Investigating the influence of topology on elasticity in spinodal microstructures

Abstract Spinodal topologies formed through self-assembly processes exhibit unique mechanical properties, such as smoothness and non-periodicity, making them resistant to buckling and manufacturing defects. While extensive research has focused on their mechanical behavior, limited attention has been given to understanding the impact of their complex topology. This study aims to investigate the relationship between the topological features of two-dimensional spinodal topologies, characterized using computational homology, and their elastic response by analyzing scaling laws. Sensitivity analysis was conducted to determine the influence of various topological characteristics on Young's modulus and Poisson's ratio. Computational homology techniques were used to measure Betti numbers, which represent the number of loops and disjoint regions in the spinodal topologies. Additionally, these techniques were also employed to determine the size of these loops and regions. Among all the topological characteristics studied, the number and size of loops were found to have the highest influence on the elastic properties, specifically Young's modulus and Poisson's ratio. Understanding the rules that govern the way two-dimensional spinodal topologies respond elastically is crucial for comprehending how they behave mechanically and for optimizing their performance. The research findings highlight the significant impact of certain topological features, specifically the number and size of loops, on the material properties. This knowledge provides valuable insights for designing and engineering spinodal structures.