Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

Continuum Mechanics Basics, Introduction and Notations

  • Rainer GlügeEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-3-662-53605-6_264-1



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


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 Open image in new windowwhere the second line is the specification of the first line for small-strain linear...

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  1. Altenbach H (2015) Kontinuumsmechanik: Einführung in die materialunabhängigen und materialabhängigen Gleichungen, 3. Auflage. Springer, Berlin/HeidelbergGoogle Scholar
  2. Bertram A (2012) Elasticity and plasticity of large deformations – an introduction, 3rd edn. Springer, BerlinGoogle Scholar
  3. Horák M, Ryckelynck D, Forest S (2017) Hyper-reduction of generalized continua. Comput Mech 59(5):753–778Google Scholar
  4. Itskov M (2007) Tensor algebra and tensor analysis fon engineers. Springer, BerlinGoogle Scholar
  5. Lurie A, Belyaev A (2010) Theory of elasticity. Foundations of engineering mechanics. Springer, Berlin/HeidelbergGoogle Scholar
  6. Miehe C (2003) Computational micro-to-macro transition for discretized micro-structures of heterogeneous materials at finite strains based on the minimization of averaged incremental energy. Comput Methods Appl Mech Eng 192:559–591Google Scholar
  7. Sochi T (2016) Tensor calculus. ArXiv Preprint Server. arXiv:1610.04347Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Fakultät für Maschinenbau, Lehrstuhl Technische Mechanik, Institut für MechanikOtto-von-Guericke-UniversitätMagdeburgGermany

Section editors and affiliations

  • Rainer Glüge
    • 1
  1. 1.Lehrstuhl Technische Mechanik, Institut für Mechanik, Fakultät für MaschinenbauOtto-von-Guericke-UniversitätMagdeburgGermany