Effective elastic properties and conductivity of minimal surface based stochastic and periodic metamaterials

There has been an increasing interest in investigating the mechanical properties of cellular materials that are designed based on triply periodic minimal surfaces (TPMS) and spinodal decomposition, but there have been no studies on comprehensively estimating and comparing their effective anisotropic properties. This study numerically investigates the effective anisotropic elastic properties and thermal conductivity of stochastic-TPMS and spinodal cellular materials using the finite element method. Both sheet- and ligament-based stochastic-TPMS and spinodal cellular materials are considered and compared with periodic TPMS lattices. The spinodal cellular materials are designed using the Gaussian random field (GRF) approach, whereas stochastic TPMS cellular materials are designed using different TPMS topologies by stochastically rotating the unit-cells within randomly distributed control volumes. Periodic sheet- and ligament-based cellular materials have demonstrated superior thermal conductivity and elastic characteristics compared to their stochastic counterparts at lower relative densities. Nevertheless, when the relative density increases, the stochastic sheet- and ligament-based cellular materials have exhibited these properties that are similar to their periodic equivalents. Ligament-based cellular materials have exhibited inferior thermal conductivity and elastic properties compared to sheet-based cellular materials of the same relative density. Moreover, sheet- and ligament-based stochastic cellular materials are found to have better isotropic characteristics compared to periodic cellular materials. Our research demonstrates that stochastic TPMS-based design process can yield stochastic cellular materials with enhanced elastic characteristics when suitable topology is employed, in comparison to spinodal cellular materials. This study helps in providing guidelines to adopting the best topologies of current metamaterials for certain applications.