Impact of Geometric and Modelling Discrepancies on the Dispersion Dynamics of Lattice Metastructures

Mechanical metamaterials (MMMs) are periodic architectures engineered to achieve extraordinary macroscopic mechanical properties. A primary objective in their design is wave propagation isolation, achieved through the generation of phononic bandgaps. These bandgaps are highly sensitive to the geometric features of the underlying unit cell, which is frequently based on a lattice topology. While additive manufacturing has become the predominant approach for fabricating these MMMs, a persistent challenge remains: standard finite element (FE) models based on nominal designs may differ from both the manufactured geometry and its numerical representation. In this context, manufacturing-induced geometric deviations and FE modelling discrepancies can both lead to dispersion characteristics that diverge from the intended behaviour. The present work focuses on the latter through a controlled numerical sensitivity study. This work assesses the impact of these FE modelling errors on the dynamic response of lattice metastructures by simulating structural deviations through conditional node addition and relocation. Specifically, we investigate the influence of two distinct scenarios that lead to significantly different outcomes: nodes subjected to Floquet–Bloch periodic boundary conditions, and interior nodes unaffected by these boundary constraints. Finally, a quantitative threshold for the maximum permissible modeling error is established for each case.