Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

Material-Independent Balances

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



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.


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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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