Mechanical strength of abalone nacre: Role of the soft organic layer

Extracting Geometry and Topology of Orange Pericarps for the Design of Bioinspired Energy Absorbing Materials

As a result of evolution, many biological materials have developed irregular structures that lead to outstanding mechanical performances, like high stiffness-to-weight ratios and good energy absorption. However, reproducing these irregular biological structures in synthetic materials remains a complex design and fabrication challenge. Here, a bioinspired material design method is presented that characterizes the irregular structure as a network of building blocks, also known as tiles, and rules to connect them. Rather than replicating the biological structure one-to-one, synthetic materials are generated with the same distributions of tiles and connectivity rules as the biological material and it is shown that these equivalent materials have structure-to-property relationships similar to the biological ones. To demonstrate the method, the pericarp of the orange, a member of the citrus family known for its protective, energy-absorbing capabilities is studied. Polymer samples are generated and characterized under quasistatic and dynamic compression and display spatially-varying stiffness and good energy absorption, as seen in the biological materials. By quantifying which tiles and connectivity rules locally deform in response to loading, it is also determined how to spatially control the stiffness and energy absorption.

Synthesis and characterization of hydroxyapatite self-assembled nanocomposites on graphene oxide sheets from seashell waste: A green process for regenerative medicine

Bone transplantation is the second most common transplantation surgery in the world. Therefore, there is an urgent need for artificial bone transplantation to repair bone defects. In bone tissue engineering, hydroxyapatite (HA) plays a major role in bone graft applications. This study deals with a facile method for synthesizing HA hexagonal nanorods from seashells by a solid-state hydrothermal transition process. The synthesized HA nanorods (∼2.29 nm) were reinforced with carbon nanotube and chitosan on graphene oxide sheets with polymeric support by in-situ synthetic approach. Among the synthesized nanocomposites viz., hydroxyapatite-graphene oxide (HA-GO), hydroxyapatite-graphene oxide-chitosan (HA-GO-CS), hydroxyapatite-graphene oxide-chitosan-carbon nanotube-polylactic acid (HA-GO-CS-CNT-PLA). Among them, the HA-GO-CS-CNT-PLA composite exhibits micro and macro porosity (∼200 to 600 μm), higher mechanical strength, (Hardness ∼90.5 ± 1.33 MPa; Tensile strength 25.62 MPa), and maximum cell viability in MG63 osteoblast-like cells (80%). The self-assembled hybrid-nanocomposite of HA-GO-CS-CNT-PLA is a promising material for bone filler application and could efficiently utilize seashell waste through the green process.

Bottom-Up Film-to-Bulk Assembly Toward Bioinspired Bulk Structural Nanocomposites

Biological materials, although composed of meager minerals and biopolymers, often exhibit amazing mechanical properties far beyond their components due to hierarchically ordered structures. Understanding their structure-properties relationships and replicating them into artificial materials would boost the development of bulk structural nanocomposites. Layered microstructure widely exists in biological materials, serving as the fundamental structure in nanosheet-based nacres and nanofiber-based Bouligand tissues, and implying superior mechanical properties. High-efficient and scalable fabrication of bioinspired bulk structural nanocomposites with precise layered microstructure is therefore important yet remains difficult. Here, one straightforward bottom-up film-to-bulk assembly strategy is focused for fabricating bioinspired layered bulk structural nanocomposites. The bottom-up assembly strategy inherently offers a methodology for precise construction of bioinspired layered microstructure in bulk form, availability for fabrication of bioinspired bulk structural nanocomposites with large sizes and complex shapes, possibility for design of multiscale interfaces, feasibility for manipulation of diverse heterogeneities. Not limited to discussing what has been achieved by using the current bottom-up film-to-bulk assembly strategy, it is also envisioned how to promote such an assembly strategy to better benefit the development of bioinspired bulk structural nanocomposites. Compared to other assembly strategies, the highlighted strategy provides great opportunities for creating bioinspired bulk structural nanocomposites on demand.

Transparent and Soft Crack-Resistant Bouligand Elastomers Inspired by Fish Scales

Nature with its abundant source offers numerous inspirations for structural and engineering designs. The oriented membranes stacked with bouligand structures in the fish scales show an outstanding combination of high strength and crack resistance. Although the applications of hard biomimetic composites are reported, the structures are rarely utilized in soft materials. Inspired by the scales of various fishes, electrospun membranes are used and stacked to fabricate bouligand elastomers, including orthogonal-plywood, single-bouligand, and double-bouligand structures. The effects of different structures on the properties of elastomers are systematically investigated and possible mechanism is explained using finite element analysis (FEA). The stiffness and fatigue characteristics of these biomimetic elastomers with the above structures are improved compared with the original membranes, especially the elastomers with a single-bouligand structure, which can undergo 5 000 cycles at a maximum strain of 35% without complete failure. The crack only propagates to half of the width of the elastomer with remaining strength of 50% of its original strength. Moreover, the mechanical performance can be adjusted by regulating the proportion of the components. The excellent crack-resistant properties and transparency promote its various potential applications.

Bioinspired Design Rules from Highly Mineralized Natural Composites for Two-Dimensional Composite Design

Discoveries of two-dimensional (2D) materials, exemplified by the recent entry of MXene, have ushered in a new era of multifunctional materials for applications from electronics to biomedical sensors due to their superior combination of mechanical, chemical, and electrical properties. MXene, for example, can be designed for specialized applications using a plethora of element combinations and surface termination layers, making them attractive for highly optimized multifunctional composites. Although multiple critical engineering applications demand that such composites balance specialized functions with mechanical demands, the current knowledge of the mechanical performance and optimized traits necessary for such composite design is severely limited. In response to this pressing need, this paper critically reviews structure-function connections for highly mineralized 2D natural composites, such as nacre and exoskeletal of windowpane oysters, to extract fundamental bioinspired design principles that provide pathways for multifunctional 2D-based engineered systems. This paper highlights key bioinspired design features, including controlling flake geometry, enhancing interface interlocks, and utilizing polymer interphases, to address the limitations of the current design. Challenges in processing, such as flake size control and incorporating interlocking mechanisms of tablet stitching and nanotube forest, are discussed along with alternative potential solutions, such as roughened interfaces and surface waviness. Finally, this paper discusses future perspectives and opportunities, including bridging the gap between theory and practice with multiscale modeling and machine learning design approaches. Overall, this review underscores the potential of bioinspired design for engineered 2D composites while acknowledging the complexities involved and providing valuable insights for researchers and engineers in this rapidly evolving field.

