Metamaterials are artificial structures that can manipulate and control sound waves in ways not possible with conventional materials. While much effort has been undertaken to widen the bandgaps produced by these materials through design of heterogeneities within unit cells, comparatively little work has considered the effect of engineering heterogeneities at the structural scale by combining different types of unit cells. In this paper, we use the relaxed micromorphic model to study wave propagation in heterogeneous metastructures composed of different unit cells. We first establish the efficacy of the relaxed micromorphic model for capturing the salient characteristics of dispersive wave propagation through comparisons with direct numerical simulations for two classes of metamaterial unit cells: namely phononic crystals and locally resonant metamaterials. We then use this model to demonstrate how spatially arranging multiple unit cells into metastructures can lead to tailored and unique properties such as spatially-dependent broadband wave attenuation, rainbow trapping, and pulse shaping. In the case of the broadband wave attenuation application, we show that by building layered metastructures from different metamaterial unit cells, we can slow down or stop wave packets in an enlarged frequency range, while letting other frequencies through. In the case of the rainbow-trapping application, we show that spatial arrangements of different unit cells can be designed to progressively slow down and eventually stop waves with different frequencies at different spatial locations. Finally, in the case of the pulse-shaping application, our results show that heterogeneous metastructures can be designed to tailor the spatial profile of a propagating wave packet. Collectively, these results show the versatility of the relaxed micromorphic model for effectively and accurately simulating wave propagation in heterogeneous metastructures, and how this model can be used to design heterogeneous metastructures with tailored wave propagation functionalities.
With the rapid proliferation of additive manufacturing and 3D printing technologies, architected cellular solids including truss-like 3D lattice topologies offer the opportunity to program the effective material response through topological design at the mesoscale. The present report summarizes several of the key findings from a 3-year Laboratory Directed Research and Development Program. The program set out to explore novel lattice topologies that can be designed to control, redirect, or dissipate energy from one or multiple insult environments relevant to Sandia missions, including crush, shock/impact, vibration, thermal, etc. In the first 4 sections, we document four novel lattice topologies stemming from this study: coulombic lattices, multi-morphology lattices, interpenetrating lattices, and pore-modified gyroid cellular solids, each with unique properties that had not been achieved by existing cellular/lattice metamaterials. The fifth section explores how unintentional lattice imperfections stemming from the manufacturing process, primarily sur face roughness in the case of laser powder bed fusion, serve to cause stochastic response but that in some cases such as elastic response the stochastic behavior is homogenized through the adoption of lattices. In the sixth section we explore a novel neural network screening process that allows such stocastic variability to be predicted. In the last three sections, we explore considerations of computational design of lattices. Specifically, in section 7 using a novel generative optimization scheme to design novel pareto-optimal lattices for multi-objective environments. In section 8, we use computational design to optimize a metallic lattice structure to absorb impact energy for a 1000 ft/s impact. And in section 9, we develop a modified micromorphic continuum model to solve wave propagation problems in lattices efficiently.
Material response to dynamic loading is often dominated by microstructure (grain structure, porosity, inclusions, defects). An example critically important to Sandia's mission is dynamic strength of polycrystalline metals where heterogeneities lead to localization of deformation and loss of shear strength. Microstructural effects are of broad importance to the scientific community and several institutions within DoD and DOE; however, current models rely on inaccurate assumptions about mechanisms at the sub-continuum or mesoscale. Consequently, there is a critical need for accurate and robust methods for modeling heterogeneous material response at this lower length scale. This report summarizes work performed as part of an LDRD effort (FY11 to FY13; project number 151364) to meet these needs.