  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.
