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

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

Resilient 3D hierarchical architected metamaterials

Hierarchically designed structures with architectural features that span across multiple length scales are found in numerous hard biomaterials, like bone, wood, and glass sponge skeletons, as well as manmade structures, like the Eiffel Tower. It has been hypothesized that their mechanical robustness and damage tolerance stem from sophisticated ordering within the constituents, but the specific role of hierarchy remains to be fully described and understood. We apply the principles of hierarchical design to create structural metamaterials from three material systems: (i) polymer, (ii) hollow ceramic, and (iii) ceramic–polymer composites that are patterned into self-similar unit cells in a fractal-like geometry. In situ nanomechanical experiments revealed (i) a nearly theoretical scaling of structural strength and stiffness with relative density, which outperforms existing nonhierarchical nanolattices; (ii) recoverability, with hollow alumina samples recovering up to 98% of their original height after compression to ≥50% strain; (iii) suppression of brittle failure and structural instabilities in hollow ceramic hierarchical nanolattices; and (iv) a range of deformation mechanisms that can be tuned by changing the slenderness ratios of the beams. Additional levels of hierarchy beyond a second order did not increase the strength or stiffness, which suggests the existence of an optimal degree of hierarchy to amplify resilience. We developed a computational model that captures local stress distributions within the nanolattices under compression and explains some of the underlying deformation mechanisms as well as validates the measured effective stiffness to be interpreted as a metamaterial property

Automated Additive Construction (AAC) for Earth and Space Using In-situ Resources

Using Automated Additive Construction (AAC), low-fidelity large-scale compressive structures can be produced out of a wide variety of materials found in the environment. Compressionintensive structures need not utilize materials that have tight specifications for internal force management, meaning that the production of the building materials do not require costly methods for their preparation. Where a certain degree of surface roughness can be tolerated, lower-fidelity numerical control of deposited materials can provide a low-cost means for automating building processes, which can be utilized in remote or extreme environments on Earth or in Space. For space missions where every kilogram of mass must be lifted out of Earth’s gravity well, the promise of using in-situ materials for the construction of outposts, facilities, and installations could prove to be enabling if significant reduction of payload mass can be achieved. In a 2015 workshop sponsored by the Keck nstitute for Space Studies, on the topic of Three Dimensional (3D) Additive Construction For Space Using In-situ Resources, was conducted with additive construction experts from around the globe in attendance. The workshop explored disparate efforts, methods, and technologies and established a proposed framework for the field of Additive Construction Using In-situ Resources. This paper defines the field of Automated Additive Construction Using In-situ Resources, describes the state-of-the-art for various methods, establishes a vision for future efforts, identifies gaps in current technologies, explores investment opportunities, and proposes potential technology demonstration missions for terrestrial, International Space Station (ISS), lunar, deep space zero-gravity, and Mars environments

Auxeticity in truss networks and the role of bending versus stretching deformation

Auxetic behavior (i.e., a negative value of Poisson's ratio) has been reported for a variety of cellular networks including truss structures. Commonly, this implies that the geometric arrangement of truss members within a periodic unit cell is designed to achieve the negative Poisson effect, e.g., in the reentrant honeycomb configuration. Here, we show that elastic periodic truss lattices can be tuned to display auxeticity by controlling the ratio of bending to stretching stiffness. If the nodal stiffness (or the bending stiffness) is low compared to the stretching stiffness of individual truss members, then the lattice is expected to exhibit a positive Poisson's ratio, showing lateral expansion upon uniaxial compression. In contrast, if the nodal or bending stiffness is high (and buckling is prevented), the lattice may reveal auxetic behavior, contracting laterally under uniaxial compression. This effect is demonstrated in two dimensions for the examples of square and triangular lattices, and it is confirmed both analytically in the limit of small strains as well as numerically for finite elastic deformation. Under large deformation, instability additionally gives rise to auxetic behavior due to truss buckling

Auxeticity in truss networks and the role of bending versus stretching deformation

Auxetic behavior (i.e., a negative value of Poisson's ratio) has been reported for a variety of cellular networks including truss structures. Commonly, this implies that the geometric arrangement of truss members within a periodic unit cell is designed to achieve the negative Poisson effect, e.g., in the reentrant honeycomb configuration. Here, we show that elastic periodic truss lattices can be tuned to display auxeticity by controlling the ratio of bending to stretching stiffness. If the nodal stiffness (or the bending stiffness) is low compared to the stretching stiffness of individual truss members, then the lattice is expected to exhibit a positive Poisson's ratio, showing lateral expansion upon uniaxial compression. In contrast, if the nodal or bending stiffness is high (and buckling is prevented), the lattice may reveal auxetic behavior, contracting laterally under uniaxial compression. This effect is demonstrated in two dimensions for the examples of square and triangular lattices, and it is confirmed both analytically in the limit of small strains as well as numerically for finite elastic deformation. Under large deformation, instability additionally gives rise to auxetic behavior due to truss buckling