<div>Segmented material systems have been shown to provide advantages over monolithic materials including the potential for combinations of properties such as strength, toughness, and ductility that are not otherwise attainable. One such class of segmented system is that of topologically interlocked material (TIM) systems. These are material systems consisting of one or more repeating unit blocks assembled in a planar configuration. When coupled with a bounding frame, this plate-like structure can withstand transverse loads without the use of adhesive or fasteners between blocks.</div><div><br></div><div>One method of generating TIM systems is to start with a 2D tiling and project each edge of the tiles at alternating angles from the tile normal. This work examines 18 unique configurations of TIM systems generated from the Archimedean and the Laves tilings. These systems are constructed as segmented plates having approximately the same number of building blocks and with equivalent overall dimensions so that the effect of the segmentation patterns on the load response of the TIM system can be investigated. Finite element models were utilized to simulate both displacement controlled loading and body force loading of each configuration with various coefficients of friction. The load responses were recorded and the characteristics of chirality and reciprocity of the load response were observed.</div><div><br></div><div>The TIM system configurations in this study resulted in a wide variety of performance. Their range of properties is presented, and a mechanism for strength in a TIM system is postulated. The findings of this work enable the material design space to be expanded by facilitating the creation of material systems with a greater range of properties than is possible with monolithic materials.</div>

<p dir="ltr">This thesis focuses on the study of wave propagation in architected material systems. Specifically of interest is wave propagation in topologically interlocking material (TIM) systems made of tetrahedra and bio-inspired blocks. TIM systems are assemblies of composed of blocks in which the block geometry constrains blocks in place. Individual blocks can only be removed by disassembling the system. This interlocking of block geometry allows these systems to bear loads without the need for adhesives. Overall, load bearing is affected by block geometry, contact interaction, and assembly architecture. Wavefronts and wave velocities are computed using an explicit finite element code. Wave propagation is investigated first in a row of interlocking tetrahedra, then in 3D planar TIM systems of tetrahedra and bio-inspired scutoid blocks.</p><p dir="ltr">The propagation of linear traveling waves through a row of interlocking tetrahedra is demonstrated by the use of finite element simulations. The wave velocity was found to be independent of wave amplitude for ideal contact conditions but dependent on impact velocity for an exponential pressure-overclosure relationship between surfaces. For a frictionless, constant contact stiffness model, the effective wave velocity is about 50% of the 1D material wave speed. In the presence of friction, the wave velocity increases to about 80% of the 1D material wave speed. The wave velocity is attributed to wave-guiding set by the geometry of the tetrahedra. The wave velocity is further modulated by the rocking motion of the tetrahedra about an axis perpendicular to the wave propagation direction. The rocking motion is affected by friction and is reduced as friction is increased. Experimental results on wave propagation in a row of 3D-printed triangular prisms demonstrate pulse-like voltage versus time wave responses. With rough and tacky surfaces, the velocity of the linear traveling waves is measured as approximately 20% the 1D material wave speed. For smooth and low friction surface conditions, significantly higher wave velocities are measured. Similarly, reducing the number of contact surfaces by fusing pairs of building blocks also results in higher measured wave velocities. Experiments on rectangular prisms lack the wave-guiding geometry and provide a reference configuration. Finite element models are used to gain detailed insight into the wave propagation process. Wave-guide models are defined to predict wave speeds based on the effective path of wave propagation. The proposed models closely predict measured and computed wave speeds for the tetrahedra and triangular prisms.</p><p dir="ltr">Scutoids are prism-like shapes containing lateral vertices between two parallel polygonal surfaces. With the lateral vertices at the midplane, scutoid blocks can be periodically and densely packed. Scutoid-based planar arrays are demonstrated to behave mechanically as TIM systems. Under quasi-static transverse loads, assembly properties (stiffness, strength, toughness) match or exceed those of the corresponding tetrahedra-based TIM systems. The scutoid-based TIM systems have unique chiral characteristics. Chirality is attributed to the combination of building block and assembly symmetry. Chirality leads to asymmetric internal load transfer patterns resulting in unbalanced in-plane reaction forces and reaction moments. Experiments confirm the computational findings. Under transverse indentation, these systems have nonlinear force-displacement responses and measurable torque responses.</p><p dir="ltr">Wave propagation following transverse impact on planar arrays of interlocking tetrahedra and scutoids is investigated. Unique wave speed and wavefront development are demonstrated to occur in these systems. The 1D material wave speed emerges as the limiting wave speed of the TIM systems, rather than the dilatational wave speed. In tetrahedra assemblies, waves propagate with a velocity of approximately 25% of the 1D material wave speed. The wave velocity is attributed to wave-guiding from the interlocking tetrahedra geometry. Tetrahedra are not perfectly space-filling and block-to-block interactions are not limited to one direction. In the scutoid assemblies, waves propagate at velocities between 80% and 90% of the 1D material wave speed. These velocities are along directions associated with dominant load paths. The wave velocities in the scutoid-based TIM systems approach the 1D material wave speed as the contact surfaces are substantially orthogonal to the assembly surface. In comparison to monolithic plates, wavefronts develop with significant spatial non-uniformity. Wave patterns exhibit the symmetry or asymmetry also observed in the quasi-static response. Overall, contact surface orientation, block geometry, and assembly architecture affect wave velocity and wavefront development.</p>