Biomimetic mineralization of nacre-inspired multiple crosslinked PVA/CaAlg/SiO2 membrane with simultaneously enhanced mechanical and separation properties

Inspired by the natural nacre structure, we propose a new strategy to fabricate mineralized, multiple crosslinked hydrogel membranes with the "rigid silica in soft polymer" nacre-like structure. In-situ SiO₂ nanoparticles (NPs) and polyvinyl alcohol/sodium alginate (PVA/NaAlg) are used to simulate the rigid "bricks" and soft "mortar" compositions of nacre, respectively. The nacre-like mineralized (PVA/CaAlg/SiO₂) membrane showed a higher tensile strength of 4.1 ± 0.08 MPa, excellent pure water flux of 170 ± 3 L/m²h, and an oil/water rejection rate of 99 %. The interwoven hierarchal structure, similar to nacre, was determined by SEM analysis. In addition, incorporating SiO₂ NPs increases the anti-swelling, roughness, and hydrophilicity of the membranes. PVA/CaAlg/SiO₂ membrane exhibited excellent superhydrophilicity (WCA value was 0°) and superoleophobicity underwater (OCA value was 162°). PVA/CaAlg/SiO₂ membrane also showed excellent separation performance for water-soluble organic pollutants and can be used for dye separation with rejection efficiencies of 99.5 %, 99.1 %, and 98.3 % for Congo red (CR), Alizarin red (AR), and Sunset yellow (SY), respectively. Moreover, PVA/CaAlg/SiO₂ membrane had outstanding long-term filtration and antifouling performance. The biomineralization-inspired structure provides a promising technique that can be used to prepare high-performance organic-inorganic membranes with great promise for wastewater separation application.

In Situ Mineralizing Spinning of Strong and Tough Silk Fibers for Optical Waveguides

Biopolymer-based optical waveguides with low-loss light guiding performance and good biocompatibility are highly desired for applications in biomedical photonic devices. Herein, we report the preparation of silk optical fiber waveguides through bioinspired in situ mineralizing spinning, which possess excellent mechanical properties and low light loss. Natural silk fibroin was used as the main precursor for the wet spinning of the regenerated silk fibroin (RSF) fibers. Calcium carbonate nanocrystals (CaCO₃ NCs) were in situ grown in the RSF network and served as nucleation templates for mineralization during the spinning, leading to the formation of strong and tough fibers. CaCO₃ NCs can guide the structure transformation of silk fibroin from random coils to β-sheets, contributing to enhanced mechanical properties. The tensile strength and toughness of the obtained fibers are up to 0.83 ± 0.15 GPa and 181.98 ± 52.42 MJ·m^-3, obviously higher than those of natural silkworm silks and even comparable to spider silks. We further investigated the performance of the fibers as optical waveguides and observed a low light loss of 0.46 dB·cm^-1, which is much lower than natural silk fibers. We believed that these silk-based fibers with excellent mechanical and light propagation properties are promising for applications in biomedical light imaging and therapy.

A Molecular-Scale Understanding of Misorientation Toughening in Corals and Seashells

Biominerals are organic-mineral composites formed by living organisms. They are the hardest and toughest tissues in those organisms, are often polycrystalline, and their mesostructure (which includes nano- and microscale crystallite size, shape, arrangement, and orientation) can vary dramatically. Marine biominerals may be aragonite, vaterite, or calcite, all calcium carbonate (CaCO₃ ) polymorphs, differing in crystal structure. Unexpectedly, diverse CaCO₃ biominerals such as coral skeletons and nacre share a similar characteristic: Adjacent crystals are slightly misoriented. This observation is documented quantitatively at the micro- and nanoscales, using polarization-dependent imaging contrast mapping (PIC mapping), and the slight misorientations is consistently between 1° and 40°. Nanoindentation shows that both polycrystalline biominerals and abiotic synthetic spherulites are tougher than single-crystalline geologic aragonite, and molecular dynamics (MD) simulations of bicrystals at the molecular scale reveals that aragonite, vaterite, and calcite exhibit toughness maxima when the bicrystals are misoriented by 10°, 20°, and 30°, respectively, demonstrating that slight misorientation alone can increase fracture toughness. Slight-misorientation-toughening can be harnessed for synthesis of bioinspired materials that only require one material, are not limited to specific top-down architecture, and are easily achieved by self-assembly of organic molecules (e.g., aspirin, chocolate), polymers, metals, and ceramics well beyond biominerals.

Experimental Study on the Tridacna squamosa Shell: Distinctive Structure and Mechanical Behavior

Tridacna squamosa, Lamarck, 1819 (Bivalvia Cardiida Cardiidae, known as the fluted giant clam) is one of the largest-sized bivalve shells, which is equipped with a strong and tough bioceramic shell to effectively protect itself from the attack of predators. To better understand the mechanical defense mechanism, the relationship between the microstructure, composition, and mechanical properties of the Tridacna squamosa shell was investigated. We find that the Tridacna squamosa shell is composed of aragonite CaCO₃ and a small portion of organic matter, which are well-arranged, assembling a multiscale, inhomogeneous, and anisotropic structure. Three levels of microstructure units are identified, including the smallest aragonite rods, medium sheets, and block-like lamellae. Such multiscale structures are the main contributor to creating abundant fracture surfaces much larger than the case for single mineral components, leading to multiple toughening mechanisms observed in Vickers indentation experiments, such as pulled-out of mineral platelet and crack deflection. The material inhomogeneity in the cross-sectional direction indicates that the material is stronger at the inner layer than that at the outer layer, which also facilitates an effective defense against the predator attack. This study may provide insights into the design of biomaterials with the desired mechanical properties.

