Bioinspired, mechanical, deterministic fractal model for hierarchical suture joints

Bio-inspired interlocking metasurfaces

Interlocking metasurfaces (ILMs) are patterned arrays of mating features that enable the joining of bodies by constraining motion and transmitting force. They offer an alternative to traditional joining solutions such as mechanical fasteners, welds, and adhesives. This study explores the development of bio-inspired ILMs using a problem-driven bioinspired design (BID) framework. We develop a taxonomy of attachment solutions that considers both biological and engineered systems and derive conventional design principles for ILM design. We conceptualize two engineering implementations to demonstrate concept development using the taxonomy and ILM conventional design principle through the BID framework: one for rapidly assembled bridge truss members and another for modular microrobots. These implementations highlight the potential of BID to enhance performance, functionality, and tunability in ILMs.

Mechanics of elliptical interlocking sutures in biological interfaces

Biological materials, such as beetle elytra and bird beaks, exhibit complex interfaces with diverse morphologies that have evolved to enhance their mechanical properties. However, the relationships between their geometric forms and mechanical properties remain inadequately understood. Here, we develop a theoretical model, supported by finite element simulations and experiments, to explore the strengthening and toughening mechanisms of biological interfaces characterized by elliptical interlocking sutures. We examine how aspect ratio, interlocking angle, and friction influence the stiffness, strength, and toughness (defined as the area under the stress-strain curve) of these interfaces. A phase diagram is presented to analyze the typical failure modes of sutured interfaces. We discuss the mechanistic advantages of various elliptical suture designs and demonstrate that the optimal aspect ratio and interlocking angle predicted by our model correspond closely with those observed in beetle elytra. This study advances our understanding of the mechanical principles governing biological sutured interfaces and provides valuable insights for the design of engineering joints, interlocking structures, and protective systems. STATEMENT OF SIGNIFICANCE: Biological interfaces characterized by elliptical interlocking sutures exist widely in nature. They exhibit superior mechanical properties and efficient biological functions. Here, we develop a theoretical model to explore their strengthening and toughening mechanisms. We reveal the effects of aspect ratio, interlocking angle, and friction of the interfaces on their load-bearing capability, deformability, and failure mechanisms. The failure modes of the sutured interfaces are deciphered and their mechanistic advantages are uncovered. The mechanically optimal suture geometries predicted by our theoretical model align with those in beetle elytra. This work deepens our understanding of the structure-property interrelations of biological sutured interfaces. The obtained results hold a promise in the design of, e.g., engineering joints, interlocking structures, and protective systems.

A Review of the Biomimetic Structural Design of Sandwich Composite Materials

Sandwich composites are widely used in engineering due to their excellent mechanical properties. Accordingly, the problem of interface bonding between their panels and core layers has always been a hot research topic. The emergence of biomimetic technology has enabled the integration of the structure and function of biological materials from living organisms or nature into the design of sandwich composites, greatly improving the interface bonding and overall performance of heterogeneous materials. In this paper, we review the most commonly used biomimetic structures and the fusion design of multi-biomimetic structures in the engineering field. They are analyzed with respect to their mechanical properties, and several biomimetic structures derived from abstraction in plants and animals are highlighted. Their structural advantages are further discussed specifically. Regarding the optimization of different interface combinations of multilayer composites, this paper explores the optimization of simulations and the contributions of molecular dynamics, machine learning, and other techniques used for optimization. Additionally, the latest molding methods for sandwich composites based on biomimetic structural design are introduced, and the materials applicable to different processes, as well as their advantages and disadvantages, are briefly analyzed. Our research results can help improve the mechanical properties of sandwich composites and promote the application of biomimetic structures in engineering.

Multiscale static and dynamic mechanical study of the Turritella terebra and Turritellinella tricarinata seashells

Marine shells are designed by nature to ensure mechanical protection from predators and shelter for molluscs living inside them. A large amount of work has been done to study the multiscale mechanical properties of their complex microstructure and to draw inspiration for the design of impact-resistant biomimetic materials. Less is known regarding the dynamic behaviour related to their structure at multiple scales. Here, we present a combined experimental and numerical study of the shells of two different species of gastropod sea snail belonging to the Turritellidae family, featuring a peculiar helicoconic shape with hierarchical spiral elements. The proposed procedure involves the use of micro-computed tomography scans for the accurate determination of geometry, atomic force microscopy and nanoindentation to evaluate local mechanical properties, surface morphology and heterogeneity, as well as resonant ultrasound spectroscopy coupled with finite element analysis simulations to determine global modal behaviour. Results indicate that the specific features of the considered shells, in particular their helicoconic and hierarchical structure, can also be linked to their vibration attenuation behaviour. Moreover, the proposed investigation method can be extended to the study of other natural systems, to determine their structure-related dynamic properties, ultimately aiding the design of bioinspired metamaterials and of structures with advanced vibration control.

