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id="toc-Adaptability-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Single_vs._Double_Bouligand_Structure" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Single_vs._Double_Bouligand_Structure"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Single vs. Double Bouligand Structure</span> </div> </a> <ul id="toc-Single_vs._Double_Bouligand_Structure-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Examples_in_Nature" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Examples_in_Nature"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Examples in Nature</span> </div> </a> <button aria-controls="toc-Examples_in_Nature-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Examples in 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src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Bouligand_structure_model_and_as_found_in_nature.png/214px-Bouligand_structure_model_and_as_found_in_nature.png" decoding="async" width="214" height="179" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/e/e7/Bouligand_structure_model_and_as_found_in_nature.png 1.5x" data-file-width="293" data-file-height="245" /></a><figcaption>Bouligand structure model and <a href="/wiki/Scanning_electron_microscope" title="Scanning electron microscope">SEM</a> image of structure as found in dactyl club of the <a href="/wiki/Mantis_shrimp" title="Mantis shrimp">mantis shrimp</a>.</figcaption></figure> <p>A <b>Bouligand structure</b> is a layered and rotated <a href="/wiki/Microstructure" title="Microstructure">microstructure</a> resembling plywood, which is frequently found in naturally evolved materials.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> It consists of multiple <a href="/wiki/Lamella_(materials)" title="Lamella (materials)">lamellae</a>, or layers, each one composed of aligned <a href="/wiki/Fibrous" class="mw-redirect" title="Fibrous">fibers</a>. Adjacent lamellae are progressively rotated with respect to their neighbors.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> This structure enhances the mechanical properties of materials, especially its fracture resistance, and enables strength and in plane <a href="/wiki/Isotropy" title="Isotropy">isotropy</a>. It is found in various natural structures, including the <a href="/wiki/Cosmoid_scale" class="mw-redirect" title="Cosmoid scale">cosmoid scale</a> of the <a href="/wiki/Coelacanth" title="Coelacanth">coelacanth</a>, and the dactyl club of the <a href="/wiki/Mantis_shrimp" title="Mantis shrimp">mantis shrimp</a> and many other <a href="/wiki/Stomatopod" class="mw-redirect" title="Stomatopod">stomatopods</a>. In physics, these structures were conceived in 1869 by Ernest Reusch <sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> and are called Reusch piles.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>Due to its desirable mechanical properties, there are ongoing attempts to replicate Bouligand arrangements in the creation of failure resistant bioinspired materials. For example, it has been shown that layered composites (such as <a href="/wiki/Carbon_fiber_reinforced_polymer" class="mw-redirect" title="Carbon fiber reinforced polymer">CFRP</a>) utilizing this structure have enhanced impact properties.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> However, replicating the structure on small length scales is challenging, and the development and advancement of manufacturing techniques continually improves the ability to replicate this desirable structure. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Mechanical_Properties">Mechanical Properties</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bouligand_structure&action=edit&section=1" title="Edit section: Mechanical Properties"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Toughening_Mechanisms">Toughening Mechanisms</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bouligand_structure&action=edit&section=2" title="Edit section: Toughening Mechanisms"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Picoindentation_of_Bouligand_Structure.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Picoindentation_of_Bouligand_Structure.png/183px-Picoindentation_of_Bouligand_Structure.png" decoding="async" width="183" height="77" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Picoindentation_of_Bouligand_Structure.png/275px-Picoindentation_of_Bouligand_Structure.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Picoindentation_of_Bouligand_Structure.png/366px-Picoindentation_of_Bouligand_Structure.png 2x" data-file-width="622" data-file-height="262" /></a><figcaption><a href="/wiki/Nanoindentation" title="Nanoindentation">Picoindentation</a> of Bouligand Structure in Dactyl Club<sup id="cite_ref-:22_6-0" class="reference"><a href="#cite_note-:22-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup></figcaption></figure> <p>The Bouligand structure found in many natural materials is credited with imparting a very high <a href="/wiki/Toughness" title="Toughness">toughness</a> and <a href="/wiki/Fracture_toughness" title="Fracture toughness">fracture resistance</a> to the overall material it is a part of. The mechanisms by which this toughening occurs are many, and no one mechanism has yet to be identified as the main source of the structure's toughness. Both computational work and physical experiments have been done to determine these pathways by which the structure resists fracture so that synthetic tough Bouligand structures can be taken advantage of.