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Mackenzie result for pressurized pore space

 

A useful exact result has been derived by Mackenzie [31], for an isotropic porous solid filled with a gas or liquid at a pressure p. The expansion of the material is given exactly by an equation involving only the bulk modulus of the solid frame, Ks, the effective bulk modulus of the porous solid, K, and the pressure p. This is analogous to the Hashin-Rosen result, where only the effective bulk modulus of the composite had to be known in order to be able to compute the effective thermal expansion. The strain ε is exactly given by:

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In 2-D, simply replace the "3" by "2" in eq. (73), and use the 2-D bulk moduli (see Sec. 6.3 for suggestions on implementing this computation and a test using Mackenzie's result).


Next: CLM Theorem Up: Exact solutions for Previous: Hashin and Rosen