Mechanical and Crack Propagating Behavior of Sierpiński Carpet Composites

Fractals, mathematically defined as "self-similar subsets at different scales", are ubiquitous in nature despite their complexity in assembly and formulation. Fractal geometry formed by simple components has long been applied to many fields, from physics and chemistry to electronics and architecture. The Sierpiński carpet (SC), a fractal with a Hausdorff dimension of approximately 1.8933, has two-dimensional space-filling abilities and therefore provides many structural applications. However, few studies have investigated its mechanical properties and fracture behaviors. Here, utilizing the lattice spring model (LSM), we constructed SC composites with two base materials and simulated tensile tests to show how fractal iterations affect their mechanical properties and crack propagation. From observing the stress-strain responses, we find that, for either the soft-base or stiff-base SC composites, the second iteration has the optimal mechanical performance in the terms of stiffness, strength, and toughness compared to the composites with higher hierarchies. The reason behind this surprising result is that the largest stress intensities occur at the corners of the smallest squares in the middle zone, which consequently induces crack nucleation. We also find that the main crack tends to deflect locally in SC composites with a soft matrix, but in global main crack behavior, SC composites with a stiff matrix have a large equivalent crack deflection. Furthermore, considering the inherent anisotropy of SC composites, we rotated the samples by 45°. The results show that the tensile strength and toughness of rotated SC composites are inferior and the crack propagating behaviors are distinct from the standard SC composites. This finding infers advanced engineering for crack control and deflection by adjusting the orientation of SC composites. Overall, our study opens the door for future engineering applications in stretchable devices, seismic metamaterials, and structural materials with tunable properties and hierarchies.

Dual-Phase Inspired Soft Electronic Sensors with Programmable and Tunable Mechanical Properties

Wearable and stretchable sensors are important components to strictly monitor the behavior and health of humans and attract extensive attention. However, traditional sensors are designed with pure horseshoes or chiral metamaterials, which restrict the biological tissue engineer applications due to their narrow regulation ranges of the elastic modulus and the poorly adjustable Poisson's ratio. Inspired by the biological spiral microstructure, a dual-phase metamaterial (chiral-horseshoes) is designed and fabricated in this work, which possesses wide and programmable mechanical properties by tailoring the geometrical parameters. Experimental, numerical, and theoretical studies are conducted, which reveal that the designed microstructures can reproduce mechanical properties of most natural animals such as frogs, snakes, and rabbits skin. Furthermore, a flexible strain sensor with the gauge factor reaching 2 under 35% strain is fabricated, which indicates that the dual-phase metamaterials have a stable monitoring ability and can be potentially applied in the electronic skin. Finally, the flexible strain sensor is attached on the human skin, and it can successfully monitor the physiological behavior signals under various actions. In addition, the dual-phase metamaterial could combine with artificial intelligence algorithms to fabricate a flexible stretchable display. The dual-phase metamaterial with negative Poisson's ratio could decrease the lateral shrinkage and image distortion during the stretching process. This study offers a strategy for designing the flexible strain sensors with programmable, tunable mechanical properties, and the fabricated soft and high-precision wearable strain sensor can accurately monitor the skin signals under different human motions and potentially be applied for flexible display.

Effect of Geometry and Orientation on the Tensile Properties and Failure Mechanisms of Compliant Suture Joints

Compliant sutures surrounded by stiff matrices are present in biological armors and carapaces, providing enhanced mechanical performance. Understanding the mechanisms through which these sutured composites achieve outstanding properties is key to developing engineering materials with improved strength and toughness. This article studies the impact of suture geometry and load direction on the performance of suture joints using a two-stage reactive polymer resin that enables facile photopatterning of mechanical heterogeneity within a single polymer network. Compliant sinusoidal sutures with varying geometries are photopatterned into stiff matrices, generating a modulus contrast of 2 orders of magnitude. Empirical relationships are developed connecting suture wavelength and amplitude to composite performance under parallel and perpendicular loading conditions. Results indicate that a greater suture interdigitation broadly improves composite performance when loading is applied perpendicular to suture joints but has deleterious effects when loading is applied parallel to the joint. Investigations into the failure mechanisms under perpendicular loading highlight the interplay between suture geometry and crack growth stability after damage initiation occurs. Our findings could enable a framework for engineering composites and bio-inspired structures in the future.