<sup id="cite_ref-:02_7-0" class="reference"><a href="#cite_note-:02-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:12_8-0" class="reference"><a href="#cite_note-:12-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:32_9-0" class="reference"><a href="#cite_note-:32-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:6_10-0" class="reference"><a href="#cite_note-:6-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>Crack deflection of one form or another is considered the main toughening mechanism in the bouligand structure.<sup id="cite_ref-:22_6-1" class="reference"><a href="#cite_note-:22-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:12_8-1" class="reference"><a href="#cite_note-:12-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:03_11-0" class="reference"><a href="#cite_note-:03-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> Deflection can take the form of crack tilting, and crack bridging.<sup id="cite_ref-:03_11-1" class="reference"><a href="#cite_note-:03-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> In the former, the crack propagates along the direction of the fiber plane; at the interface with the matrix material.<sup id="cite_ref-:03_11-2" class="reference"><a href="#cite_note-:03-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> Once the energy release rate at the tip is sufficiently low, the crack can no longer propagate along the fiber direction and must switch to crack bridging.<sup id="cite_ref-:03_11-3" class="reference"><a href="#cite_note-:03-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> This mode involves the crack changing direction drastically and cutting through fibers to reach a new plane to propagate along.<sup id="cite_ref-:03_11-4" class="reference"><a href="#cite_note-:03-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> A combination of crack tilting and crack bridging in the bouligand structure results in a highly distorted and enlarged crack.<sup id="cite_ref-:03_11-5" class="reference"><a href="#cite_note-:03-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> This causes the new surface area created by the propagating crack to increase dramatically relative to a straight crack; making further propagation less and less favorable and in turn toughening the material.<sup id="cite_ref-:22_6-2" class="reference"><a href="#cite_note-:22-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:03_11-6" class="reference"><a href="#cite_note-:03-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>In addition to crack deflection which simply causes a single crack to change direction and follow a more tortuous path, the bouligand structure can also tolerate multiple cracks to form and keep them from coalescing.<sup id="cite_ref-:22_6-3" class="reference"><a href="#cite_note-:22-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> This is sometimes termed crack twisting.<sup id="cite_ref-:22_6-4" class="reference"><a href="#cite_note-:22-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>Inherently accompanying crack deflection, tilting, bridging and twisting is the mixing of fracture modes.<sup id="cite_ref-:12_8-2" class="reference"><a href="#cite_note-:12-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Fracture_mechanics" title="Fracture mechanics">Fracture modes</a> include opening, in-plane shear, and out-of-plane shear. The mixing of these modes via crack bridging, tilting and twisting all greatly complicate the stress fields experienced by the material; helping to dissipate the force on any one laminate plane.<sup id="cite_ref-:12_8-3" class="reference"><a href="#cite_note-:12-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Impact_Resistance">Impact Resistance</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bouligand_structure&action=edit&section=3" title="Edit section: Impact Resistance"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Impact_Resistance_as_a_Function_of_Pitch_in_Bouligand_Structure.