Reduced order modeling of cellular resonator-based mechanical metamaterials under impact and GA-based parameter extraction

Cellular resonator-based mechanical metamaterial can be used to create media that efficiently absorb large impact loadings. Modelling arrays of these structures over time can be computationally intensive with traditional finite element analysis (FEA), as arrays of these metamaterials can contain large numbers of cells that each have relatively small elements. Reduced order modelling was employed to minimize the computational complexity of simulating these arrays. Modelling mechanical resonators as complex mass-spring systems, a versatile reduced order model (ROM) was created and compared with a continuum model employing traditional FEA. To further improve model fit and better understand the limitations of the ROM, its parameters were optimized with a genetic algorithm (GA). Analysis of the models showed that the ROM could accurately model metamaterial arrays. The GA optimization was also shown to significantly improve the model performance and highlighted the edge cells behavior as a potential challenge faced by an unoptimized ROM of metamaterial arrays. Reduced order modelling provides potential to rapidly analyze metamaterial resonators with a high degree of accuracy, allowing for efficient analysis of large, more complex systems and streamlining the optimization of graded designs for desired array performance.