How suture networks improve the protective function of natural structures: A multiscale investigation

Myriad natural protective structures consist of bone plates joined by convoluted unmineralized (soft) collagenous sutures. Examples of such protective structures include: shells of turtles, craniums of almost all animals (including humans), alligator armour, armadillo armour, and others. The function of sutures has been well researched. However, whether, and if so how, sutures improve protective performance during a predator attack has received limited attention. Sutures are ubiquitous in protective structures, and this motivates the question as to whether sutures optimize the protective function of the structure. Hence, in this work the behaviour of structures that contain sutures during predator attacks is investigated. We show that sutures decrease the maximum strain energy density that turtle shells experience during predator attacks by more than an order of magnitude. Hence, sutures make turtle shells far more resilient to material failure, such as, fracture, damage, and plastic deformations. Additionally, sutures increase the viscous behaviour of the shell causing increased dissipation of energy during predator attacks. Further investigations into the influence of sutures on behaviour during locomotion and breathing are also presented. The results presented in this work motivate the inclusion of sutures in biomimetically designed protective structures, such as helmets and protective clothing. STATEMENT OF SIGNIFICANCE: Myriad bony protective structures contain networks of sutures, that is con- voluted soft collagenous tissue. Their ubiquity motivates the question, whether, and if so how, sutures improve protective performance. Hence, this work inves- tigates how sutures affect protective performance using computational experi- ments. Due to the length scale of sutures being far smaller than the structures in which they reside, classical modelling approaches are prohibitively expensive. Hence, in this work, a multiscale approach is taken. To our knowledge, this is the first multiscale investigation of structures that contain sutures. Among other insights, we show that sutures decrease the maximum strain energy density in structures during predator attacks by over an order of mag- nitude. Hence, sutures make structures far more resilient to failure.

Biomimetic Approaches for the Design and Fabrication of Bone-to-Soft Tissue Interfaces

Bone-to-soft tissue interfaces are responsible for transferring loads between tissues with significantly dissimilar material properties. The examples of connective soft tissues are ligaments, tendons, and cartilages. Such natural tissue interfaces have unique microstructural properties and characteristics which avoid the abrupt transitions between two tissues and prevent formation of stress concentration at their connections. Here, we review some of the important characteristics of these natural interfaces. The native bone-to-soft tissue interfaces consist of several hierarchical levels which are formed in a highly specialized anisotropic fashion and are composed of different types of heterogeneously distributed cells. The characteristics of a natural interface can rely on two main design principles, namely by changing the local microarchitectural features (e.g., complex cell arrangements, and introducing interlocking mechanisms at the interfaces through various geometrical designs) and changing the local chemical compositions (e.g., a smooth and gradual transition in the level of mineralization). Implementing such design principles appears to be a promising approach that can be used in the design, reconstruction, and regeneration of engineered biomimetic tissue interfaces. Furthermore, prominent fabrication techniques such as additive manufacturing (AM) including 3D printing and electrospinning can be used to ease these implementation processes. Biomimetic interfaces have several biological applications, for example, to create synthetic scaffolds for osteochondral tissue repair.

Mechanical Properties of PolyJet 3D-Printed Composites Inspired by Space-Filling Peano Curves

This paper proposes a design of novel composite materials inspired by the Peano curve and manufactured using PolyJet 3D printing technology with Agilus30 (flexible phase) and VeroMagentaV (rigid phase) materials. Mechanical properties were evaluated through tensile and compression tests. The general rule of mixture (ROM) for composites was employed to approximate the tensile properties of the hybrid materials and compare them to the experimental results. The effect of reinforcement alignments and different hierarchies are discussed. The results indicated that the 5% inclusion of the Peano reinforcement in tensile samples contributed to the improvement in the elastic modulus by up to 6 MPa, but provided no obvious enhancement in ultimate tensile strength. Additionally, compressive strengths between 2 MPa and 6 MPa were observed for compression cubes with first-order reinforcement, while lower values around 2 MPa were found for samples with second-order reinforcement. That is to say, the first-order reinforcement has been demonstrated more effectively than the second-order reinforcement, given the same reinforcement volume fraction of 10% in compression cubes. Different second-order designs exhibited slightly different mechanical properties based on the ratio of reinforcement parallel to the loading direction.

