Structural hierarchy confers error tolerance in biological materials.

Structural hierarchy, in which materials possess distinct features on multiple length scales, is ubiquitous in nature. Diverse biological materials, such as bone, cellulose, and muscle, have as many as 10 hierarchical levels. Structural hierarchy confers many mechanical advantages, including improved toughness and economy of material. However, it also presents a problem: Each hierarchical level adds a new source of assembly errors and substantially increases the information required for proper assembly. This seems to conflict with the prevalence of naturally occurring hierarchical structures, suggesting that a common mechanical source of hierarchical robustness may exist. However, our ability to identify such a unifying phenomenon is limited by the lack of a general mechanical framework for structures exhibiting organization on disparate length scales. Here, we use simulations to substantiate a generalized model for the tensile stiffness of hierarchical filamentous networks with a nested, dilute triangular lattice structure. Following seminal work by Maxwell and others on criteria for stiff frames, we extend the concept of connectivity in network mechanics and find a similar dependence of material stiffness upon each hierarchical level. Using this model, we find that stiffness becomes less sensitive to errors in assembly with additional levels of hierarchy; although surprising, we show that this result is analytically predictable from first principles and thus potentially model independent. More broadly, this work helps account for the success of hierarchical, filamentous materials in biology and materials design and offers a heuristic for ensuring that desired material properties are achieved within the required tolerance.

Hierarchical Nanoporous Copper Architectures via 3D Printing Technique for Highly Efficient Catalysts.

Nanoporous metals represent a class of functional materials with unique bicontinuous open porous structural properties, making them ideal candidates for various catalyst applications. However, the pursuit of nanoporous properties, extremely small pores, and high surface area, results in the restriction of mass transport. Herein, a free-standing hierarchical nanoporous Cu material, prepared by a selective laser melting 3D printing technique and a one-step dealloying process, is presented as a highly efficient electrocatalyst for methanol oxidation. It is demonstrated that the digitally controlled hierarchical structure with macro- and nano-scaled pores can be utilized for promoting and directing mass transport as well as for the enhancement of catalytic properties. This work highlights a facile, low-cost, and alternative strategy for hierarchical nanoporous structure design that can be applied to binary, ternary, and quaternary metal alloys for various functional applications.

Structural hierarchy of autism spectrum disorder symptoms: an integrative framework.

BACKGROUND: In an attempt to resolve questions regarding the symptom classification of autism spectrum disorder (ASD), previous research generally aimed to demonstrate superiority of one model over another. Rather than adjudicating which model may be optimal, we propose an alternative approach that integrates competing models using Goldberg's bass-ackwards method, providing a comprehensive understanding of the underlying symptom structure of ASD. METHODS: The study sample comprised 3,825 individuals, consecutive referrals to a university hospital developmental disabilities specialty clinic or a child psychiatry outpatient clinic. This study analyzed DSM-IV-referenced ASD symptom statements from parent and teacher versions of the Child and Adolescent Symptom Inventory-4R. A series of exploratory structural equation models was conducted in order to produce interpretable latent factors that account for multivariate covariance. RESULTS: Results indicated that ASD symptoms were structured into an interpretable hierarchy across multiple informants. This hierarchy includes five levels; key features of ASD bifurcate into different constructs with increasing specificity. CONCLUSIONS: This is the first study to examine an underlying structural hierarchy of ASD symptomatology using the bass-ackwards method. This hierarchy demonstrates how core features of ASD relate at differing levels of resolution, providing a model for conceptualizing ASD heterogeneity and a structure for integrating divergent theories of cognitive processes and behavioral features that define the disorder. These findings suggest that a more coherent and complete understanding of the structure of ASD symptoms may be reflected in a metastructure rather than at one level of resolution.

Natural Composite Systems for Bioinspired Materials.

From a relatively limited selection of base materials, nature has steered the development of truly remarkable materials. The simplest and often overlooked organisms have demonstrated the ability to manufacture multi-faceted, molecular-level hierarchical structures that combine mechanical properties rarely seen in synthetic materials. Indeed, these natural composite systems, composed of an array of intricately arranged and functionally relevant organic and inorganic substances serve as inspiration for materials design. A better understanding of these composite systems, specifically at the interface of the hetero-assemblies, would encourage faster development of environmentally friendly "green" materials with molecular level specificities.

Disrupting Density-Dependent Property Scaling in Hierarchically Architected Foams.

