Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

Material-Independent Balances

  • Rainer Glüge
Living reference work entry
DOI: https://doi.org/10.1007/978-3-662-53605-6_260-1

Synonyms

Definition

A balance equation expresses the change of physical quantities with respect to time. For three-dimensional bodies, the physical quantity can flow through the surface of the balance volume and be generated or vanish inside the volume. Balancing the conserved quantities’ mass, momentum, and moment of momentum yields the fundamental equations of mechanics. Balancing the conserved quantity energy and the non-conserved entropy yields the laws of thermodynamics.

Overview

The material-independent principles of continuum mechanics are:
  • balance of mass

  • balance of momentum

  • balance of moment of momentum

  • balance of energy

  • balance of entropy.

Here, we will only deal with the first three conservation laws. The thermodynamical balance equations are treated in Hütter ( 2019). Other accounts to this topic include Liu ( 2002) and Narasimhan ( 1993).
We introduce the balances in a...
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References

  1. Altenbach H (2018) Kontinuumsmechanik: Einführung in die materialunabhängigen und materialabhängigen Gleichungen, 4. Auflage. Springer, Berlin/HeidelbergCrossRefGoogle Scholar
  2. Cosserat F, Cosserat E (1909) Théorie des corps déformables. A. Hermann et filszbMATHGoogle Scholar
  3. Germain P (1973) The method of virtual power in continuum mechanics. Part 2: microstructure. SIAM J Appl Math 25(3):556–575CrossRefGoogle Scholar
  4. Glüge R (2019) Continuum mechanics basics, introduction and notations. In: Glüge R (ed) Encyclopedia of continuum mechanics. Springer, Berlin/Heidelberg, pp 1–8. https://doi.org/10.1007/978-3-662-53605-6_264-1 Google Scholar
  5. Hadjesfandiari A, Dargush G (2011) Couple stress theory for solids. Int J Solids Struct 48(18):2496–2510CrossRefGoogle Scholar
  6. Hütter G (2019) Coleman–Noll procedure for classical and generalized continuum theories. In: Ivanova E (ed) Encyclopedia of continuum mechanics. Springer, Berlin/Heidelberg, pp 1–8. https://doi.org/10.1007/978-3-662-53605-6_57-1 Google Scholar
  7. Liu IS (2002) Continuum mechanics. Springer, BerlinCrossRefGoogle Scholar
  8. Narasimhan M (1993) Principles of continuum mechanics. Cambridge University Press, Cambridge, WileyzbMATHGoogle Scholar
  9. Naumenko K, Altenbach H (2016) Modeling high temperature materials behavior for structural analysis: part I: continuum mechanics foundations and constitutive models. Advanced structured materials. Springer International. https://books.google.de/books?id=sK8qDAAAQBAJ Google Scholar
  10. Truesdell C (1968) Whence the law of moment of momentum? Springer, Berlin/Heidelberg, pp 239–271Google Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Universität MagdeburgMagdeburgGermany

Section editors and affiliations

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