# Reduced Order Modeling of Dynamic Mechanical Metamaterials for Analysis of Infinite and Finite Systems

## TL;DR

This paper introduces a generalized reduced order modeling approach for dynamic mechanical metamaterials that enables fast, accurate analysis of both infinite and finite systems, facilitating design and optimization processes.

## Contribution

The work develops a parameterized ROM method that simplifies MM dynamics modeling using minimal parameters and small matrices, improving computational efficiency and accuracy.

## Key findings

- Enables rapid eigen-study computations for periodic MM arrays.
- Provides accurate dynamic response predictions for finite MM systems.
- Streamlines the modeling process for MM design and optimization.

## Abstract

Dynamic mechanical metamaterials (MMs) are artificial media composed of periodic micro-structures, designed to manipulate wave propagation. Modeling and designing these materials can be computationally demanding due to the broad design space spanned by a range of geometric and material parameters. This work aims to develop a generalized reduced order modeling (ROM) approach for determining MM dynamics in low frequency ranges with accuracy and speed, using a limited number of parameters and small matrices. The MM unit cells are treated as assemblies of structural elements and discrete degrees of freedom, whose effective stiffness and inertia are determined by optimizing energy criteria based on continuum results derived from a small number of eigen-study simulations. This proposed approach offers a parameterized and discretized representation of MM systems, which leads to fast and accurate computation of eigen-study results for periodic arrays of repeating unit cells, as well as dynamic responses for finite-sized arrays. The high computational efficiency and physical accuracy of this method will help to streamline the modeling process and aid in design discovery and optimization, especially in combination with scientific machine learning and data-driven techniques.