Buckling of multi-layer semi-auxetic meta-plates

Cellular meta-plates combine the advantages of mechanical metamaterials and cellular materials, but their application is often limited by low post-buckling stiffness and premature failure under compression. Here, we studied the buckling and post-buckling behavior of bi-layer and multi-layer semi-auxetic meta-plates composed of layers with mismatched Poisson’s ratios. Finite element modelling was used to simulate the behavior of 3D printed samples under compression. Both experimental and numerical results demonstrated that layered structures could enhance the normalized critical buckling stress relative to the single-layer auxetic configuration with the same thickness. For instance, a tri-layer meta-plate showed a comparative increase of about 176% while maintaining s stable post-buckling behavior. In contrast, post-buckling stiffness of semi-auxetics could not compete with that of the single-layer auxetic or non-auxetic plates. Furthermore, the results suggest that, among the investigated bi-layer configurations, a greater mismatch in the volume fraction of layers improves both post-buckling stiffness and critical stress, thereby improving stability under compressive loads. Curvature analysis revealed that bending semi-auxetic meta-plates in their longitudinal direction, as with conventional single-layer plates, results in programmable curvature in the transverse direction. These results offer a promising rational design strategy for lightweight, thin, and buckling-resistant components in fields such as soft robotics, flexible electronics, and implantable medical devices with inherently curved geometries.