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Material-Independent Balances

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  • First Online:
Encyclopedia of Continuum Mechanics

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Synonyms

Balance of Energy; Balance of Entropy; Balance of Mass; Balance of Momentum; Balance of Moment of Momentum

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

  • Altenbach H (2018) Kontinuumsmechanik: Einführung in die materialunabhängigen und materialabhängigen Gleichungen, 4. Auflage. Springer, Berlin/Heidelberg

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  • Hadjesfandiari A, Dargush G (2011) Couple stress theory for solids. Int J Solids Struct 48(18):2496–2510

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  • 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

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  • Liu IS (2002) Continuum mechanics. Springer, Berlin

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  • Narasimhan M (1993) Principles of continuum mechanics. Cambridge University Press, Cambridge, Wiley

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  • 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

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  • Truesdell C (1968) Whence the law of moment of momentum? Springer, Berlin/Heidelberg, pp 239–271

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Author information

Authors and Affiliations

  1. Universität Magdeburg, Magdeburg, Germany

    Rainer Glüge

Authors
  1. Rainer Glüge
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Corresponding author

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, QLD, Australia

    Andreas Öchsner

Section Editor information

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

    Rainer Glüge

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Glüge, R. (2018). Material-Independent Balances. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_260-1

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  • DOI: https://doi.org/10.1007/978-3-662-53605-6_260-1

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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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