The Effect of Fluid and Solid Properties on the Auxetic Behavior of Porous Materials Having Rock-like Microstructures

Materials with a negative Poisson's Ratio (PR), known as auxetics, exhibit the counterintuitive behavior of becoming wider when uniaxially stretched and thinner when compressed. Though negative PR is characteristic of polymer foams or cellular solids, tight as well as highly porous rocks have also been reported to exhibit a negative Poisson's ratio, both from dynamic (PRd) and static measurements. We propose a novel auxetic structure based on pore-space configuration observed in rocks. First, we performed 2D and 3D imaging of a pumice and tight basalt to analyze their rock microstructure as well as similarities to natural structures of auxetic materials - e.g., cork. Based on these analyses, we developed a theoretical auxetic 3D model consisting of rotating rigid bodies having pore configurations similar to those observed in rocks. To alleviate the mechanical assumption of rotating bodies, the theoretical model was modified to include crack-like features being represented by intersecting, elliptic cylinders. We then used a 3D printer to create a physical version of the modified model, whose PRd was tested. We also numerically explored how the compressibility of fluids located in the pore-space of the modified model as well as how the elastic properties of the material from which the model is made of affect its auxetic behavior. We conclude that for a porous medium composed of a single material saturated with a single fluid (a) the more compliant the fluid is and (b) the lower the PR of the solid material, the lower the PR value of the composite material.