Elastic wave propagation in cubic lattices with triply periodic minimal surfaces

Abstract

In this work, the goal was to explore the application of periodic boundary conditions to any three-dimensional model and leverage the benefit of unit cell models over computationally heavy time-domain analysis models. Ultimately, the periodic boundary conditions are applied to complex topological models such as Triply Periodic Minimal Surfaces (TPMS). The first hurdle was to accurately describe the frequency response of simple one-dimensional models followed by two dimensional and three dimensional models. The final hurdle was to model various TPMS structures using approximated trigonometric functions to define their unit cell structure and apply periodic boundary conditions for frequency response behavior. An analysis of the unit cell was accomplished to determine and characterize the dispersion curves for Schwarz Primitive, Schwarz Diamond, Gyroid, Fischer Koch S, IWp, and FRD. The analysis was accomplished by applying the Floquet boundary conditions using Python scripting in Abaqus. By applying constraint equations on the unit cells, eigenfrequencies are plotted for the First Irreducible Brillouin Zone. TPMS structures have garnered significant interest due to their lightweight and high strength properties, along with their porous nature. In the aerospace discipline, much research is being conducted to create lightweight metamaterials with high strength properties. Defining the frequency dispersion plots for these structures has the added advantage of engineering wave propagation properties to customize shock absorption, wave-beaming, and the introduction of resonance engineering for double structures of different material properties.