Tunable auxeticity and elastomechanical symmetry in a class of very low density core-shell cubic crystals

Thin-walled metamaterials based on triply periodic surfaces are relatively simple, light-weight structures that, as shown in the following, possess extraordinary material properties. As opposed to their filled counterparts, these structures can be tuned to be elastically isotropic and isotropically auxetic - the latter is the material property of extending in all directions under tensile loading in one direction. Considering level surfaces topologically equivalent to the triply periodic minimal surfaces of types Primitive, Diamond, Gyroid and I-WP, we focus on stiffness, symmetry, auxeticity, Cauchy pressure and proximity to Born mechanical instability. Our findings show that core-shell structures respond drastically differently not only in their stiffness but also for each of these observed properties compared to their counterparts with complete filling. Only core-shell topology makes elastic isotropy possible. Diamond core-shell structures are the only ones which show negative Cauchy pressure p_C<0. Most notably, for the Diamond core-shell structures we observe an auxetic behavior spanning over the whole range from non-auxetic to isotropically auxetic. For the structures possessing auxeticity, negativity in the Poisson's ratio is retained for a wide deformation range spanning from small-strain tension to large-strain compression.