Engineering with keratin: A functional material and a source of bioinspiration

Keratin is a highly multifunctional biopolymer serving various roles in nature due to its diverse material properties, wide spectrum of structural designs, and impressive performance. Keratin-based materials are mechanically robust, thermally insulating, lightweight, capable of undergoing reversible adhesion through van der Waals forces, and exhibit structural coloration and hydrophobic surfaces. Thus, they have become templates for bioinspired designs and have even been applied as a functional material for biomedical applications and environmentally sustainable fiber-reinforced composites. This review aims to highlight keratin's remarkable capabilities as a biological component, a source of design inspiration, and an engineering material. We conclude with future directions for the exploration of keratinous materials.

Elastic and viscoelastic flexural wave motion in woodpecker-beak-inspired structures

This paper comprehensively investigates elastic and viscoelastic flexural wave propagation in structures that are inspired by the unique suture configurations present in a woodpecker's beak, in order to understand their ability to attenuate velocity amplitudes and wave speeds. Waveguides characterized by sinusoidal depth variations, both plain and variously graded along the length, mimicking the suture geometry, are considered in this work. Elastic and viscoelastic wave propagation analyses, along with prior static and free vibration studies, are carried out using a novel superconvergent finite element formulation. In elastic wave propagation analysis, firstly the attenuation characteristics are appraised in relation to the high amplitude and frequency waves of three different plain waveguides with differing depth profile orientations. This prompted us to next consider waveguides of hybrid configurations derived from them. Further, waveguides with lengthwise graded sinusoidal segments, as observed in nature, are studied for better wave attenuation properties compared to plain waveguides. This is followed by viscoelastic wave propagation analysis. Regarding the important role of the suture geometry, which is the focus of this work, the results from the elastic analyses revealed the nature of the reduction in wave speeds and amplitudes, both qualitatively and quantitatively, in such waveguides, and their dependence on the orientation and magnitude of the sinusoidal depth variation. Some waveguide configurations with remarkable wave attenuation characteristics, in terms of both wave speeds and amplitudes, are presented, along with their implications regarding impact mitigation applications.

Noise-induced scaling in skull suture interdigitation

Sutures, the thin, soft tissue between skull bones, serve as the major craniofacial growth centers during postnatal development. In a newborn skull, the sutures are straight; however, as the skull develops, the sutures wind dynamically to form an interdigitation pattern. Moreover, the final winding pattern had been shown to have fractal characteristics. Although various molecules involved in suture development have been identified, the mechanism underlying the pattern formation remains unknown. In a previous study, we reproduced the formation of the interdigitation pattern in a mathematical model combining an interface equation and a convolution kernel. However, the generated pattern had a specific characteristic length, and the model was unable to produce a fractal structure with the model. In the present study, we focused on the anterior part of the sagittal suture and formulated a new mathematical model with time–space-dependent noise that was able to generate the fractal structure. We reduced our previous model to represent the linear dynamics of the centerline of the suture tissue and included a time–space-dependent noise term. We showed theoretically that the final pattern from the model follows a scaling law due to the scaling of the dispersion relation in the full model, which we confirmed numerically. Furthermore, we observed experimentally that stochastic fluctuation of the osteogenic signal exists in the developing skull, and found that actual suture patterns followed a scaling law similar to that of the theoretical prediction.

Enamel-inspired materials design achieving balance of high stiffness and large energy dissipation

Owing to the unique non-self-similar hierarchical microstructure, enamel achieves the balance of high stiffness and toughness, and in turn provides important ideas for the bio-inspired materials design. In this study, a multiscale numerical study has been conducted to investigate whether the property of high stiffness and large energy dissipation could be duplicated in engineering materials through certain material design principles. Motivated by the structure of enamel, the bio-inspired materials consisting of hard and soft phases were considered, and the designing parameters including the cross-sectional shape, volume fraction, and inclination angle of the reinforcement, and other three parameters related to the waviness of the reinforcement were taken into account. It was found that by employing the non-self-similar hierarchical structure, the designed composites exhibited the balance between stiffness and toughness, which has not been achieved in many engineering materials yet. Furthermore, the influences of the aforementioned designing parameters on the mechanical performance of the composites have been elucidated. The findings of this study have provided a guideline for designing bio-inspired composites achieving the balance between stiffness and toughness.

