Topological High-Entropy Disorder Mechanical Metamaterial Made of Honeycomb with Hat Cell

People have always hoped to be able to fill an entire plane with 'single unit cells' without periodicity. This wish was realized after the mathematician discovered a 13-sided ``single cell'' named `einstein', we also refer to it as a hat tiling. These non-periodic tessellations generally exhibit anisotropic properties, making them superior in terms of mechanical performance compared to periodic structures, the application of non-periodic hat tiling in the study of honeycomb metamaterial structures. From the perspective of information entropy, the reason behind the improved mechanical properties of these structures is the higher entropy associated with non-periodic configurations. To quantify the disorder of non-periodic structures, we propose an entropy expression for the `einstein' metamaterial. To demonstrate the mechanical properties of these high-entropy structures, we fabricate specimens using 3D printing and conducte mechanical experiments. For comparative analysis, we also use ABAQUS to perform finite element analysis of the problem. The research results reveal that the mechanical properties of high-entropy structures created by the non-periodic stacking of cells are significantly improved compared to those of low-entropy structures created by periodic stacking. The conclusions drawn from the study of individual issues are generalizable and may be of assistance in future material and structural design.