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Mechanical properties of porous materials such as bones for example are controlled by the geometry and structure of the pore space. Traditionally, most attempts to understand the effect of pore structure on mechanical properties have assumed that the pores can be modeled as ellipsoids Eshelby [9] etc. Nevertheless pictures taken by SEM show that pore shapes are never as simple as circles or ellipses. But the use of real pore shapes in the modeling process has been hindered by the lack of analytical solutions for these shapes. Zimmermann [24] suggested that the pore compressibility Cpc scales approximately with where A is the area of the pore space and P is the perimeter surrounding the pore space. Forcing this scaling law to be exact for a circular hole leads to the approximation . Zimmerman [25] showed that this approximation has an error of less than 8% for all hypotrochoids and an error of about 23% for thin, crack-like pores, which he suggested might be the "worst-case" shape.