Interfacial toughening effect of suture structures

Suture interfaces are one of the most common architectural designs in natural material-systems and are critical for ensuring multiple functionalities by providing flexibility while maintaining connectivity. Despite intensive studies on the mechanical role of suture structures, there is still a lack of understanding on the fracture mechanics of suture interfaces in terms of their interactions with impinging cracks. Here we reveal an interfacial toughening effect of suture structures by means of "excluding" cracks away from interfaces based on a dimensionless micro-mechanical model for single-leveled and hierarchical suture interfaces with triangular-shaped suture teeth. The effective stress-intensity driving forces for crack deflection along, versus penetration through, an interface at first impingement and on subsequent kinking are formulated and compared with the corresponding resistances. Quantitative criteria are established for discerning the cracking modes and fracture resistance of suture interfaces with their dependences on sutural tooth sharpness and interfacial toughness clarified. Additionally, the effects of structural hierarchy are elucidated through a consideration of hierarchical suture interfaces with fractal-like geometries. This study may offer guidance for designing bioinspired suture structures, especially for toughening materials where interfaces are a key weakness. STATEMENT OF SIGNIFICANCE: Suture interfaces are one of the most common architectural material designs in biological systems, and are found in a wide range of species including armadillo osteoderms, boxfish armor, pangolin scales and insect cuticles. They are designed to provide flexibility while maintaining connectivity. Despite many studies on the mechanical role of suture structures, there is still little understanding of their role in terms of interactions with impinging cracks. Here we reveal an interfacial toughening effect of suture structures by means of "excluding" cracks away from interfaces based on a dimensionless micro-mechanical model for single-leveled and hierarchical suture interfaces with triangular-shaped suture teeth. Quantitative criteria are established for discerning the cracking mode and fracture resistance of the interfaces with their dependences on sutural tooth sharpness and interfacial toughness clarified.

The quest for mechanically and biologically functional soft biomaterials via soft network composites

Developing multifunctional soft biomaterials capable of addressing all the requirements of the complex tissue regeneration process is a multifaceted problem. In order to tackle the current challenges, recent research efforts are increasingly being directed towards biomimetic design concepts that can be translated into soft biomaterials via advanced manufacturing technologies. Among those, soft network composites consisting of a continuous hydrogel matrix and a reinforcing fibrous network closely resemble native soft biological materials in terms of design and composition as well as physicochemical properties. This article reviews soft network composite systems with a particular emphasis on the design, biomaterial and fabrication aspects within the context of soft tissue engineering and drug delivery applications.

Pangolin armor: Overlapping, structure, and mechanical properties of the keratinous scales

The pangolin has a flexible dermal armor consisting of overlapping keratinous scales. Although they show potential for bioinspired flexible armor, the design principles of pangolin armor are barely known. Here we report on the overlapping organization, hierarchical structure (from the nano to the mesolevel), and mechanical response of scales from ground (Chinese) and arboreal (African tree) pangolins. Both scales exhibit the same overlapping organization, with each scale at the center of neighboring scales arranged in a hexagonal pattern. The scales have a cuticle of several layers of loosely attached flattened keratinized cells, while the interior structure exhibits three regions distinguished by the geometry and orientations of the keratinized cells, which form densely packed lamellae; each one corresponds to one layer of cells. Unlike most other keratinous materials, the scales show a crossed-lamellar structure (∼5μm) and crossed fibers (∼50μm). A nano-scale suture structure, observed for the first time, outlines cell membranes and leads to an interlocking interface between lamellae, thus enhancing the bonding and shear resistance. The tensile response of the scales shows an elastic limit followed by a short plateau prior to failure, with Young's modulus ∼1 GPa and tensile strength 60-100MPa. The mechanical response is transversely isotropic, a result of the cross lamellar structure. The strain rate sensitivity in the range of 10(-5)-10(-1)s(-1) region is found to be equal to 0.07-0.08, typical of other keratins and polymers. The mechanical response is highly dependent on the degree of hydration, a characteristic of keratins.

