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Sufficient conditions for hyperbolicity and consistency of the dynamic equations for fluid-saturated solids

Osinov, Vladimir A.

Abstract:
Previous studies showed that the dynamic equations for a porous fluid-saturated solid may lose hyperbolicity and thus render the boundary-value problem ill-posed while the equations for the same but dry solid remain hyperbolic. This paper presents sufficient conditions for hyperbolicity in both dry and saturated states. Fluid-saturated solids are described by two different systems of equations depending on whether the permeability is zero or nonzero (locally undrained and drained conditions, respectively). The paper also introduces a notion of wave speed consistency between the two systems as a necessary condition which must be satisfied in order for the solution in the locally drained case to tend to the undrained solution as the permeability tends to zero. It is shown that the symmetry and positive definiteness of the acoustic tensor of the skeleton guarantee both hyperbolicity and the wave speed consistency of the equations.

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Verlagsausgabe §
DOI: 10.5445/IR/1000130923
Veröffentlicht am 25.03.2021
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Bodenmechanik und Felsmechanik (IBF)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2021
Sprache Englisch
Identifikator ISSN: 0939-1533, 0020-1154, 1432-0681
KITopen-ID: 1000130923
Erschienen in Archive of Applied Mechanics
Verlag Springer
Nachgewiesen in Scopus
Web of Science
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