Astronomy and Astrophysics – Astronomy
Scientific paper
Dec 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008geoji.175.1309b&link_type=abstract
Geophysical Journal International, Volume 175, Issue 5, pp. 1309-1320.
Astronomy and Astrophysics
Astronomy
Microstructure, Permeability And Porosity, Seismic Anisotropy, Wave Propagation, Acoustic Properties
Scientific paper
We derive double inequalities providing the bounds for components of the effective stiffness tensor of a two-phase, porous-cracked medium with aligned ellipsoidal inclusions. The bounds are derived on the basis of the Hashin-Shtrikman variational principle, and the conditions for positive semi-definiteness of quadratic forms. Inequalities are presented for isotropic, cubic, hexagonal and orthorhombic overall symmetries. The results obtained for orthorhombic symmetry are valid for the general determination of transport properties (effective permeability, thermal and electrical conductivity). We conclude that inequalities for diagonal components of the effective tensor have the form of bounds, whereas in general these bounds do not exist for off-diagonal components. One important implication of this is that Voigt-Reuss averages do not provide the upper and lower bounds for off-diagonal components of the effective tensor, as is sometimes assumed. We also present numerical results for stiffness bounds obtained by modelling various shales with isotropic, transverse isotropic and orthorhombic overall symmetries.
Bayuk Irina O.
Chesnokov Evgeni M.
Gay Juliana K.
Hooper John M.
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