Cuttlebone, the endoskeleton of cuttlefish, offers an intriguing biological structural model for designing low-density cellular ceramics with high stiffness and damage tolerance. Cuttlebone is highly porous (porosity ~93%) and lightweight (density less than 20% of seawater), constructed mainly by brittle aragonite (95 wt%), but capable of sustaining hydrostatic water pressures over 20 atmospheres and exhibits energy dissipation capability under compression comparable to many metallic foams (~4.4 kJ/kg). Here we computationally investigate how such a remarkable mechanical efficiency is enabled by the multiscale structure of cuttlebone. Using the common cuttlefish, Sepia Officinalis, as a model system, we first conducted high-resolution synchrotron micro-computed tomography (µ-CT) and quantified the cuttlebone's multiscale geometry, including the 3D asymmetric shape of individual walls, the wall assembly patterns, and the long-range structural gradient of walls across the entire cuttlebone (ca. 40 chambers). The acquired 3D structural information enables systematic finite-element simulations, which further reveal the multiscale mechanical design of cuttlebone: at the wall level, wall asymmetry provides optimized energy dissipation while maintaining high structural stiffness; at the chamber level, variation of walls (number, pattern, and waviness amplitude) contributes to progressive damage; at the entire skeletal level, the gradient of chamber heights tailors the local mechanical anisotropy of the cuttlebone for reduced stress concentration. Our results provide integrated insights into understanding the cuttlebone's multiscale mechanical design and provide useful knowledge for the designs of lightweight cellular ceramics. Upon the prior curvature analysis of the cuttlebone walls, we discovered that the walls were primarily "saddle-shaped". Thus, the characterization of different curvatures, varying between flat, domed, saddled, or cylindrical surfaces, were explored. A mathematical model was utilized to generate multiple walls with different curvature characteristics. We observed the mechanical performance of these walls via finite-element analysis and formulated different techniques for designing effective ceramic structures through incorporation of curvature. / Master of Science / The cuttlefish is a marine species that instead of having an inflatable swim bladder like fish, is a mollusk capable of swimming by utilizing their skeleton, called the cuttlebone. The cuttlefish can freely traverse the waters by controlling the flow of water in and out of their brittle skeletons, changing their buoyancy. For this reason, the cuttlebone must be very porous yet strong to withstand the deep-water pressures, enticing an interest for closer observation of the structure which may be useful in engineering applications involving ceramic structures. In this study, we examined an actual cuttlebone structure to better visualize its features with high-resolution synchrotron micro-computed tomography (µ-CT) and tabulated its mechanical performance through a variety of tests using computational software. The skeletal design of the cuttlebone consists of multiple layered chambers supported by wavy, pillar-like walls. It was revealed that the cuttlebone is remarkable due to its multiscale design: the asymmetric geometry of the walls are designed to tolerate considerable amounts of energy while a stiff construction; at the chamber level, variation of walls (number, pattern, and waviness amplitude) helps avoid complete destruction of the structure in the event of an excessive force; at the entire skeletal level, various of chamber heights reduces inflicted stress in concentrated regions of the cuttlebone. The wavy walls were also observed to retain a saddle-shaped curviness, versus simple flat, domed, or cylindrical shaped walls. This created an incentive to explore the effects of curvature on the structural integrity of brittle ceramic structures. We developed an effective way for generating walls with different curvatures and observed the mechanical performance of each wall by crushing them in computer simulations. It was identified that adding curvature to brittle walls prolonged the failure period significantly. While the cylindrical walls were found to be rather stiff, saddle-shaped walls, although not capable of withstanding as much force as flat or cylindrical walls, has a more progressive failure behavior meanwhile maintaining high energy absorption, hence the saddled walls of the cuttlebone to allow maintenance and self-repair in damaged regions.

Natural life history of cephalopods have been puzzling marine biologists for a long time. Fishery scientists also met with great difficulty in managing resources of squids as well as cuttlefishes. The lack of the accurate equation defining growth through time is one of the major reasons. This was due mainly to no stable characteristic for age determinations. It was known that in anatomy, stripe layers of cuttlebone are similar in embryonic development as shells of the bivalve, which has been used for age determinations. This study suggested that by taking the stripe marks on the bottom surface of the cuttlebone as quasi-daily-aging characters, it is possible to define the trend of growth of cuttlefish by (either a von Bertalanffy or Gompertz) growth equation. A semi-automatic computer processing system was designed and organized to measure the stripe area lengths (SAL) and lengths of stripe margin (LSM) for all stripe marks upon individual cuttlebone (analogous to scale reading in fishery research for the same purpose) of ¡]Sepia pharaonic Ehrenberg¡A1831¡^. A total of 21 cuttlebones were measured and the data analyzed. It appeared that the growth of the cuttlefishes are still on the stage of acceleration, and is not suitable to be represented by the VBGF curve traditionally used. Using SAL= and LSM= ' as length indicators respectively, two Gompertz growth equations were respectively estimated as followed. = 30.00*exp[-3.73*exp(-0.012*t)] ' = 23.18*exp[-4.27*exp(-0.015*t)] Two functional linear regression formulas were also prepared as: = -1.2684 + 0.7729 * L ' = -0.7829 + 0.6297 * L The above formulas can be used for the transformation between SAL (or LAM) and body length. The well-known Rosa Lee¡¦s phenomenon was not found either based on the character of SAL or LSM, implying that during the trend of growing, the mortality of Sepia pharaonic were not significantly different among different sizes of organisms. It was expected that with this breakthrough in technique and theory, additional knowledge on the populations biology of cuttlefish can be known in more detail.

