Geometric Bounds for Buckling-Induced Auxetic Metamaterials Undergoing Large Deformation

The performance of a metamaterial is dominated by the geometric features and deformation mechanisms of its microstructure. For a certain mechanism, the geometric features have bounds in which the performance of a metamaterial such as negative Poisson’s ratio (NPR) can be designed. Previous investigation on buckling-induced auxetic metamaterial revealed that there is a geometric limit for its microstructure to exhibit auxetic behaviour in infinitesimal deformation. However, the limit for auxetic metamaterials undergoing large deformation is different from that under small deformation and has not been reported yet. In this paper, the geometric limit was investigated in an elastic and infinitesimal deformation range using linear buckling analysis. Furthermore, experimentally validated finite element models were used to identify the geometric limits for auxetic metamaterials undergoing large deformation. Depending on the control parameters of the topology, the bounds were represented by a line strip for one control parameter, an area for two control parameters and spatial domain surrounded by a 3D surface for three parameters. The limit was determined by the shape and size of the void of the metamaterials and it was identified through the large deformation analysis as well as the linear buckling analysis. We found that there was a significant difference in the geometric bounds obtained through those two methods. The results from this study can be used to design an auxetic metamaterial for different applications and to control the auxetic performance.