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• W2131409989 abstract "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." @default.
• W2131409989 created "2016-06-24" @default.
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• W2131409989 date "2008-12-01" @default.
• W2131409989 modified "2023-09-27" @default.
• W2131409989 title "Upper and lower stiffness bounds for porous anisotropic rocks" @default.
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• W2131409989 doi "https://doi.org/10.1111/j.1365-246x.2008.03925.x" @default.
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