Model Reduction of Self-Repeating Structures with Applications to Metamaterial Modeling

Abstract

The dynamic behavior of metamaterials and metastructures is often modeled using finite elements; however, these models can become quite large and therefore computationally expensive to simulate. Traditionally, large models are made smaller using any of the array of model reduction methods, such as Guyan or Craig-Bampton reduction. The regularized nature of metamaterials makes them excellent candidates for reduced-order modeling because the system is essentially comprised of a repeating pattern of unit cell components. These unit cell components can be reduced and then assembled to form a reduced-order system-level model with equivalent dynamics. The process is demonstrated using a finite element model of a 1-D axially vibrating metamaterial bar using Guyan, SEREP, and Craig-Bampton reduction methods. The process is shown to provide substantial reduction in the time needed to simulate the dynamic response of a representative metamaterial while maintaining the dynamics of the system and resonators.