Amorphous materials exhibit complex mechanical behaviors owing to their unique disordered structures. Among these, auxetic materials, which possess a negative Poisson's ratio (NPR), have garnered considerable attention for their superior properties. A key bottleneck in this research area is the pervasive non‐affinity in amorphous networks, wherein the displacements of internal nodes are nonlinearly correlated with the strain field imposed at the boundaries. This non‐affinity precludes the a priori identification of structural motifs that dominantly contribute to the network's auxetic behavior. Consequently, a globally optimal strategy for guiding the design of network structures with specific NPR values has been lacking. This creates a vicious cycle in theoretical research: The absence of an a priori theory prevents the development of a globally optimal design methodology. This lack of a design methodology, in turn, hinders the acquisition of sufficient research samples, which are necessary to develop such a theory. This Review summarizes the theoretical and experimental progress concerning these key physical mechanisms. It further introduces how machine learning can be leveraged to break this vicious cycle and elucidate the origins of NPR in disordered structures. The articulation of this research process provides a valuable case study for the “AI for Science” paradigm.
Lü et al. (Sun,) studied this question.