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Dislocations and Cracks in Generalized Continua

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Encyclopedia of Continuum Mechanics

Synonyms

Cracks; Defects; Dislocation core; Dislocations; Eigenstrain; Generalized continua; Gradient elasticity; Higher-order continua; Nonlocality; Non-singular dislocation continuum theory; Regularization

Definitions

Dislocations play a key role in the understanding of many phenomena in solid-state physics, materials science, crystallography, and engineering. Dislocations are line defects producing distortions and self-stresses in an otherwise perfect crystal lattice. In particular, dislocations are the primary carrier of crystal plasticity and in dislocation-based fracture mechanics.

Using classical continuum theories, the fields produced by defects (dislocations, disclinations, and cracks) possess singularities since classical continuum theories are not valid near the defect (Kröner, 1958; de Wit, 1973). Singularities and infinities are an important problem in classical continuum theories. In order to obtain singularity-free fields, a proper regularization method must be used.

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Acknowledgements

The author acknowledges a grant obtained from the Deutsche Forschungsgemeinschaft (grant number La1974/4-1).

Author information

Authors and Affiliations

  1. Department of Physics, Institute of Solid State Physics, Darmstadt University of Technology, Darmstadt, Germany

    Markus Lazar

Authors
  1. Markus Lazar
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Corresponding author

Correspondence to Markus Lazar .

Editor information

Editors and Affiliations

  1. Institut für Mechanik, Otto-von-Guericke-Universität Institut für Mechanik, Magdeburg, Germany

    Holm Altenbach

  2. Griffith University (Gold Coast Campus), Griffith School of Engineering Griffith University (Gold Coast Campus), Southport, Queensland, Australia

    Andreas Öchsner

Section Editor information

  1. Centre des Matériaux UMR 7633, Mines ParisTech CNRS, 10 rue Henri Desbruères, BP 87, 91003, Evry Cedex, France

    Samuel Forest

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Lazar, M. (2018). Dislocations and Cracks in Generalized Continua. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_153-1

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  • DOI: https://doi.org/10.1007/978-3-662-53605-6_153-1

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53605-6

  • Online ISBN: 978-3-662-53605-6

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

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