On well-posedness of the dynamic problem for an anisotropic fluid-saturated solid |
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Authors: | V A Osinov |
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Institution: | (1) Institute of Geotechnical Engineering, University of Natural Resources and Applied Life Sciences, Feistmantelstr. 4, 1180 Vienna, Austria |
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Abstract: | It is known that a high degree of anisotropy in the constitutive behaviour of a solid may result in the loss of hyperbolicity
of the dynamic equations in the form of either complex-conjugate or purely imaginary characteristic wave speeds (flutter ill-posedness
and shear band formation, respectively). In the present paper we investigate the characteristic wave speeds in the dynamic
problem for a transversely isotropic fluid-saturated porous solid. Three cases are considered: a dry solid and a saturated
solid under locally undrained and drained conditions. It is shown that, for given constitutive parameters of the solid skeleton,
the dynamic problem for a drained solid may become ill-posed due to the flutter-type loss of hyperbolicity, while the dynamic
equations for a dry and an undrained solids remain hyperbolic. For a given solid skeleton, the characteristic wave speeds
are strongly influenced by the pore fluid compressibility which, in turn, is extremely sensitive to the presence of a small
amount of free gas. |
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Keywords: | Fluid-saturated solid Wave speeds Hyperbolicity Flutter ill-posedness Transverse isotropy |
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