A modified scaling law for stiffness of nanoporous materials based on gyroid cell model

Gibson-Ashby model can't well describe the experimental stiffness of nanoporous materials as the ligament size decreases to the nanoscale. We theoretically developed a refined continuum model based on a cubic, periodic arrangement of a gyroid unit cell with three-fold node connectivity. Our modified scaling law is given as E/E-s = C-1 phi + C-2 phi(2), where C-1 and C-2 account for the stretching and bending deformation mode, respectively. We found a good agreement between the simulation and theoretical calculations of the stiffness. We identified other morphological factors such as ligament aspect ratio and node to ligament volume ratio that affect the deformation behavior of the gyroid unit cell besides the relative density. A mixture of bending and stretching modes is observed in the gyroid unit cell under uniaxial tensile loading. We observed a transition from bending-stretching to stretching-dominant deformation by increasing the relative density of the gyroid unit cell.