kursdaten des Fachbereichs Maschinenbau und Verfahrenstechnik ersetzen die Modulbeschreibungen im KIS und wuden mit Ausnahme folgender Studiengänge am 28.10.2020 verabschiedet.

Ausnahmen:

# Course MV-TM-86010-K-4

## Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
2 V Lecture 3.0 CP 28 h 62 h
(2V) 3.0 CP 28 h 62 h

## Basedata

SWS 2V 3.0 CP = 90 h 1 Sem. in SuSe [4] Bachelor (Specialization) [DE] German Andrä, Heiko, Dr. habil. (EXT | DEPT: MV) Müller, Ralf, Prof. Dr.-Ing. (PROF | DEPT: MV) Sator, Christian, Dr.-Ing. (WMA | DEPT: MV) [MV-LTM] Applied Mechanics [NORM] Active

## Contents

In the lecture, partial aspects of mechanics are taught which cannot be taught in the basic lectures. The mathematical basics of tensor calculation in curvilinear coordinates are dealt with. The concepts are applied in shell theory, micromechanics and plasticity theory.
• Introduction to Tensor Calculus and Shell Theory
• Euclidean vector space
• covariant and contravariant coordinates
• vector and tensor algebra in curvilinear coordinates
• covariant derivatives, vector and tensor analysis
• membrane and bending theory for shells
• Micro Mechanics
• Eshelby solution for inclusions and inhomogeneities
• analytical homogenization
• Theory of Plasticity
• fundamentals of plastic deformation
• von Mises, Tresca, and Mohr yield surfaces
• associated and not associated flow rules
• rate dependent and rate independent plasticity

## Competencies / intended learning achievements

Students can
• state fundamental principles of tensor calculus
• analyze shell problems via membrane and bending theory
• apply the Eshelby solution to inclusions and inhomogeneities
• state and apply numerical homogenization methods
• formulate, apply, and numerically implement rate dependent and rate independent plasticity models

## Literature

• E. Klingbeil: Tensorrechnung für Ingenieure, B.I.-Hochschultaschenbuch
• D. Gross, Th. Seelig: Bruchmechanik - Mit einer Einführung in die Mikromechanik, Springer

## Materials

Blackboard, print and digital media

## Requirements for attendance (informal)

Basic knowledge in applied mechanics and higher mathematics

None

## References to Course [MV-TM-86010-K-4]

Module Name Context
[PHY-SP-4-M-7] Schwerpunktmodul Technische Mechanik WP: Obligation to choose 2V, 3.0 LP