Sine-based lattice plates: additive manufacturing and their mechanical properties when loaded out of plane

Purpose Demanding applications could benefit from the mathematical parametrization of lattice structures as this could lead not only to the characterization of structure–property relation but also facilitates the tailoring of the effective mechanical properties. This paper aims to characterize the mechanical performance of sine-based lattices. The characterization includes the results of in-plane Poisson’s ratio plates models, and the stiffness of additively manufactured lattice plates when loaded in the out-of-plane direction, with the objective of obtaining a relation with their geometrical parameters. Design/methodology/approach The geometrical parameter–Poisson’s ratio relationship was characterized via finite element (FE) simulations. The stiffness was also measured on additively manufactured polylactic acid lattice plates and contrasted with FE computations. Findings The characterization of auxetic lattice plates performed using in-plane and out-of-plane loading leads to key properties when deciding the geometry specific for applications: relative density, auxetic behavior and stiffness. Approximately 26% reduction of stiffness was observed between the square lattice and sine-based lattices of the same volume fraction. Originality/value Auxetic metamaterials are potential candidates for applications in biomedical engineering, smart sensors, sports and soft robotics. This paper aims to contribute to the existing gap in the study of auxetic metamaterials subjected to complex loading conditions, other than simple tension and compression, required for the mentioned applications.