Tensile and Viscoelastic Behavior in Nacre-Inspired Nanocomposites: A Coarse-Grained Molecular Dynamics Study

Organisms hold an extraordinarily evolutionary advantage in forming complex, hierarchical structures across different length scales that exhibit superior mechanical properties. Mimicking these structures for synthesizing high-performance materials has long held a fascination and has seen rapid growth in the recent past thanks to high-resolution microscopy, design, synthesis, and testing methodologies. Among the class of natural materials, nacre, found in mollusk shells, exhibits remarkably high mechanical strength and toughness. The highly organized "brick and mortar" structure at different length scales is a basis for excellent mechanical properties and the capability to dissipate energy and propagation in nacre. Here, we employ large-scale atomistic coarse-grained molecular dynamics simulations to study the mechanical and viscoelastic behavior of nacre-like microstructures. Uniaxial tension and oscillatory shear simulations were performed to gain insight into the role of complex structure-property relationships. Specifically, the role played by the effect of microstructure (arrangement of the crystalline domain) and polymer-crystal interactions on the mechanical and viscoelastic behavior is elucidated. The tensile property of the nanocomposite was seen to be sensitive to the microstructure, with a staggered arrangement of the crystalline tablets giving rise to a 20-30% higher modulus and lower tensile strength compared to a columnar arrangement. Importantly, the staggered microstructure is shown to have a highly tunable mechanical behavior with respect to the polymer-crystal interactions. The underlying reasons for the mechanical behavior are explained by showing the effect of polymer chain mobility and orientation and the load-carrying capacity for the constituents. Viscoelastic responses in terms of the storage and loss moduli and loss tangent are studied over three decades in frequency and again highlight the differences brought about by the microstructure. We show that our coarse-grained models offer promising insights into the design of novel biomimetic structures for structural applications.

Rubbing-Assisted Approach for Fabricating Oriented Nanobiomaterials

The highly-oriented structures in biological tissues play an important role in determining the functions of the tissues. In order to artificially fabricate oriented nanostructures similar to biological tissues, it is necessary to understand the oriented mechanism and invent the techniques for controlling the oriented structure of nanobiomaterials. In this review, the oriented structures in biological tissues were reviewed and the techniques for producing highly-oriented nanobiomaterials by imitating the oriented organic/inorganic nanocomposite mechanism of the biological tissues were summarized. In particular, we introduce a fabrication technology for the highly-oriented structure of nanobiomaterials on the surface of a rubbed polyimide film that has physicochemical anisotropy in order to further form the highly-oriented organic/inorganic nanocomposite structures based on interface interaction. This is an effective technology to fabricate one-directional nanobiomaterials by a biomimetic process, indicating the potential for wide application in the biomedical field.

Nacre-like composites with superior specific damping performance

Biological materials such as nacre have evolved microstructural design principles that result in outstanding mechanical properties. While nacre's design concepts have led to bio-inspired materials with enhanced fracture toughness, the microstructural features underlying the remarkable damping properties of this biological material have not yet been fully explored in synthetic composites. Here, we study the damping behavior of nacre-like composites containing mineral bridges and platelet asperities as nanoscale structural features within its brick-and-mortar architecture. Dynamic mechanical analysis was performed to experimentally elucidate the role of these features on the damping response of the nacre-like composites. By enhancing stress transfer between platelets and at the brick/mortar interface, mineral bridges and nano-asperities were found to improve the damping performance of the composite to levels that surpass many biological and man-made materials. Surprisingly, the improved properties are achieved without reaching the perfect organization of the biological counterparts. Our nacre-like composites display a loss modulus 2.4-fold higher than natural nacre and 1.4-fold more than highly dissipative natural fiber composites. These findings shed light on the role of nanoscale structural features on the dynamic mechanical properties of nacre and offer design concepts for the manufacturing of bio-inspired composites for high-performance damping applications.

Parasitism by metacercariae modulates the morphological, organic and mechanical responses of the shell of an intertidal bivalve to environmental drivers

Environmental variation alters biological interactions and their ecological and evolutionary consequences. In coastal systems, trematode parasites affect their hosts by disrupting their life-history traits. However, the effects of parasitism could be variable and dependent on the prevailing environmental conditions where the host-parasite interaction occurs. This study compared the effect of a trematode parasite in the family Renicolidae (metacercariae) on the body size and the shell organic and mechanical characteristics of the intertidal mussels Perumytilus purpuratus, inhabiting two environmentally contrasting localities in northern and central Chile (ca. 1600 km apart). Congruent with the environmental gradient along the Chilean coast, higher levels of temperature, salinity and pCO₂, and a lower pH characterise the northern locality compared to that of central Chile. In the north, parasitised individuals showed lower body size and shell resistance than non-parasitised individuals, while in central Chile, the opposite pattern was observed. Protein level in the organic matter of the shell was lower in the parasitised hosts than in the non-parasitised ones regardless of the locality. However, an increase in polysaccharide levels was observed in the parasitised individuals from central Chile. These results evidence that body size and shell properties of P. purpuratus vary between local populations and that they respond differently when confronting the parasitism impacts. Considering that the parasite prevalence reaches around 50% in both populations, if parasitism is not included in the analysis, the true response of the host species would be masked by the effects of the parasite, skewing our understanding of how environmental variables will affect marine species. Considering parasitism and identifying its effects on host species faced with environmental drivers is essential to understand and accurately predict the ecological consequences of climate change.

DCSr-NL: A Novel Method to Semiquantitatively Probe the Growth Rate of Nacre

Matrix proteins play critical roles in regulating the prismatic and nacreous layer formation in the shell. However, due to the dearth of in vivo experiments, their specific roles during shell formation are still unclear. In this study, a new method to detect the content of Sr in the nacreous layer (DCSr-NL), which can semiquantitatively measure the nacreous growth rate, has been proposed. In vitro experiments show that during in vitro crystallization, the Sr element can replace Ca partially, resulting in isomorphism. In vivo experiments show that the best labeling conditions are when the Sr/Ca in seawater is 0.3, at 24 °C, and at 4 days of culture. Although a surface morphological difference in the inner layer of nacre is seldom detected by scanning electron microscopy (SEM), knockdown of the classical gene nacrein or unknown gene NU9, combined with DCSr-NL, shows that both significantly decrease the nacreous layer formation rate. The knockdown of the classical gene Pif177 or unknown genes NU3 or MRPN affects the surface morphology and decreases the nacreous layer formation rate. In general, thanks to DCSr-NL, we can efficiently analyze the growth rate of the nacre with or without morphological changes by SEM, and it is of considerable significance for exploring the target gene's function in forming the nacre in vivo.