<p>A topologically interlocked material (TIM) system belongs to a class of architectured materials and is known to perform outstanding mechanical properties such as stiffness, strength, and toughness. TIM systems are assemblies of polyhedral or building blocks, where individual elements constrain each other on inclined sides of building blocks. This thesis first focuses on developing novel designs of TIM plates composed of building blocks that interact with each other. The resulting TIM systems can be characterized concerning their periodicity and symmetry. Consequently, this study investigates how the proposed geometric features enhance mechanical properties and contribute to emerging properties. Specifically, four research questions provide a clear direction and framework for the investigation. For efficient analysis, finite element calculations are employed, and physical validation methods are used to verify them.</p> <p>The first research question is how the mechanical properties of aperiodic systems differ from those of periodic systems. Aperiodic systems offer diverse possibilities in terms of forms and arrangements. In this thesis, aperiodicity is further divided into two aspects: disrupting symmetry and preserving symmetry. In the approach that disrupts symmetry, the shapes of the tiles are randomly generated. An aperiodic system does not necessarily possess inherently superior or inferior mechanical properties compared to a periodic system. However, the flexibility of aperiodic systems allows for numerous forms and arrangements, presenting promising alternatives to identify factors or patterns that contribute to improved mechanical performance. To simplify these complex configurations, network theory is employed.</p> <p>Each building and its contact interfaces are represented as nodes and links. By utilizing network theory, a focused analysis of the links is conducted, enabling a comprehensive understanding of force propagation across TIM systems. The quantification of the significance of each link assists in reinforcing critical links while potentially sacrificing less critical ones.</p> <p>This approach not only simplifies the research problem but also facilitates the creation of customized design systems by adjusting the links.</p> <p>The other approach to achieve aperiodicity while preserving symmetry utilizes quasicrystal structures. This is based on another research question: What are the benefits of creating TIM systems with quasi-crystal tilting? Quasi-crystals possess a unique characteristic of maintaining 5-fold rotational symmetry while breaking away from periodic patterns observed in traditional systems. The arrangement of elements in quasi-crystal structures extends in a non-repetitive pattern from the center outward, offering a multitude of potential possibilities for TIM systems. By incorporating quasi-crystal tiling, TIM systems are expected to open up exceptional mechanical properties and unconventional behaviors.</p> <p>The third research question investigates whether the influence on mechanical performance varies based on the symmetry level of TIM systems. Despite using identical unit blocks, the arrangement of an assembly can lead to different levels of symmetry. Furthermore, it is possible to modify the symmetry of the unit block, thereby impacting the overall symmetry of the assembly. To achieve this, the symmetry of a unit block is adjusted by modifying the angles of side faces, transitioning from larger angles to smaller angles or vice versa. This modification introduces directionality (rotational symmetry) to the unit block and creates a greater variety of symmetry levels depending on the arrangements of these blocks. By implementing a broader range of symmetry levels that conventional TIM systems cannot achieve, this research aims to investigate the relationship between these symmetries and mechanical properties.</p> <p>The fourth research question is about what emerging properties could be present in TIM systems. While the primary application of TIMs is to enhance the damage tolerance of brittle materials against an external load, there have been ongoing attempts to research emerging properties like negative stiffness, sound absorption, and chirality. Chirality, in particular, serves as a valuable geometric property to describe a circulation of force propagation. Generally, the ability of TIM systems to carry transverse loads is explained through equivalent Mises truss along x− and y − axis. However, chirality enables the representation of not only axial force paths but also circulations of forces within TIM systems. In addition, a rich variety of geometric patches are observed in quasi-crystal structures. In crystal structures, a limited number of patches are repetitively arranged, resulting in a restricted range of properties. However, quasi-crystals like Penrose are non-periodic and possess a greater capacity to generate diverse patches, allowing for the selection of various mechanical properties.</p>