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Einführung in die Materialtheorie (20/6)

Introduction to Theory of Materials (20/6)

Announcements

The presentation of the examination projects will take place on September 4th 2019. The project tasks will be assigned via email at least 4 weeks in advance.

The first lecture will be on Wednesday, 03.04.2019.

A consultation hour for matlab questions will be offered in the CIP pool every tuesday between 15.00h and 16.00h, starting on May 13.


Contents

 

The course gives an introduction into fundamental concepts and algorithmic formulations of the continuum-mechanics-based modelling of materials. The general thermodynamical framework including solid-mechanics-specific dissipative mechanisms is discussed in detail. Typical archetypes of such inelastic material behaviour are viscosity and plasticity, which can be combined to mimic complex non-linear and time-dependent response of various engineering materials. The course is restricted to deformations at small strains and covers the following topics:

  • Continuum Thermodynamics
  • Elasticity
  • Viscoelasticity
  • Plasticity
  • Advanced Plasticity

 
A main goal of the course is to implement the different constitutive models in a so-called constitutive driver by using MATLAB. To iterate, for instance, a uni-axial stress state, an iterative Newton algorithm is used to solve the system of non-linear equations. The underlying tangent operator possesses the same form as those required on the level of integration points within finite element simulations, so that the models and algorithms developed in this course can directly be embedded into finite element formulations.


Lectures

 

Semester Lecturer Date Location
SS 2019  Dr.-Ing. Thorsten Bartel

Wednesday, 10:15-11:45

Friday, 12:15-13:45

MB-Building,
Room 165

 

Accompanying documents for the lectures

 

Note: The lecture notes do not fully coincide with the slides provided here. Therefore, these slides are to be considered as additional and auxiliary documents.

Documents

Contents

Chapter 0

Contents

Chapter 1

Introduction

Chapter 2

Continuum Thermodynamics

Chapter 3

Elasticity

Chapter 4

Viscoelasticity

Chapter 5

Plasticity - Basic Concepts

Chapter 6

Plasticity - Advanced Concepts

Additional Material: Anisotropy

Planes of mirror symmetry

 


Tutorials

 

Semester Date Location
SS 2019

Wednesday, 10:15-11:45

Friday, 12:15-13:45

MB-Building,
Room 163
(CIP-Pool)

 

Accompanying documents for the tutorials

The documents accompanying the tutorials are to be used in preparation of each exercise. All participants are requested to become acquainted with the exercises dealing with the subject of the respective tutorial. This will ensure that all participants are on the same level of knowledge for each individual lesson.

Tutorial No.

Date

Description

Files

1

12.04.2019

First and second law of thermodynamics,

Constitutive equations

tutorial

2

17.04.2019

+

26.04.2019

Isotropic elasticity

tutorial, template, reference plots (isochoric deformation, uniaxial tension)

3

03.05.2019

Constitutive driver

tutorial, template

4

08.05.2019

Numerical tangents

tutorial, template

5

17.05.2019

Transverse isotropy

tutorial, template,

reference plots (.zip compressed folder),

animation (link to TU Dortmund fileserver)

6

05.06.2019

Viscoelasticity

tutorial, template

7

21.06.2019

Plasticity

tutorial, template, reference plots

8

10.07.2019

Temperature evolution

tutorial, template, example results (uncomment cyclic loading path!)


Examinations

Type of exam: programming homework (in small groups) concluded by a presentation including discussion.

Registration: 26.06.2019

Exam task: ---

Exam date: ---


References

 

J.C. Simo and T.J.R. Hughes. Computational Inelasticity. Springer, 1998. ebook/UB TU Dortmund
N.S. Ottosen and M. Ristinmaa. The Mechanics of Constitutive Modelling. Elsevier, 2005. ebook/UB TU Dortmund
J. Lemaitre and J.-L. Chaboche. Mechanics of Solid Materials. Cambridge University Press, 1990.
G.A. Maugin. The Thermomechanics of Plasticity and Fracture. Cambridge University Press, 1992.
P. Wriggers. Nonlinear Finite Element Methods. Springer, 2008.
P. Wriggers, W. Hauger and D. Gross Technische Mechanik 4. Springer, 2014. ebook/UB TU