Orientation-dependent micromechanical behavior of nacre: In situ TEM experiments and finite element simulations

Nacre's superior mechanical properties and failure behavior are strongly orientation-dependent due to its brick-and-mortar microstructure. In this work, the anisotropic microscopic deformation and the resulting macroscopic mechanical properties are evaluated under different loading conditions. Our in situ transmission electron microscopy deformation experiments and finite element simulations reveal that nacre possesses enhanced indentation resistance along the direction normal to the tablets through delocalization of indentation-induced deformation by taking advantage of its layered structure. In addition, nacre's ability to recover from large deformations is observed. We study the strong loading direction dependence of nacre's macroscopic mechanical properties and elucidate the underlying microscopic deformation patterns in the tablets and the soft matrix. Particularly, its performance along the transverse direction is optimized to withstand the loading conditions in nature. We show the importance of the vertical matrix for the initial stiffness and fracture toughness of the composite. These findings provide guidelines for designing nacre-inspired artificial composites with enhanced mechanical properties. STATEMENT OF SIGNIFICANCE: Nacre is widely recognized as an excellent structural model for designing bio-inspired tough and strong artificial composites. Due to its brick-and-mortar microstructure, it exhibits loading direction-dependent mechanical behavior. In this contribution, we investigate the macroscopic mechanical properties and microscopic deformation behavior of nacre under different loading conditions by means of in situ TEM deformation tests and FE simulations. It is found that effective elastic moduli and microscopic deformation strongly depend on the loading direction. The organic matrix is highly deformable. The indentation resistance along the direction normal to tablets is enhanced via deformation delocalization. Our quantitative and qualitative results provide guidelines on optimizing the mechanical properties of nacre-inspired novel composites.

Biomineralized Materials as Model Systems for Structural Composites: 3D Architecture

Biomineralized materials are sophisticated material systems with hierarchical 3D material architectures, which are broadly used as model systems for fundamental mechanical, materials science, and biomimetic studies. The current knowledge of the structure of biological materials is mainly based on 2D imaging, which often impedes comprehensive and accurate understanding of the materials' intricate 3D microstructure and consequently their mechanics, functions, and bioinspired designs. The development of 3D techniques such as tomography, additive manufacturing, and 4D testing has opened pathways to study biological materials fully in 3D. This review discusses how applying 3D techniques can provide new insights into biomineralized materials that are either well known or possess complex microstructures that are challenging to understand in the 2D framework. The diverse structures of biomineralized materials are characterized based on four universal structural motifs. Nacre is selected as an example to demonstrate how the progression of knowledge from 2D to 3D can bring substantial improvements to understanding the growth mechanism, biomechanics, and bioinspired designs. State-of-the-art multiscale 3D tomographic techniques are discussed with a focus on their integration with 3D geometric quantification, 4D in situ experiments, and multiscale modeling. Outlook is given on the emerging approaches to investigate the synthesis-structure-function-biomimetics relationship.

Distinctive Impact of Heat Treatment on the Mechanical Behavior of Nacreous and Crossed-Lamellar Structures in Biological Shells: Critical Role of Organic Matrix

As biological ceramic composites, mollusk shells exhibit an excellent strength-toughness combination that should be dependent on aragonite/organic matrix interfaces. The mechanical properties and fracture mechanisms of the nacreous structure in the Cristaria plicata (C. plicata) shell and crossed-lamellar structures in the Cymbiola nobilis (C. nobilis) shell were investigated, focusing on the critical role of the organic matrix/aragonite interface bonding that can be adjusted by heat treatments. It is found that heat treatments have a negative impact on the fracture behavior of the nacreous structure in the C. plicata shell, and both the bending and shear properties decrease with increasing heat-treatment temperature because of the loss of water and organic matrix. In contrast, for the crossed-lamellar structure in C. nobilis shell, the water loss in heat treatment slightly decreases its bending properties. When the organic matrix is melted after an appropriate heat treatment at 300°C for 15 min, its bending properties can be greatly enhanced; in this case, remarkable toughening mechanisms involving crack deflection and the fiber pull-out are exhibited, although the interfacial bonding strength reduces. Therefore, an appropriate heat treatment would bring about a positive impact on the fracture behavior of crossed-lamellar structure in the C. nobilis shell. The major research findings have provided an important inspiration that the inducement of moderately weak interfaces rather than all strong interfaces might enhance the comprehensive mechanical properties of fiber-reinforced ceramic composites.

Evaluation of remodeling and geometry on the biomechanical properties of nacreous bivalve shells

Mollusks have developed a broad diversity of shelled structures to protect against challenges imposed by biological interactions(e.g., predation) and constraints (e.g., [Formula: see text]-induced ocean acidification and wave-forces). Although the study of shell biomechanical properties with nacreous microstructure has provided understanding about the role of shell integrity and functionality on mollusk performance and survival, there are no studies, to our knowledge, that delve into the variability of these properties during the mollusk ontogeny, between both shells of bivalves or across the shell length. In this study, using as a model the intertidal mussel Perumytilus purpuratus to obtain, for the first time, the mechanical properties of its shells with nacreous microstructure; we perform uniaxial compression tests oriented in three orthogonal axes corresponding to the orthotropic directions of the shell material behavior (thickness, longitudinal, and transversal). Thus, we evaluated whether the shell material's stress and strain strength and elastic modulus showed differences in mechanical behavior in mussels of different sizes, between valves, and across the shell length. Our results showed that the biomechanical properties of the material building the P. purpuratus shells are symmetrical in both valves and homogeneous across the shell length. However, uniaxial compression tests performed across the shell thickness showed that biomechanical performance depends on the shell size (aging); and that mechanical properties such as the elastic modulus, maximum stress, and strain become degraded during ontogeny. SEM observations evidenced that compression induced a tortuous fracture with a delamination effect on the aragonite mineralogical structure of the shell. Findings suggest that P. purpuratus may become vulnerable to durophagous predators and wave forces in older stages, with implications in mussel beds ecology and biodiversity of intertidal habitats.

Advances in Field-Assisted 3D Printing of Bio-Inspired Composites: From Bioprototyping to Manufacturing

Biocomposite systems evolve to superior structural strategies in adapting to their living environments, using limited materials to form functionality superior to their inherent properties. The synergy of physical-field and Three-dimensional （3D） printing technologies creates unprecedented opportunities that overcome the limitations of traditional manufacturing methods and enable the precise replication of bio-enhanced structures. Here, an overview of typical structural designs in biocomposite systems, their functions and properties, are provided and the recent advances in bio-inspired composites using mechanical, electrical, magnetic, and ultrasound-field-assisted 3D printing techniques are highlighted. Finally, in order to realize the preparation of bionic functional devices and equipment with more superior functions, here an outlook on the development of field-assisted 3D printing technology from three aspects are provided: Materials, technology, and post-processing.

