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Continuum Mechanics Basics, Introduction and Notations

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Encyclopedia of Continuum Mechanics

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Synonyms

Mechanical field theory; Tensor notation

Definition

Continuum mechanics is the branch of mechanics that seeks to describe the mechanical behavior of bodies in terms of fields.

Overview

Continuum mechanics is a theory thats seeks to describe the mechanical behavior of bodies in terms of fields, presuming a continuous distribution of matter in space. It is classically divided into three parts, namely, kinematics, general balances, and material modeling.

Kinematics is the geometry of deformable solids, concerned with defining appropriate deformation measures that are extracted, for example, from the displacement field of a body. These deformation measures enter the material modeling, which specify the stress tensor field for a given movement of a body. The latter has to satisfy the local balances of momentum and moment of momentum. Thus, the overall structure is where the second line is the specification of the first line for small-strain linear quasistatic elasticity. While...

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References

  • Altenbach H (2015) Kontinuumsmechanik: Einführung in die materialunabhängigen und materialabhängigen Gleichungen, 3. Auflage. Springer, Berlin/Heidelberg

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Author information

Authors and Affiliations

  1. Fakultät für Maschinenbau, Lehrstuhl Technische Mechanik, Institut für Mechanik, Otto-von-Guericke-Universität, Magdeburg, Germany

    Rainer Glüge

Authors
  1. Rainer Glüge
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Correspondence to Rainer Glüge .

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. Lehrstuhl Technische Mechanik, Institut für Mechanik, Fakultät für Maschinenbau, Otto-von-Guericke-Universität, Universitätsplatz 2, 39106, Magdeburg, Germany

    Rainer Glüge

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Glüge, R. (2018). Continuum Mechanics Basics, Introduction and Notations. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_264-1

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  • DOI: https://doi.org/10.1007/978-3-662-53605-6_264-1

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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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