While the structure and mechanical properties of natural cellular solids such as wood and trabecular bone have been extensively studied in the past, the structural design and underlying deformation mechanisms of natural cellular solids with very high mineral contents (> 90 wt%), which we term as natural ceramic cellular solids, are largely unexplored. Many of these natural ceramic cellular solids, despite their inherent brittle constituent biominerals (e.g., calcite or aragonite), exhibit remarkable mechanical properties, such as high stiffness and damage tolerance. In this thesis, by carefully selecting three biomineralized skeletal models with distinctly different cellular morphologies, including the honeycomb-like structure in cuttlefish bone (or cuttlebone), the stochastic open-cell structure in sea urchin spines, and the periodic open-cell structure in starfish ossicles, I systematically investigate the mechanical design strategies of these natural ceramic cellular solids. The three model systems are cuttlefish Sepia officinalis, sea urchin Heterocentrotus mammillatus, and starfish Protoreaster nodosus, respectively. By investigating the relationship between their mechanical properties and structural characteristics, this thesis reveals some novel structural design strategies for developing lightweight, tough, strong, and stiff ceramic cellular solids. The internal skeleton of S. officinalis, also known as cuttlebone, has a porosity of 93 vol% (constituent material: 90 wt% aragonite), which is a multichambered structure consisting of horizontal septa and thin vertical walls with corrugated cross-sectional profiles. Through systematic ex-situ and synchrotron-based in-situ mechanical measurements and collaborative computational modeling, we reveal that the vertical walls in the cuttlebone exhibit an optimal waviness gradient, which leads to compression-dominant deformation and asymmetric wall fracture, accomplishing both high stiffness (8.4 MN∙m/kg) and high energy absorption (4.4 kJ/kg). Moreover, the distribution of walls reduces stress concentrations within the horizontal septa, facilitating a larger chamber crushing stress and more significant densification. For the stochastic open-cell foam-like structure, also known as stereom (porosity: 60-80 vol%, constituent material: 99 wt% calcite) in H. mammillatus, we first developed a computer vision-based algorithm that allows for quantitative analysis of the cellular network of these structures at both local individual branch and node level as well as the global network level. This open-source algorithm could be used for analyzing both biological and engineering open-cell foams. I further show that the smooth, highly curved branch morphology with near-constant surface curvature in stereom results in low-stress concentration, which further leads to dispersed crack formation upon loading. Combined synchrotron in-situ analysis, electron microscopic analysis, and computational modeling further reveal that the fractured branches are efficiently jammed by the small throat openings within the cellular structure. This further leads to the formation of damage bands with densely packed fracture pieces. The continuous widening of the damage bands through progressive microfracture of branches at the boundaries contributes to the observed high plateau stress during compression, thereby contributing to its high energy absorption (17.7 kJ/kg), which is comparable and even greater than many synthetic metal- and polymer-based foams. Lastly, this thesis leads to the discovery of a unique dual-scale single-crystalline porous lattice structure (porosity: 50 vol%, constituent material: 99 wt% calcite) in the ossicles of P. nodosus. At the atomic level, the ossicle is composed of single-crystal biogenic calcite. At the lattice level, the ossicle's microstructure organizes as a diamond-triply periodic minimal surface (TPMS) structure. Moreover, the crystallographic axes at atomic and lattice levels are aligned, i.e., the c-axis of calcite is aligned with the [111] direction of the diamond-TPMS lattice. This single crystallinity co-alignment at two levels mitigates the compliance of calcite in the c-axis direction by utilizing the stiff <111> direction of the diamond-TPMS lattice. Furthermore, 3D in-situ mechanical characterizations reveal that the presence of crystal defects such as 60° and screw dislocations at the lattice level suppresses slip-like fracture along the {111} planes of the calcitic diamond-TPMS lattice upon loading, achieving an enhanced energy absorption capability. Even though the skeleton of echinoderm is made up of single-crystal calcite, the structure fractures in a conchoidal manner rather than along the clipping plane, which can continuously fracture the fragments into small pieces and enhance energy dissipation. / Doctor of Philosophy / The application of engineering ceramic cellular solids as structural components is limited by their brittleness and flaw sensitivity. In contrast, nature has evolved ceramic cellular materials such as sea sponge, sea urchin spine, and diatom shells that are simultaneously lightweight, strong, and damage-tolerant. These properties are thought to be achieved by the structure design of the component of those materials. Learning design strategies from these natural ceramic cellular solids is significant for developing lightweight bio-inspired ceramic materials with improved mechanical performance. In this thesis, I investigated mechanical design strategies from natural ceramic cellular solids in three model systems, i.e., cuttlebone from cuttlefish Sepia officinalis, spines from sea urchin Heterocentrotus mammillatus, ossicles from starfish Protoreaster nodosus. These three natural ceramic porous solids have high mineral content in the constituent materials (> 90 wt%) and have a highly porous structure (porosity: 50 vol%-93 vol%). These three model systems are selected to represent the analogs of three typical structure forms of synthetic cellular solids, i.e., honeycomb-like structures, stochastic and periodic open-cell structures, respectively. This thesis aims to establish a quantitative relationship between the 3D multiscale structure and deformation/toughening behavior for these selected natural ceramic cellular solids via a combination of different experimental and computational approaches.