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/Impact_Resistance_as_a_Function_of_Pitch_in_Bouligand_Structure.png/440px-Impact_Resistance_as_a_Function_of_Pitch_in_Bouligand_Structure.png" decoding="async" width="440" height="169" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/7/72/Impact_Resistance_as_a_Function_of_Pitch_in_Bouligand_Structure.png 1.5x" data-file-width="641" data-file-height="246" /></a><figcaption>Density, Specific <a href="/wiki/Ballistics" title="Ballistics">Ballistic Limit Velocity</a>, and Specific Energy Absorption as a Function of Pitch in Bouligand Structured <a href="/wiki/Nanocellulose" title="Nanocellulose">Nanocellulose</a> Film<sup id="cite_ref-:02_7-1" class="reference"><a href="#cite_note-:02-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup></figcaption></figure> <p>Impact resistance in materials is differentiated from toughening in general by the rate at which stress is applied. In impact testing, the rate at which either <a href="/wiki/Stress_(mechanics)" title="Stress (mechanics)">stress</a> or strain is applied to the sample is much higher than so-called static testing. In synthetic <a href="/wiki/Nanocellulose" title="Nanocellulose">nano-cellulose</a> films formed into bouligand structures, it was shown that as the pitch angle was increased, the <a href="/wiki/Density" title="Density">density</a> quickly drops to a roughly constant value as the films are not able to neatly stack onto each other.<sup id="cite_ref-:02_7-2" class="reference"><a href="#cite_note-:02-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> This value rises again between 42 and 60 degrees and re-stabilizes at higher angles.<sup id="cite_ref-:02_7-3" class="reference"><a href="#cite_note-:02-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> This reduction in density is accompanied by a sharp increase in both specific ballistic limit velocity, and specific energy absorption.<sup id="cite_ref-:02_7-4" class="reference"><a href="#cite_note-:02-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> The relatively small angles of 18 to 42 degrees that correlate to the lowest density for the bouligand structure also are shown to have better impact resistance, and better energy adsorption than traditional synthetic quasi-isotropic structures made for impact resistance.<sup id="cite_ref-:02_7-5" class="reference"><a href="#cite_note-:02-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> This experimentally optimized range of angles for impact resistance is consistent with the range of angles between fiber layers found in natural examples of the bouligand structure.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:53_13-0" class="reference"><a href="#cite_note-:53-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p><p>Another means of toughening the bouligand structure is by shear wave filtering.<sup id="cite_ref-:53_13-1" class="reference"><a href="#cite_note-:53-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> The periodic and hierarchical nature of the Bouligand structure, creates a shear wave filtering effect that is especially effective during high intensity dynamic loads. As the force is applied, specific frequencies that are in shear are not permitted to transmit through the layered structure, creating a band gap in the transmitted energies and decreasing the effective energy felt by the system. The pitch angle of the layers, thickness of the layers, and number of layers present in the material all effect which frequencies are filtered out.<sup id="cite_ref-:53_13-2" class="reference"><a href="#cite_note-:53-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Adaptability">Adaptability</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bouligand_structure&action=edit&section=4" title="Edit section: Adaptability"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Adjustment of the Bouligand structure during loading has been measured using small angle X-ray scattering (<a href="/wiki/Small-angle_X-ray_scattering" title="Small-angle X-ray scattering">SAXS</a>). The two adjustment effects are the change in angle between the collagen fibrils and tensile axis, and the stretching of collagen fibrils. There are four mechanisms through which these adjustments occur.<sup id="cite_ref-:32_9-1" class="reference"><a href="#cite_note-:32-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <ol><li>Fibrils rotate because of interfibrillar shear: As a tensile force is applied, fibrils rotate to align with the tensile direction. During deformation, the shear component of the applied stress causes the hydrogen bonds between fibrils to break and then reform after fibril adjustment.<sup id="cite_ref-:32_9-2" class="reference"><a href="#cite_note-:32-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup></li> <li>Collagen fibrils stretch: Collagen fibrils can elastically stretch, resulting in fibrils re-orientating to align with the tensile direction.<sup id="cite_ref-:32_9-3" class="reference"><a href="#cite_note-:32-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup></li> <li>Tensile opening of interfibrillar gaps: Fibrils highly misoriented with the tensile direction can separate, creating an opening.<sup id="cite_ref-:32_9-4" class="reference"><a href="#cite_note-:32-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup></li> <li>"Sympathetic" lamella rotation: A lamella is able to rotate away from the tensile direction if it is sandwiched between two lamellae that are reorienting themselves towards the tensile direction. This can happen if the bonding between these lamellae is high.