Sawtooth patterns in flexural force curves of structural biological materials are not signatures of toughness enhancement: Part I

Layered architectures are prevalent in tough biological composites, such as nacre and bone. Another example of a biological composite with layered architecture is the skeletal elements-called spicules-from the sponge Euplectella aspergillum. Based on the similarities between the architectures, it has been speculated that the spicules are also tough. Such speculation is in part supported by a sequence of sudden force drops (sawtooth patterns) that are observed in the spicules' force-displacement curves from flexural tests, which are thought to reflect the operation of fracture toughness enhancing mechanisms. In this study, we performed three-point bending tests on the spicules, which also yielded the aforementioned sawtooth patterns. However, based on the analysis of the micrographs obtained during the tests, we found that the sawtooth patterns were in fact a consequence of slip events in the flexural tests. This is put into perspective by our recent study, in which we showed that the spicules' layered architecture contributes minimally to their toughness, and that the toughness enhancement in them is meager in comparison to what is observed in bone and nacre [Monn MA, Vijaykumar K, Kochiyama S, Kesari H (2020): Nat Commun 11:373]. Our past and current results underline the importance of inferring a material's fracture toughness through direct measurements, rather than relying on visual similarities in architectures or force-displacement curve patterns. Our results also suggest that since the spicules do not possess remarkable toughness, re-examining the mechanical function of the spicule's intricate architecture could lead to the discovery of new engineering design principles.

Geographical variability and parasitism on body size, reproduction and shell characteristics of the keyhole limpet Fissurella crassa (Mollusca: Vetigastropoda)

Environmental variation may alter biological interactions and their ecological consequences. For instance, in marine ecosystems hosts and parasites are subject to environmental variability across latitudinal gradients, and their co-evolutionary dynamics may be the result of the interplay with local physical-chemical variables in seawater. Thus, assessing the environmental conditions required for a host in order to improve their survival is essential to understand the host-parasite interaction and dynamics. In this study, we evaluated the impact of parasitism by Proctoeces humboldti on the body size and reproduction of the intertidal keyhole limpet Fissurella crassa collected from three populations spanning ca. 1500 km along the latitudinal gradient of the Chilean coast. In addition, for the first time, we explore whether the effect of parasitism can be extended to changes in the organic composition and mechanical properties of the host shell. Our results show that parasitism prevalence and intensity, and body size of F. crassa increased in central Chile (ca. 33°S). Unlike body size, which was greater in parasitized limpets than in non-parasitized limpets at the three study sites, reproductive performance followed this trend only in central Chile populations, with no differences between parasitized and non-parasitized limpets collected in the northern Chilean (ca. 23°S), and lower in parasitized than non-parasitized individuals from the south-central Chile (ca. 37°S). The organic composition of F. crassa shells showed significant differences between parasite conditions (e.g. polysaccharides and water decreased in parasitized limpets) and across sites (e.g. proteins levels increase in shell of parasitized limpets from central Chile, but decreased at south-central Chile). However, variability in shell mechanical properties (e.g. toughness and elastic module) do not showed significant differences across sites and parasitism condition. These results suggest the interplay of both parasitism and environmental fluctuations upon the reproductive performance and morphology of the host. In addition, our result highlight that the host may also trade-offs reproduction, growth and shell organic composition to maintain the shell functionality (e.g. protection for mechanical forces and durophagous predators).

Natural arrangement of fiber-like aragonites and its impact on mechanical behavior of mollusk shells: A review

During billions of years of evolution, creatures in nature have possessed nearly perfect structures and functions for survival. Multiscale structures in biological materials over several length scales play a pivotal role in achieving structural and functional integrity. Fiber, as a common principal structural element in nature, can be easily constructed in different ways, thus resulting in various natural structures. In this review, we summarized the decades of investigations on a typical biological structure constructed by fiber aragonites in mollusk shells. Crossed-lamellar structure, as one of the most widespread structures in mollusk shells, reconciles the strength-toughness trade-off dilemma successfully due to the presence of highly-hierarchical architectures. This distinctive structure includes several orders of sub-lamellae, and the different order lamellae present a cross-ply feature in one macro crossed-lamellar layer. When a mollusk shell has more than one macro-layer, the crossed-lamellar structure exhibits various forms of architectures including 0°/90°, 0°/90°/0° typical-sandwich, 15°/75°/0° quasi-sandwich, and 0°/90°/0°/90° arranged modes. The fracture resistance and the relevant toughening mechanisms are directly related to the highly-hierarchical crossed-lamellar structures on different length scales. This article is aimed to review the different arranged modes of crossed-lamellar structures existing in nature, with special attention to their impact on the mechanical behavior and salient toughening mechanisms over several length scales, for seeking the design guidelines for the fabrication of bio-inspired advanced engineering materials that are adaptive to different loading conditions.

Calcifiers can Adjust Shell Building at the Nanoscale to Resist Ocean Acidification

Ocean acidification is considered detrimental to marine calcifiers based on laboratory studies showing that increased seawater acidity weakens their ability to build calcareous shells needed for growth and protection. In the natural environment, however, the effects of ocean acidification are subject to ecological and evolutionary processes that may allow calcifiers to buffer or reverse these short-term negative effects through adaptive mechanisms. Using marine snails inhabiting a naturally CO₂ -enriched environment over multiple generations, it is discovered herein that they build more durable shells (i.e., mechanically more resilient) by adjusting the building blocks of their shells (i.e., calcium carbonate crystals), such as atomic rearrangement to reduce nanotwin thickness and increased incorporation of organic matter. However, these adaptive adjustments to future levels of ocean acidification (year 2100) are eroded at extreme CO₂ concentrations, leading to construction of more fragile shells. The discovery of adaptive mechanisms of shell building at the nanoscale provides a new perspective on why some calcifiers may thrive and others collapse in acidifying oceans, and highlights the inherent adaptability that some species possess in adjusting to human-caused environmental change.

Crack path selection in orientationally ordered composites

While cracks in isotropic homogeneous materials propagate straight, perpendicularly to the tensile axis, cracks in natural and synthetic composites deflect from a straight path, often increasing the toughness of the material. Here we combine experiments and simulations to identify materials properties that predict whether cracks propagate straight or kink on a macroscale larger than the composite microstructure. Those properties include the anisotropy of the fracture energy, which we vary several fold by increasing the volume fraction of orientationally ordered alumina (Al_{2}O_{3}) platelets inside a polymer matrix, and a microstructure-dependent process zone size that is found to modulate the additional stabilizing or destabilizing effect of the nonsingular stress acting parallel to the crack. Those properties predict the existence of an anisotropy threshold for crack kinking and explain the surprisingly strong dependence of this threshold on sample geometry and load distribution.

