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Introduction to Geometrically Nonlinear Continuum Dislocation Theory

FE Implementation and Application on Subgrain Formation in Cubic Single Crystals Under Large Strains

  • Book
  • © 2021

Overview

Authors:
  1. Christian B. Silbermann

    1. Institute of Mechanics and Thermodynamics, Chemnitz University of Technology, Chemnitz, Germany

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  2. Matthias Baitsch

    1. Bau- und Umweltingenieurwesen, Bochum University of Applied Sciences, Bochum, Germany

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  3. Jörn Ihlemann

    1. Institute of Mechanics and Thermodynamics, Chemnitz University of Technology, Chemnitz, Germany

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  • Comprehensive introduction to single crystal plasticity with continuously distributed dislocations
  • Provides a straightforward preparation for the implementation into FEM codes
  • Presents simulations introducing the characteristics of pattern forming systems

Part of the book series: SpringerBriefs in Applied Sciences and Technology (BRIEFSAPPLSCIENCES)

Part of the book sub series: SpringerBriefs in Continuum Mechanics (BRIEFSCONTINU)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Introduction

    • Christian B. Silbermann, Matthias Baitsch, Jörn Ihlemann
    Pages 1-3

  3. Nonlinear Kinematics of a Continuously Dislocated Crystal

    • Christian B. Silbermann, Matthias Baitsch, Jörn Ihlemann
    Pages 5-13

  4. Crystal Kinetics and -Thermodynamics

    • Christian B. Silbermann, Matthias Baitsch, Jörn Ihlemann
    Pages 15-26

  5. Special Cases Included in the Theory

    • Christian B. Silbermann, Matthias Baitsch, Jörn Ihlemann
    Pages 27-31

  6. Variational Formulation of the Theory

    • Christian B. Silbermann, Matthias Baitsch, Jörn Ihlemann
    Pages 33-41

  7. Numerical Solution with the Finite Element Method

    • Christian B. Silbermann, Matthias Baitsch, Jörn Ihlemann
    Pages 43-55

  8. FE Simulation Results

    • Christian B. Silbermann, Matthias Baitsch, Jörn Ihlemann
    Pages 57-77

  9. Outlook

    • Christian B. Silbermann, Matthias Baitsch, Jörn Ihlemann
    Pages 79-84

  10. Back Matter

    Pages 85-94
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Keywords

About this book

This book provides an introduction to geometrically non-linear single crystal plasticity with continuously distributed dislocations. A symbolic tensor notation is used to focus on the physics. The book also shows the implementation of the theory into the finite element method. Moreover, a simple simulation example demonstrates the capability of the theory to describe the emergence of planar lattice defects (subgrain boundaries) and introduces characteristics of pattern forming systems. Numerical challenges involved in the localization phenomena are discussed in detail.

Authors and Affiliations

  • Institute of Mechanics and Thermodynamics, Chemnitz University of Technology, Chemnitz, Germany

    Christian B. Silbermann, Jörn Ihlemann

  • Bau- und Umweltingenieurwesen, Bochum University of Applied Sciences, Bochum, Germany

    Matthias Baitsch

About the authors

Christian B. Silbermann studied Mechanical Engineering at the University of Technology (TU) Chemnitz, with focus on applied mechanics and thermodynamics. Currently he is Scientific Assistant at TU Chemnitz at the Institute of Mechanics and Thermodynamics, Professorship of Solid Mechanics. This book is based on the author’s doctoral thesis.

Bibliographic Information

  • Book Title: Introduction to Geometrically Nonlinear Continuum Dislocation Theory

  • Book Subtitle: FE Implementation and Application on Subgrain Formation in Cubic Single Crystals Under Large Strains

  • Authors: Christian B. Silbermann, Matthias Baitsch, Jörn Ihlemann

  • Series Title: SpringerBriefs in Applied Sciences and Technology

  • DOI: https://doi.org/10.1007/978-3-030-63696-8

  • Publisher: Springer Cham

  • eBook Packages: Chemistry and Materials Science, Chemistry and Material Science (R0)

  • Copyright Information: The Author(s), under exclusive license to Springer Nature Switzerland AG 2021

  • Softcover ISBN: 978-3-030-63695-1Published: 03 March 2021

  • eBook ISBN: 978-3-030-63696-8Published: 02 March 2021

  • Series ISSN: 2191-530X

  • Series E-ISSN: 2191-5318

  • Edition Number: 1

  • Number of Pages: XIII, 94

  • Number of Illustrations: 43 b/w illustrations, 18 illustrations in colour

  • Topics: Structural Materials, Classical and Continuum Physics

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