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Computational Methods for Coupled Problems

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Encyclopedia of Continuum Mechanics

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Synonyms

Mathematical models for coupled problems

Definitions

Real materials very often appear as a mixture or a porous medium consisting of a solid matrix saturated by one or more fluid phases. Classical continuum mechanics can represent (but not always) their behaviors only by using very “ad hoc” phenomenological relationships. A more efficient modeling approach is to introduce balance equations for each component, that are usually smeared or “averaged” over the entire volume of the body. These equations contain also terms representing the physical (and/or chemical) interactions between the material components. The following definitions may be proposed (Markert, 2013):

  1. (1)

    coupled problem: is a problem in which physically or computationally heterogeneous components interact dynamically. The interaction is multi-way in the sense that the solution must be obtained by a simultaneous analysis of the coupled equations which model the problem;

  2. (2)

    coupled multi-field problem: is a problem...

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Authors and Affiliations

  1. Department of Civil, Environmental and Architectural Engineering, University of Padova, Padova, Italy

    Luciano Simoni & Bernhard A. Schrefler

Authors
  1. Luciano Simoni
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  2. Bernhard A. Schrefler
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Corresponding author

Correspondence to Luciano Simoni .

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. University of Sheffield, Mappin Street, Sir Frederick Mappin Building, S1 3JD, Sheffield, UK

    René de Borst

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Simoni, L., Schrefler, B.A. (2018). Computational Methods for Coupled Problems. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_23-1

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  • DOI: https://doi.org/10.1007/978-3-662-53605-6_23-1

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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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