STATEMENT OF SIGNIFICANCE

Although many fish and reptiles have protective scales and carapaces, mammals are characteristically fast and light. The pangolin is one of the few mammal possessing a flexible dermal armor for protection from predators, such as lions. Here we study the arrangement of the scales as well as their hierarchical structure from the nano to the mesolevel and correlate it to the mechanical properties. The study reveals a unique structure consisting of crossed lamellae and interlocking sutures that provide exceptional performance and in-plane isotropy.

A Review of Natural Joint Systems and Numerical Investigation of Bio-Inspired GFRP-to-Steel Joints

There are a great variety of joint types used in nature which can inspire engineering joints. In order to design such biomimetic joints, it is at first important to understand how biological joints work. A comprehensive literature review, considering natural joints from a mechanical point of view, was undertaken. This was used to develop a taxonomy based on the different methods/functions that nature successfully uses to attach dissimilar tissues. One of the key methods that nature uses to join dissimilar materials is a transitional zone of stiffness at the insertion site. This method was used to propose bio-inspired solutions with a transitional zone of stiffness at the joint site for several glass fibre reinforced plastic (GFRP) to steel adhesively bonded joint configurations. The transition zone was used to reduce the material stiffness mismatch of the joint parts. A numerical finite element model was used to identify the optimum variation in material stiffness that minimises potential failure of the joint. The best bio-inspired joints showed a 118% increase of joint strength compared to the standard joints.

Structural Design Elements in Biological Materials: Application to Bioinspiration

Eight structural elements in biological materials are identified as the most common amongst a variety of animal taxa. These are proposed as a new paradigm in the field of biological materials science as they can serve as a toolbox for rationalizing the complex mechanical behavior of structural biological materials and for systematizing the development of bioinspired designs for structural applications. They are employed to improve the mechanical properties, namely strength, wear resistance, stiffness, flexibility, fracture toughness, and energy absorption of different biological materials for a variety of functions (e.g., body support, joint movement, impact protection, weight reduction). The structural elements identified are: fibrous, helical, gradient, layered, tubular, cellular, suture, and overlapping. For each of the structural design elements, critical design parameters are presented along with constitutive equations with a focus on mechanical properties. Additionally, example organisms from varying biological classes are presented for each case to display the wide variety of environments where each of these elements is present. Examples of current bioinspired materials are also introduced for each element.

The armored carapace of the boxfish

The boxfish (Lactoria cornuta) has a carapace consisting of dermal scutes with a highly mineralized surface plate and a compliant collagen base. This carapace must provide effective protection against predators as it comes at the high cost of reduced mobility and speed. The mineralized hydroxyapatite plates, predominantly hexagonal in shape, are reinforced with raised struts that extend from the center toward the edges of each scute. Below the mineralized plates are non-mineralized collagen fibers arranged in through-the-thickness layers of ladder-like formations. At the interfaces between scutes, the mineralized plates form suture-like teeth structures below which the collagen fibers bridge the gap between neighboring scutes. These sutures are unlike most others as they have no bridging Sharpey's fibers and appear to add little mechanical strength to the overall carapace. It is proposed that the sutured interface either allows for accommodation of the changing pressures of the boxfish's ocean habitat or growth, which occurs without molting or shedding. In both tension and punch testing the mineralized sutures remain relatively intact while most failures occur within the collagen fibers, allowing for the individual scutes to maintain their integrity. This complex structure allows for elevated strength of the carapace through an increase in the stressed area when attacked by predators in both penetrating and crushing modes.

Defect-Tolerant Bioinspired Hierarchical Composites: Simulation and Experiment

Defect tolerance, the capacity of a material to maintain strength even under the presence of cracks or flaws, is one of the essential demands in the design of composite materials, as manufacturing induced defects, or those generated during operation, can lead to catastrophic failure and dramatically reduce the mechanical performance. In this paper, we combine computational modeling and advanced multimaterial 3D printing to examine the mechanics of several different classes of defect-tolerant bioinspired hierarchical composites, built from two base materials with contrasting mechanical properties (stiff and soft). We find that in contrast to the brittle base constituents of the composites, the existence of a hierarchical architecture leads to superior defect-tolerant properties. We show that composites with more hierarchical levels dramatically improve the defect tolerance of the material. We also examine the effect of adding both self-similar and dissimilar hierarchical levels to the materials architecture, and show that the geometries with multiple hierarchical levels can retain a significant portion of their fracture strength in the presence of either large edge cracklike flaws or multiple small distributed defects in the material. We compare the stress distributions in materials with different numbers of hierarchies in both simulation and experiment and find a more uniform stress distribution in the uncracked region of materials with higher hierarchy levels. These results provide micromechanical insights into the origin of the higher defect tolerance observed in simulation and experiment.