Soft Defect-Tolerant Material Inspired by American Lobsters

The joint membrane of the American lobster shows an excellent combination of high strength, toughness, and defect tolerance due to the periodic helicoidal stacking of the fiber layers that are connected by a weak continuous matrix. Inspired by the joint membrane of American lobsters, we simply use nonwoven fabrics and silicon rubber to fabricate a multilayer soft composite with the helicoidal stacking and controllable matrix. The influences of stacking structure, matrix strength, fabrics strength, and notch size on the fracture behavior of the soft composite during the tensile process are systematically analyzed by both experimental tests and finite element analysis (FEA). We find that similar to the joint membrane, the soft composite demonstrates a gradual failure process and a linear relationship between tensile strength/toughness and notch size. Such phenomena demonstrate the strong defect-tolerant ability, thereby imparting the soft composite with both high strength and toughness. The defect-tolerant ability is closely related to the helicoidal stacking and weak matrix between the fabrics layers, which induce crack deflection and inhibit the propagation of cracks across the sample.

Metal Mimics: Lightweight, Strong, and Tough Nanocomposites and Nanomaterial Assemblies

The ideal structural material would have high strength and stiffness with a tough ductile failure, all with a low density. Historically, no such material exists, and materials engineers have had to sacrifice a desired property during materials selection, with metals (high density), fiber composites (brittle failure), and polymers (low stiffness) having fundamental limitations on at least one front. The ongoing revolution of nanomaterials provides a potential route to build on the potential of fiber-reinforced composites, matching their strength while integrating toughening behaviors akin to metal deformations, all while using low-weight constituents. Here, the challenges, approaches, and recent developments of nanomaterials for structural applications are discussed, with an emphasis on improving toughening mechanisms, which is often the neglected factor in a field that chases strength and stiffness.

Mechanical Properties of Nacre-Like Composites: A Bottom-Up Approach

Nacre is a highly organized hierarchical structure of the mineral and organic components at all scales down to the molecular-scale guided by organic molecules. The mechanical properties of the mineral component of nacre have been studied and well established for decades. In the present work, the shear modulus of the organic matrix of nacre was obtained using two of its important proteineous components, Perlucin and Lustrin A. The shear modulus value of the organic matrix was computed to be in the range of 1.25–1.45 GPa using atomistic molecular dynamics (MD) simulations. Moreover, finite element (FE) simulations were conducted on the three-dimensional (3D) models of the nacre-like composite while varying the relative composition of mineral and organic constituents. The nacre-like composite models with 10–20% by volume of organic part estimated high toughness. The exact optimum value will depend on the mechanical properties of the organic matrix used in the synthesis of nacre-like material. The study is an advancement in the modeling of nacre, sheds light on macroscale properties of nacre-like composites, and opens up new avenues for continuum studies of nacre mechanics, including its mysterious toughening mechanism.

Kinking and cracking behavior in nacre under stepwise compressive loading

The damage evolution of nacre under compressive loading has not been well understood, despite numerous investigations on its compressive behavior. In the present work, quasi-in-situ loading-unloading-reloading stepwise compressive tests were performed on nacre in Pinctada maxima shell, which exhibits a distinctive gradient feature with the thickness of platelets decreasing from the external to internal parts. In the loading direction parallel to the platelets, multiple microcracks and kink bands can absorb much deformation energy, leading to a graceful failure. Kinking only occurs at the final stage of fracture process, and it thus has no obvious influence on the strength of nacre, but contributes to a much larger strain. In the loading direction perpendicular to the platelets, nacre exhibits concurrently much higher compressive strength and fracture strain, as the damage can be effectively restricted. This is attributed to the presence of gradient structure, which disperses the stress concentration in front of the crack tip, and arouses the toughening mechanisms including damage localization and crack deflection. The findings obtained in this study are expected to provide fundamental insights into the design of bio-inspired advanced engineering materials.

An insight into the structure, composition and hardness of a biological material: the shell of freshwater mussels

The shell of the freshwater mussel (Mollusca: Bivalvia) is a composite biological material linked with multifunctional roles in sustaining ecosystem services. Apart from providing mechanical strength and support, the shell is an important site for adherence and growth of multiple types of algae and periphyton. Variations in the shell architecture are observed in the mussels both within a species and among different species. Considering the prospective utility of the shell of the freshwater mussels as a biological material, an assessment of the shell characteristics was accomplished using Corbicula bensoni and Lamellidens marginalis as model species. The calcium carbonate (CaCO₃) content of the shells, physical features and mechanical strength were assessed along with the morphometric analysis. The CaCO₃ content of the shell (upto 95% to 96% of the shell weight) of both the mussels was positively correlated with the shell length, suggesting increased deposition of CaCO₃ in shells with the growth of the species. The cross sectioned views of FE-SEM images of the shells exhibited distinct layered structure with external periostracum and inner nacreous layer varying distinctly. In the growing region, the growth line was prominent in the mussel shells revealed through the FESEM images. In addition XRD, FTIR and EDS studies on the mussel shells confirmed the existence of both aragonite and calcite forms of the calcium carbonate crystals with the incidence of various functional groups. The mechanical strength of the mussel shells was explored through nanoindentation experiments, revealed significant strength at the nanoparticle level of the shells. It was apparent from the results that the shell of the freshwater mussel L. marginalis and C. bensoni qualify as a biological material with prospective multiple applications for human well-being and sustaining environmental quality.

Freshwater mussel shells: prospects as multifunctional biological material.

Materials Research & Measurement Needs for Ceramics Additive Manufacturing

We report on a recent workshop dedicated to additive manufacturing (AM) of ceramics that was held at the National Institute of Standards and Technology (NIST) in November 2019. This two-day all-invited meeting brought together experts from industry, government agencies and academia to review the state of the field and identify the most pressing applied materials research and metrology issues which, if addressed, could accelerate the incorporation of AM methods into commercial ceramic manufacturing. Besides the AM technologies, the discussions included consideration of the necessary post-processing steps. We highlight some of the successes and challenges for the adoption of ceramics AM on an industrial scale, as viewed by the workshop participants. We also propose actions for the ceramic community to facilitate the wider commercialization of these fabrication methods.

