Conductivity and Young's modulus of porous metamaterials based on Gibson-Ashby cells

The effective conductivity and Young's modulus of metamaterials based on Gibson-Ashby cells have been calculated numerically. It is shown that the porosity dependences of these properties do not follow the Gibson-Ashby relations for open-cell foams, although the latter have been derived on the basis of this model. For low-porosity metamaterials with porosity 0.016 the relative conductivity and Young's modulus are still as low as 0.80 and 0.65, respectively. It is shown that these low relative property values are caused by the strongly oblate shape of the pores, which become microcrack-like voids as zero porosity is approached.