Hierarchical multiscale structure-property relationships of the red-bellied woodpecker (Melanerpes carolinus) beak

We experimentally studied beaks of the red-bellied woodpecker to elucidate the hierarchical multiscale structure-property relationships. At the macroscale, the beak comprises three structural layers: an outer rhamphotheca layer (keratin sheath), a middle foam layer and an inner bony layer. The area fraction of each layer changes along the length of the beak giving rise to a varying constitutive behaviour similar to functionally graded materials. At the microscale, the rhamphotheca comprises keratin scales that are placed in an overlapping pattern; the middle foam layer has a porous structure; and the bony layer has a big centre cavity. At the nanoscale, a wavy gap between the keratin scales similar to a suture line was evidenced in the rhamphotheca; the middle foam layer joins two dissimilar materials; and mineralized collagen fibres were revealed in the inner bony layer. The nano- and micro-indentation tests revealed that the hardness (associated with the strength, modulus and stiffness) of the rhamphotheca layer (approx. 470 MPa for nano and approx. 320 MPa for micro) was two to three times less than that of the bony layer (approx. 1200 MPa for nano and approx. 630 MPa for micro). When compared to other birds (chicken, finch and toucan), the woodpecker's beak has more elongated keratin scales that can slide over each other thus admitting dissipation via shearing; has much less porosity in the bony layer thus strengthening the beak and focusing the stress wave; and has a wavy suture that admits local shearing at the nanoscale. The analysis of the woodpeckers' beaks provides some understanding of biological structural materials' mechanisms for energy absorption.

On the mechanical behavior of bio-inspired materials with non-self-similar hierarchy

Biological materials exhibiting non-self-similar hierarchical structures possess desirable mechanical properties. Motivated by their penetration resistance and fracture toughness, the mechanical performance of model materials with non-self-similar hierarchical structures was explored and the distinct advantages were identified. A numerical model was developed, based on microscopic observation of enamel prisms. Computational simulations showed that the systems with non-self-similar hierarchy displayed lateral expansion when subjected to longitudinal tensile loading, which reflected negative Poisson׳s ratio and potential for greater volume strain energies when compared with conventional materials with positive Poisson׳s ratio. Employing the non-self-similar hierarchical design, the capability of resilience can be improved. Additionally, the non-self-similar hierarchical structure exhibited larger toughness, resulting from the large pull-out work of the reinforcements. The findings of this study not only elucidate the deformation mechanisms of biological materials with non-self-similar hierarchical structure, but also provide a new path for bio-inspired materials design.

Optimization of fractal space frames under gentle compressive load

The principle of hierarchical design is a prominent theme in many natural systems where mechanical efficiency is of importance. Here we establish the properties of a particular hierarchical structure, showing that high mechanical efficiency is found in certain loading regimes. We show that in the limit of gentle loading, the optimal hierarchical order increases without bound. We show that the scaling of material required for stability against loading to be withstood can be altered in a systematic, beneficial manner through manipulation of the number of structural length scales optimized upon. We establish the relationship between the Hausdorff dimension of the optimal structure and loading for which the structure is optimized. Practicalities of fabrication are discussed and examples of hierarchical frames of the same geometry constructed from solid beams are shown.

Towards high-performance bioinspired composites

Biological composites have evolved elaborate hierarchical structures to achieve outstanding mechanical properties using weak but readily available building blocks. Combining the underlying design principles of such biological materials with the rich chemistry accessible in synthetic systems may enable the creation of artificial composites with unprecedented properties and functionalities. This bioinspired approach requires identification, understanding, and quantification of natural design principles and their replication in synthetic materials, taking into account the intrinsic properties of the stronger artificial building blocks and the boundary conditions of engineering applications. In this progress report, the scientific and technological questions that have to be addressed to achieve this goal are highlighted, and examples of recent research efforts to tackle them are presented. These include the local characterization of the heterogeneous architecture of biological materials, the investigation of structure-function relationships to help unveil natural design principles, and the development of synthetic processing routes that can potentially be used to implement some of these principles in synthetic materials. The importance of replicating the design principles of biological materials rather than their structure per se is highlighted, and possible directions for further progress in this fascinating, interdisciplinary field are discussed.