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Computational Methods for Coupled Problems

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Mathematical models for coupled problems


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...


  • Thermodynamically Constrained Averaging Theory (TCAT)
  • Porous Media Mechanics
  • Schrefler
  • Solid Momentum Balance
  • Hydraulic Fracturing

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Correspondence to Luciano Simoni .

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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.

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  • Print ISBN: 978-3-662-53605-6

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