3D Printed Tubulanes as Lightweight Hypervelocity Impact Resistant Structures

Lightweight materials with high ballistic impact resistance and load-bearing capabilities are regarded as a holy grail in materials design. Nature builds these complementary properties into materials using soft organic materials with optimized, complex geometries. Here, the compressive deformation and ballistic impact properties of three different 3D printed polymer structures, named tubulanes, are reported, which are the architectural analogues of cross-linked carbon nanotubes. The results show that macroscopic tubulanes are remarkable high load-bearing, hypervelocity impact-resistant lightweight structures. They exhibit a lamellar deformation mechanism, arising from the tubulane ordered pore structure, manifested across multiple length scales from nano to macro dimensions. This approach of using complex geometries inspired by atomic and nanoscale models to generate macroscale printed structures allows innovative morphological engineering of materials with tunable mechanical responses.

Hard-particle rotation enabled soft-hard integrated auxetic mechanical metamaterials

An auxetic design is proposed by soft-hard material integration and demonstrate negative Poisson's ratio (NPR) can be achieved by leveraging unique rotation features of non-connected hard particles in a soft matrix. A theoretical mechanics framework that describes rotation of hard particles in a soft matrix under a mechanical loading is incorporated with overall Poisson's ratio of the soft-hard integrated metamaterials. The theoretical analysis shows that the auxetic behaviour of the soft-hard integrated structures not only relies critically on geometry of particles, but also depends on their periodic arrangements in the soft matrix. Extensive finite-element analyses (FEA) are performed and validate the theoretical predictions of hard-particle rotation and overall Poisson's ratio of soft-hard integrated structures. Furthermore, uniaxial tensile tests are carried out on three-dimensional printed soft-hard integrated structures and confirm auxetic behaviour of soft-hard integrated structures enabled by the rotation of hard particles. Besides, Poisson's ratio varies nonlinearly with the thickness of specimens and reaches a maximum NPR far out of the bounds of plane stress and plane strain situations, which agrees well with FEA. This work provides a theoretical foundation for the design of mechanical metamaterials enabled by soft-hard material integration with auxetic deformation behaviour.

Fracture Behavior of Bio-Inspired Functionally Graded Soft-Hard Composites Made by Multi-Material 3D Printing: The Case of Colinear Cracks

The functional gradient is a concept often occurring in nature. This concept can be implemented in the design and fabrication of advanced materials with specific functionalities and properties. Functionally graded materials (FGMs) can effectively eliminate the interface problems in extremely hard-soft connections, and, thus, have numerous and diverse applications in high-tech industries, such as those in biomedical and aerospace fields. Here, using voxel-based multi-material additive manufacturing (AM, = 3D printing) techniques, which works on the basis of material jetting, we studied the fracture behavior of functionally graded soft-hard composites with a pre-existing crack colinear with the gradient direction. We designed, additively manufactured, and mechanically tested the two main types of functionally graded composites, namely, composites with step-wise and continuous gradients. In addition, we changed the length of the transition zone between the hard and soft materials such that it covered 5%, 25%, 50%, or 100% of the width (W) of the specimens. The results showed that except for the fracture strain, the fracture properties of the graded specimens decreased as the length of the transition zone increased. Additionally, it was found that specimens with abrupt hard-soft transitions have significantly better fracture properties than those with continuous gradients. Among the composites with gradients, those with step-wise gradients showed a slightly better fracture resistance compared to those with continuous gradients. In contrast, FGMs with continuous gradients showed higher values of elastic stiffness and fracture energy, which makes each gradient function suitable for different loading scenarios. Moreover, regardless of the gradient function used in the design of the specimens, decreasing the length of the transition zone from 100%W to 5%W increased the fracture resistance of FGMs. We discuss the important underlying fracture mechanisms using data collected from digital image correlation (DIC), digital image microscopy, and scanning electron microscopy (SEM), which were used to analyze the fracture surface.

Bioinspired Materials: From Living Systems to New Concepts in Materials Chemistry

Nature successfully employs inorganic solid-state materials (i.e., biominerals) and hierarchical composites as sensing elements, weapons, tools, and shelters. Optimized over hundreds of millions of years under evolutionary pressure, these materials are exceptionally well adapted to the specifications of the functions that they perform. As such, they serve today as an extensive library of engineering solutions. Key to their design is the interplay between components across length scales. This hierarchical design-a hallmark of biogenic materials-creates emergent functionality not present in the individual constituents and, moreover, confers a distinctly increased functional density, i.e., less material is needed to provide the same performance. The latter aspect is of special importance today, as climate change drives the need for the sustainable and energy-efficient production of materials. Made from mundane materials, these bioceramics act as blueprints for new concepts in the synthesis and morphosynthesis of multifunctional hierarchical materials under mild conditions. In this review, which also may serve as an introductory guide for those entering this field, we demonstrate how the pursuit of studying biomineralization transforms and enlarges our view on solid-state material design and synthesis, and how bioinspiration may allow us to overcome both conceptual and technical boundaries.

DNP NMR spectroscopy reveals new structures, residues and interactions in wild spider silks

DNP solid state NMR spectroscopy allows non-targeted analysis of wild spider silk in unprecedented detail at natural abundance, revealing hitherto unreported features across several species. A >50-fold signal enhancement for each silk, enables the detection of novel H-bonding networks and arginine conformations, and the post-translational modified amino acid, hydroxyproline.

Host- and pathogen-dependent susceptibility and predisposition to dermatophytosis

Dermatophytes are a highly specialized group of keratinophilic and keratinolytic filamentous fungi causing a ringworm disease called dermatophytosis or superficial mycoses. Although dermatophyte infections do not threaten the host's life, they lower its quality in humans by causing discomfort related to cosmetic problems and through their epidemiological significance, whereas in farm animals they are responsible for economic losses and constitute a source of the spread of spores. Evidence from countless observational studies that have been conducted over the last 90 years indicates that dermatophytes infect humans of every age, race, gender and socioeconomic status with strikingly high rates, as well as both farmed and wild animals in various health conditions and with various epidemiological statuses. However, the prevalence of superficial fungal infections is highly variable, since it depends on several parameters associated with the infected individual and the dermatophyte, their mutual interactions, and epidemiological and geographical factors. The curious disparity in dermatophyte infection patterns has prompted many investigators to search for a link between the host, the host's predispositions and susceptibility to the disease, and the dermatophyte species and virulence. Thus, the question arises as to whether, in addition to the generally recognized factors predisposing hosts to diseases, there are some other predispositions to dermatophyte infections in a species-specific host. In this review, we describe recent findings about the mechanism of dermatophyte infections, focusing on the adaptation of the fungi to the host and conditions predisposing each side to the disease.

