Tunable hyperbolic out-of-plane deformation of 3D-printed auxetic PLA shape memory arrays

Auxetic metamaterials attract wide attention due to their unusual mechanical behaviours. This work explores the tunability of the bidirectionally hyperbolic deformation of thin plates under uniaxial compression, instead of the Euler buckling deformation. Inspired by the horseshoe structures, through tuning the radius and thickness of the central circles of the horseshoes, as well as the thickness and subtending arc angles of the four branches, bidirectionally hyperbolic out of plane deformation was achieved together with auxetic behaviour. Finally, finite element simulations, theoretical analyses, and experimental verifications have been carried out to design the out of plane bidirectionally hyperbolic deformation by the tailorable temperature sensitivity and shape memory effect in unit cells.