Waves in Porous and Granular Materials

  • K. Wilmanski
Part of the International Centre for Mechanical Sciences book series (CISM, volume 400)


The work contains an exposition of continuum theories of wave propagation in porous and granular materials. After a brief presentation of some observations which distinguish multicomponent systems from other macroscopic bodies we remind the theory of waves in a single component linear elastic material. On this example we point out the neccessity of research in the field of scattering of waves on microscopic heterogeneities which are characteristic for porous and granular materials. A simple example from the theory of mixtures of fluids which indicates the existence of many modes of propagation of sound waves justifies the choice of a multicomponent model for the description of porous and granular media. The most extensive part of the work is devoted to the analysis of wave propagation in two-component systems under isothermal conditions. We use the author’s model containing an additional balance equation for porosity which, in turn, enables to require the hyperbolicity of the set of field equations. A compact review of classical models stemming from the famous work of Biot is also presented in these notes. We concentrate particularly on contributions of Russian scientists whose work is less known in the western hemisphere. Some remarks are also made on the propagation of shock waves. This part is rather short as the results in this field of research are still very scarce. The work is completed by a rather extensive list of references. Its aim is to simplify the beginning of an own research in the field of wave propagation in multicomponent systems.


Shock Wave Porous Medium Field Equation Porous Material Constitutive Relation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Wien 1999

Authors and Affiliations

  • K. Wilmanski
    • 1
  1. 1.Weierstrass Institute for Applied Analysis and StochasticsBerlinGermany

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