Computational Modeling of the Mechanics of Elastic Structural Lattices: Effects of Lattice Architecture and Hierarchy

Abstract

This thesis establishes advanced theoretical-computational techniques to understand and predict the mechanical properties of structural lattice metamaterials with a focus on the effective elastic properties. First, attention is devoted to the effective stiffness of hierarchical nanolattices, which depends on lattice topology, architecture, and inherent geometric imperfections. A computational substructuring technique is applied to predict the mechanics of hierarchical truss networks containing thousands to millions of truss members, with each solid, hollow-tube, or composite truss member requiring full-detail 3D resolution. By applying this methodology to hierarchical nanolattices structural hierarchy is shown to span several decades of relative density and effective stiffness with near-ideal effective stiffness scaling. Comparisons between experimental data and model predictions show convincing agreement and highlight the lattice sensitivity to fabrication-induced geometric imperfection. Second, elastic stress wave propagation in structural lattices is investigated with a focus on wave beaming (i.e., directional energy flow) under harmonic mechanical excitation. A new technique is introduced to obtain pseudo-continuous maps of group velocity magnitude vs. propagation direction vs. frequency to predict directional wave propagation, demonstrating traditional beaming prediction techniques are insufficient for many scenarios. The method is applied to two-dimensional structural lattices to predict directional energy flow. Predictions are verified by comparison to explicit dynamic simulations showing the limitations of the classical dispersion relation method. Overall, improved computational techniques are presented to better described, understand, predict and optimize the elastic behavior of truss lattices.