Fluid and solid substitution of bulk modulus are exact and unique for materials whose elastic bulk and/or shear moduli fall on the Hashin-Shtrikman bounds. For materials whose moduli lie between the bounds, solid and fluid substitution of bulk moduli can be computed exactly, but not uniquely. Every initial bulk modulus can be realized with an infinite number of microstructures and therefore transform to an infinite number of moduli upon substitution of the pore fill. This nonuniqueness arises when detailed information on the material pore geometry is not available. We evaluated four embedded-bound constructions for fluid and solid substitution that were based on realizable materials. In the limiting case of pore fluids, two of these constructions reduced to the bounds of Gibiansky and Torquato, which illustrated that those bounds were optimum. For solids, the first two constructions corresponded to a homogeneous pore stiffness and predicted the smallest change in modulus. The third construction prediction corresponded to a pore space with heterogeneous stiffness, and it predicted a much larger change in modulus.

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