Deep Learning to Speed up the Development of Structure-Property Relations For Hexagonal Boron Nitride and Graphene

Structure-property maps play a key role in accelerated materials discovery. The current norm for developing these maps includes computationally expensive physics-based simulations. Here, the capabilities of deep learning agents are explored such as convolutional neural networks (CNNs) and multilayer perceptrons (MLPs) to predict structure-property relations and reduce dependence on simulations. This study contains simulated hexagonal boron nitride (h-BN) microstructures damaged by various levels of radiation and temperature, with the objective to predict their residual strengths from the final atomic positions. By developing low dimensional physical descriptors to statistically describe the defects, these results show that purpose-specific microstructure representation can help in achieving a good prediction accuracy at low computational cost. Furthermore, the adaptability of the trained deep learning agents is explored to predict structure-property maps of other 2D materials using transfer learning. It is shown that in order to achieve good predictions accuracy (≈95% R² ), an agent that is training for the first time ("learning from scratch") requires 23-45% of simulated data, whereas an agent adapting to a different material ("transfer learning") requires only about 10% or less. This suggests that transfer learning is a potential game changer in material discovery and characterization approaches.

Re-designing materials for biomedical applications: from biomimicry to nature-inspired chemical engineering

Gathering inspiration from nature for the design of new materials, products and processes is a topic gaining rapid interest among scientists and engineers. In this review, we introduce the concept of nature-inspired chemical engineering (NICE). We critically examine how this approach offers advantages over straightforward biomimicry and distinguishes itself from bio-integrated design, as a systematic methodology to present innovative solutions to challenging problems. The scope of application of the nature-inspired approach is demonstrated via examples from the field of biomedicine, where much of the inspiration is still more narrowly focused on imitation or bio-integration. We conclude with an outlook on prospective future applications, offered by the more systematic and mechanistically based NICE approach, complemented by rapid progress in manufacturing, computation and robotics. This article is part of the theme issue 'Bioinspired materials and surfaces for green science and technology'.

Quantifying the role of mineral bridges on the fracture resistance of nacre-like composites

The nacreous layer of mollusk shells holds design concepts that can effectively enhance the fracture resistance of lightweight brittle materials. Mineral bridges are known to increase the fracture resistance of nacre-inspired materials, but their role is difficult to quantify due to the lack of experimental systems where only this parameter is controllably varied. In this study, we fabricate tunable nacre-like composites that are used as a model to experimentally quantify the influence of the density of mineral bridges alone on the fracture properties of nacre-like architectures. The composites exhibit a brick-and-mortar architecture comprising highly aligned alumina platelets that are interconnected by titania mineral bridges and infiltrated by an epoxy organic phase. By combining experimental mechanical data with image analysis of such composite microstructures, an analytical model is put forward based on a simple balance of forces acting on an individual bridged platelet. Based on this model, we predict the flexural strength of the nacre-like composite to scale linearly with the density of mineral bridges, as long as the mineral interconnectivity is low enough to keep fracture in a platelet pullout mode. Increasing the mineral interconnectivity beyond this limit leads to platelet fracture and catastrophic failure of the composite. This structure-property correlation provides powerful quantitative guidelines for the design of lightweight brittle materials with enhanced fracture resistance. We illustrate this potential by fabricating nacre-like bulk composites with unparalleled flexural strength combined with noncatastrophic failure.

Crack initiation and growth in a special quasi-sandwich crossed-lamellar structure in Cymbiola nobilis seashell

Sandwich structure consisting of three crossed-lamellar layers (inner, middle and outer) is one of the most common structures found in mollusk shells, and is normally arranged in a 0°/90°/0° or 90°/0°/90° mode. However, the Cymbiola nobilis seashell in the present study is observed to exhibit a unique quasi-sandwich structure, where the inner and middle layers have an ~15° rotation in comparison with those of typical sandwich structures, resulting in a 15°/75°/0° or 75°/15°/90° mode. This has been identified as the weak/tough/weak and tough/weak/tough modes, and the sample arranged in the 15°/75°/0° mode with a tough layer in the middle has a higher strength than that arranged in the 75°/15°/90° mode with a weak layer in the middle. The fracture resistances of these two types of structural arrangements depend mainly on crack propagation. The interfaces between the macrolayers can effectively arrest the crack propagation especially when the tough layer is positioned in the middle (15°/75°/0° mode), hence increasing the strength and toughness of materials. Salient toughening mechanisms involving crack deflection together with zig-zag crack propagation paths as well as the fiber pull-out of second-order lamellae are identified. Moreover, triangular fracture paths with a convex morphology are observed to form due to the concurrent occurrence of fiber fracturing and channel cracking in single 1st-order lamellae. These findings shed light on the superb crack propagation resistance of the unique quasi-sandwich structure in the C. nobilis shell, thus paving the way for the development of bio-inspired advanced structural materials.

Microstructure analysis and mechanical properties by instrumented indentation of Charonia Lampas Lampas shell

Scanning electron microscopy, X-ray diffraction and Fourier transformed infrared spectroscopy have been used to characterize the microstructure and instrumented microindentation for the determination of the mechanical properties of Charonia Lampas Lampas shell. Both elastic modulus and hardness are found to be dependent on the texture of the three distinct layers. From the analysis of load-depth curves, the shell exhibits small viscoelastic behaviour at low indentation loads and mainly elastoplastic behaviour at higher loads. These phenomena were attributed to the influence of the organic matter present in the shell. Both elastic modulus and hardness are found to be load-dependent in each layer in relation to their microstructure and, accordingly, to the anisotropy of the predominant mineral part. At a macroscopic scale, this tendency is explained by using a rule of mixture and jointly by the anisotropy of the aragonite. The Bull and Page model is subsequently applied to the hardness variation in order to compute the macrohardness which is the characteristic hardness number of a material and the hardness parameter related to the indentation size effect. This model describes well the experimental results for the relative higher depths, and deviates for the small depths due to the effect of the viscoelastic behaviour which then requires a more appropriate model to describe this phenomenon.