Creating lightweight architected foams as strong and stiff as their bulk constituent material has been a long-standing effort. Typically, the strength, stiffness, and energy dissipation capabilities of materials severely degrade with increasing porosity. We report nearly constant stiffness-to-density and energy dissipation-to-density ratios─a linear scaling with density─in hierarchical vertically aligned carbon nanotube (VACNT) foams with a mesoscale architecture of hexagonally close-packed thin concentric cylinders. We observe a transformation from an inefficient higher-order density-dependent scaling of the average modulus and energy dissipated to a desirable linear scaling as a function of the increasing internal gap between the concentric cylinders. From the scanning electron microscopy of the compressed samples, we observe an alteration in the deformation modality from local shell buckling at a smaller gap to column buckling at a larger gap, governed by an enhancement in the number density of CNTs with the increasing internal gap, leading to better structural stiffness at low densities. This transformation simultaneously improves the foams' damping capacity and energy absorption efficiency as well and allows us to access the ultra-lightweight regime in the property space. Such synergistic scaling of material properties is desirable for protective applications in extreme environments.

Hierarchical modeling of elastic moduli of equine hoof wall.

This study predicts analytically effective elastic moduli of substructures within an equine hoof wall. The hoof wall is represented as a composite material with a hierarchical structure comprised of a sequence of length scales. A bottom-up approach is employed. Thus, the outputs from a lower spatial scale serve as the inputs for the following scale. The models include the Halpin-Tsai model, composite cylinders model, a sutured interface model, and classical laminate theory. The length scales span macroscale, mesoscale, sub-mesoscale, microscale, sub-microscale, and nanoscale. The macroscale represents the hoof wall, consisting of tubules within a matrix at the mesoscale. At the sub-mesoscale, a single hollow tubule is reinforced by a tubule wall made of lamellae; the surrounding intertubular material also has a lamellar structure. The lamellae contain sutured and layered cells at the microscale. A single cell is made of crystalline macrofibrils arranged in an amorphous matrix at the sub-microscale. A macrofibril contains aligned crystalline rod-like intermediate filaments at the nanoscale. Experimentally obtained parameters are used in the modeling as inputs for geometry and nanoscale properties. The predicted properties of the hoof wall material agree with experimental measurements at the mesoscale and macroscale. We observe that the hierarchical structure of the hoof wall leads to a decrease in the elastic modulus with increasing scale, from the nanoscale to the macroscale. Such behavior is an intrinsic characteristic of hierarchical biological materials. This study can serve as a framework for designing impact-resistant hoof-inspired materials and structures.

Plastic Crushing Failure of Bio-Inspired Cellular Hierarchical Topological Sandwich Core.

Bio-inspired self-similar hierarchical honeycombs are multifunctional cellular topologies used for resisting various loadings. However, the crushing behavior under large plastic deformation is still unknown. This paper investigates the in-plane compressive response of selective laser melting (SLM) fabricated hierarchical honeycombs. The effects of hierarchical order, relative density as well as constituent material are evaluated. The results show that at small deformation, the AlSi10Mg alloy hierarchical honeycombs show great advantages over the elastic modulus and compressive strength than 316L steel hierarchical honeycombs. As the relative density and hierarchical order increase, the failure mechanism of AlSi10Mg alloy honeycombs gradually changes from a bending-dominated mode to a fracture-dominated mode; whereas all the 316L steel honeycombs fail due to the distortion of original unit cells. At large deformation, the AlSi10Mg alloy honeycombs behave with brittle responses, while the 316L steel honeycombs exhibit ductile responses, showing a negative Poisson's ratio behavior and gradient deformation of hierarchical unit cells. The addition of unit cell refinements improves the elastic modulus of AlSi10Mg alloy honeycombs and advances the densification of 316L steel honeycombs. In addition, the effect of constituent material on the compressive response of hierarchical honeycombs has been discussed. This study facilitates the development and future potential application of multifunctional ultra-light sandwich structures.

Extraordinary structural complexity of ilmajokite: a multilevel hierarchical framework structure of natural origin.

The crystal structure of ilmajokite, a rare Na-K-Ba-Ce-titanosilicate from the Khibiny mountains, Kola peninsula, Russia, has been solved using single-crystal X-ray diffraction data. The crystal structure is based on a 3D titanosilicate framework consisting of trigonal prismatic titanosilicate (TPTS) clusters centered by Ce3+ in [9]-coordination. Four adjacent TPTS clusters are linked into four-membered rings within the (010) plane and connected via ribbons parallel to 101. The ribbons are organized into layers parallel to (010) and modulated along the a axis with a modulation wavelength of csinß = 32.91 Šand an amplitude of ∼b/2 = 13.89 Å. The layers are linked by additional silicate tetrahedra. Na+, K+, Ba2+ and H2O groups occur in the framework cavities and have different occupancies and coordination environments. The crystal structure of ilmajokite can be separated into eight hierarchical levels: atoms, coordination polyhedra, TPTS clusters, rings, ribbons, layers, the framework and the whole structure. The information-based analysis allows estimation of the complexity of the structure as 8.468 bits per atom and 11990.129 bits per cell. According to this analysis, ilmajokite is the third-most complex mineral known to date after ewingite and morrisonite, and is the most complex mineral framework structure, comparable in complexity to paulingite-(Ca) (11 590.532 bits per cell).

