Mechanical attributes and wave propagation characteristics of TPMS lattice structures

The current work investigates the mechanical properties and wave propagation characteristics of sheet and solid type triply periodic minimal surface structures (TPMSs), including the gyroid, primitive, diamond, and IWP lattices over a broad range of relative density values. Their effective Young's and shear moduli, as well as their Poisson's ratio are characterized for relative densities in the range 0.15–0.6. It is found that higher-order polynomial expressions can robustly capture the entire metamaterial design space for both sheet and solid-type structures, with the mechanical performance of solid-type TPMS lattices to substantially differ from the corresponding sheet-type designs. The numerical results are experimentally verified using 3D-printed TPMS specimens. The static attributes are thereafter used to investigate the effect of the relative density and propagating direction on the long-wavelength wave characteristics of sheet and solid type TPMS lattices. It is found that the shear and longitudinal phase velocities differ the most and least in well-defined propagation directions with an in-plane angular difference of 45° for both sheet and solid-type TPMS lattices. Moreover, the primitive-type TPMS lattices are found to exhibit the highest anisotropy among the considered structures.