Multiscale designs of the chitinous nanocomposite of beetle horn towards an enhanced biomechanical functionality.

Operating mainly as a type of weapon, the beetle horn develops an impressive mechanical efficiency based on chitinous materials to maximize the injury to opponent and simultaneously minimize the damage to itself and underlying brain under stringent loading conditions. Here the cephalic horn of the beetle Allomyrina dichotoma is probed using multiscale characterization combined with finite element simulations to explore the origins of its biomechanical functionality from the perspective of materials science. The horn is revealed to be highly regulated from the macroscopic shape, geometry, and connection with the body to the meso- and microscopic architecture, moisture content, and chemical and structural characteristics. Varying kinds of gradients are integrated at all length-scales. Such designs are demonstrated to benefit the mechanical performance by mitigating stress concentrations, retarding crack propagation, and modulating local properties to better adapt to stress. Enhanced rigidity, robustness and stability are additionally generated from the constrained flexibility endowed by the nanocomposite plywood structure through the reorientation of chitin nanofibrils within the proteinaceous matrix. These findings shed light on the intriguing materials-design strategies of nature in creating synergy of offence and persistence. They may even offer inspiration for the synthesis of high-performance materials and structures, in particular beams to resist bending and torsion.

Bioinspired Wood Nanotechnology for Functional Materials.

It is a challenging task to realize the vision of hierarchically structured nanomaterials for large-scale applications. Herein, the biomaterial wood as a large-scale biotemplate for functionalization at multiple scales is discussed, to provide an increased property range to this renewable and CO2 -storing bioresource, which is available at low cost and in large quantities. The Progress Report reviews the emerging field of functional wood materials in view of the specific features of the structural template and novel nanotechnological approaches for the development of wood-polymer composites and wood-mineral hybrids for advanced property profiles and new functions.

Structural design of the minute clypeasteroid echinoid Echinocyamus pusillus.

The clypeasteroid echinoid skeleton is a multi-plated, light-weight shell construction produced by biomineralization processes. In shell constructions, joints between individual elements are considered as weak points, yet these echinoid skeletons show an extensive preservation potential in both Recent and fossil environments. The remarkable strength of the test is achieved by skeletal reinforcement structures and their constructional layouts. Micro-computed tomography and scanning electron microscopy are used for microstructural and volumetric analyses of the echinoid's skeleton. It is shown that strengthening mechanisms act on different hierarchical levels from the overall shape of the skeleton to skeletal interlocking. The tight-fitting and interlocking plate joints lead to a shell considered to behave as a monolithic structure. The plate's architecture features distinct regions interpreted as a significant load-transferring system. The internal support system follows the segmentation of the remaining skeleton, where sutural layout and stereom distribution are designed for effective load transfer. The structural analysis of the multi-plated, yet monolithic skeleton of Echinocyamus pusillus reveals new aspects of the micro-morphology and its structural relevance for the load-bearing behaviour. The analysed structural principles allow E. pusillus to be considered as a role model for the development of multi-element, light-weight shell constructions.

Bioinspired Structural Hierarchy within Macroscopic Volumes of Synthetic Composites.

A key challenge in developing bioinspired composites is the fabrication of well-defined 3D hierarchical structures ranging from nano to the macroscale. Herein, the development of a synthetic polymer-apatite composite realized by integrating bottom-up self-assembly and additive manufacturing (AM) is described. The resulting composite exhibits a bioinspired hierarchical structure over its 3D macroscopic volume. The composite is assembled in a bottom-up manner, where periodic nanoscale assemblies of organic micellar fibrils and inorganic apatite nanocrystals are organized as bundles of mineralized microstructures. These microstructural bundles are preferentially oriented throughout the macroscopic volume of the material via extrusion based AM. The obtained structural hierarchy is investigated in 3D using electron microscopy and small angle X-ray scattering tensor tomography and correlated to the structural hierarchy and anisotropy observed in biological tissues such as bone and the bone-cartilage interface. This work demonstrates the possibility to form polymer-apatite composites with a well-defined hierarchical structure throughout its macroscopic volume, which is crucial for the development of mechanically optimized materials for applications such as bone and osteochondral implants.

Giant Thermal Expansion in 2D and 3D Cellular Materials.

When temperature increases, the volume of an object changes. This property was quantified as the coefficient of thermal expansion only a few hundred years ago. Part of the reason is that the change of volume due to the variation of temperature is in general extremely small and imperceptible. Here, abnormal giant linear thermal expansions in different types of two-ingredient microstructured hierarchical and self-similar cellular materials are reported. The cellular materials can be 2D or 3D, and isotropic or anisotropic, with a positive or negative thermal expansion due to the convex or/and concave shape in their representative volume elements respectively. The magnitude of the thermal expansion coefficient can be several times larger than the highest value reported in the literature. This study suggests an innovative approach to develop temperature-sensitive functional materials and devices.

Hierarchical Analysis of Bioactive Matched Molecular Pairs, Encoded Chemical Transformations, and Associated Substructures.

The matched molecular pair (MMP) concept has become popular to assess molecular property changes resulting from small chemical modifications and study structure-activity relationships (SARs). In this study, we further extend MMP analysis by introducing an MMP-based hierarchical analysis scheme. Specifically, we report a large-scale analysis of MMPs derived from bioactive compounds following a defined "MMP-transformation-substructure" hierarchy. This makes it also possible to categorize transformations and corresponding substructures on the basis of activity information. MMPs were systematically generated for compounds active against current pharmaceutical targets and stepwise decomposed into transformations and substructures. Surprisingly, most chemical transformations were only associated with single MMPs. Hence, the structural context of transformations was unexpectedly narrow. In addition, nearly half of all substructures were found to exclusively form single-target transformations. Taken together, the results of our analysis provide a detailed view of MMP-transformation-substructure hierarchy and further increase the knowledge base of the MMP approach.

A materials perspective of Martyniaceae fruits: Exploring structural and micromechanical properties.

Several species of the plant family Martyniaceae are characterised by unique lignified capsules with hook-shaped extensions that interlock with hooves and ankles of large mammals to disperse the seeds. The arrangement of fruit endocarp fibre tissues is exceptional and intriguing among plants. Structure-function-relationships of these slender, curved, but mechanically highly stressed fruit extensions are of particular interest that may inspire advanced biomimetic composite materials. In the present study, we analyse mechanical properties and fracture behaviour of the hook-shaped fruit extensions under different load conditions. The results are correlated with calculated stress distributions, the specific cell wall structure, and chemical composition, providing a detailed interpretation of the complex fruit tissue microstructure. At the cell wall level, both a large microfibril angle and greater strain rates resulted in Young's moduli of 4-9 GPa, leading to structural plasticity. Longitudinally arranged fibre bundles contribute to a great tensile strength. At the tissue level, transversely oriented fibres absorb radial stresses upon bending, whereas cells encompass and pervade longitudinal fibre bundles, thus, stabilise them against buckling. During bending and torsion, microcracks between axial fibre bundles are probably spanned analogous to a circular anchor. Our study fathoms a highly specialized plant structure, substantiating former assumptions about epizoochory as dispersal mode. While the increased flexibility allows for proper attachment of fruits during dynamical locomotion, the high strength and stability prevent a premature failure due to heavy loads exerted by the animal.

Nanoporous Metal Papers for Scalable Hierarchical Electrode.

Nanoporous metals similar to paper in form are developed using Japanese washi paper as a template to create hierarchical porous electrodes. This method is used to create a trimodal -nanoporous Au electrode, as a well as a hierarchical NiMn electrode that achieves high electrochemical capacitance and a rapid rate of oxygen evolution.

Ultrastructural organization and micromechanical properties of shark tooth enameloid.

The outer part of shark teeth is formed by the hard and mineral-rich enameloid that has excellent mechanical properties, which makes it a very interesting model system for the development of new bio-inspired dental materials. We characterized the microstructure, chemical composition and resulting local mechanical properties of the enameloid from teeth of Isurus oxyrinchus (shortfin mako shark) by performing an in-depth analysis using various high-resolution analytical techniques, including scanning electron microscopy, qualitative energy-dispersive X-ray spectroscopy and nanoindentation. Shark tooth enameloid reveals an intricate hierarchical arrangement of thin (50-80nm) and long (>1µm) crystallites of fluoroapatite with a high degree of structural anisotropy, which leads to exceptional mechanical properties. Both stiffness and hardness are surprisingly homogeneous in the shiny layer as well as in the enameloid: although both tooth phases differ in structure and composition, they show almost no orientation dependence with respect to the loading direction of the enameloid crystallites. The results were used to determine the structural hierarchy of shark teeth, which can be used as a base for establishing design criteria for synthetic bio-inspired and biomimetic dental composites.