<sup id="cite_ref-:32_9-5" class="reference"><a href="#cite_note-:32-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup></li></ol> <p>Ψ refers to the angle between the tensile axis and the collagen fibril. Mechanisms 1 and 2 both decrease Ψ. Mechanisms 3 and 4 can increase Ψ, as in, the fibril moves away from the tensile axis. Fibrils with a small Ψ stretch elastically. Fibrils with a large Ψ are compressed, since adjacent lamellae contract in accordance with <a href="/wiki/Poisson%27s_ratio" title="Poisson's ratio">Poisson's ratio</a>, which is a function of strain <a href="/wiki/Anisotropy" title="Anisotropy">anisotropy</a>.<sup id="cite_ref-:32_9-6" class="reference"><a href="#cite_note-:32-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Single_vs._Double_Bouligand_Structure">Single vs. Double Bouligand Structure</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bouligand_structure&action=edit&section=5" title="Edit section: Single vs. Double Bouligand Structure"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The most common Bouligand structure found in nature is the twisted plywood structure where there is a constant angle of misalignment between layers. A rare variation of this structure is the so-called "double twisted" Bouligand structure seen in <a href="/wiki/Coelacanth" title="Coelacanth">Coelacanth</a>. This structure uses stacks of two as units to be twisted with respect to each other at some constant misalignment angle. The two fibril layers in each of these units in this case lay such that their fibril orientation is perpendicular to each other.<sup id="cite_ref-:12_8-4" class="reference"><a href="#cite_note-:12-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>The mechanical differences between the single and double twisted bouligand structure has been observed.<sup id="cite_ref-:12_8-5" class="reference"><a href="#cite_note-:12-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> It was shown that the double bouligand structure is stiffer and tougher than the more common single bouligand structure. The increase in stiffness is also accompanied by a reduction of flexibility.<sup id="cite_ref-:12_8-6" class="reference"><a href="#cite_note-:12-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> The increased strength is attributed in part to an addition to the structure of "inter-bundle fibrils" that run up and down the stack of layers, perpendicular to the twisted fiber planes.<sup id="cite_ref-:12_8-7" class="reference"><a href="#cite_note-:12-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> These fiber bundles help keep the structure together by greatly increasing the energy needed for inter-fibril sliding.<sup id="cite_ref-:12_8-8" class="reference"><a href="#cite_note-:12-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> These bundles are coupled with the double twisted nature of the plywood arraignment, which shifts the direction a crack would like to grow drastically with each layer.<sup id="cite_ref-:12_8-9" class="reference"><a href="#cite_note-:12-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>It has also been observed that a structure can form mostly similar to the single twisted bouligand structure, but with a non-constant angle of misalignment. It is still unclear how this particular structural difference affects mechanical properties.<sup id="cite_ref-:32_9-7" class="reference"><a href="#cite_note-:32-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Examples_in_Nature">Examples in Nature</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bouligand_structure&action=edit&section=6" title="Edit section: Examples in Nature"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Arthropods">Arthropods</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bouligand_structure&action=edit&section=7" title="Edit section: Arthropods"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Arthropod" title="Arthropod">arthropod</a> <a href="/wiki/Exoskeleton" title="Exoskeleton">exoskeleton</a> is highly hierarchical. Polysaccharide chitin fibrils arrange with proteins to form fibers, the fibers coalesce into bundles, and then the bundles arrange into horizontal planes which are stacked helicoidally, forming the twisted plywood Bouligand structure.<sup id="cite_ref-:1_14-0" class="reference"><a href="#cite_note-:1-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> Repeating Bouligand structures form the <a href="/wiki/Arthropod_cuticle" class="mw-redirect" title="Arthropod cuticle">exocuticle</a> and endocuticle.<sup id="cite_ref-:1_14-1" class="reference"><a href="#cite_note-:1-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> Differences in the Bouligand structure of the exocuticle and endocuticle have been found to be critical for analyzing the mechanical properties of both regions. </p><p>Arthropods have exoskeletons that provide protection from the environment, mechanical load support, and body structure. The outer layer, called the <a href="/wiki/Arthropod_cuticle" class="mw-redirect" title="Arthropod cuticle">epicuticle</a>, is thin and waxy and is the main waterproofing barrier. Below is the procuticle, which is designed as the main structural element to the body. The procuticle is made of two sections, the <a href="/wiki/Exocuticle" class="mw-redirect" title="Exocuticle">exocuticle</a> on the outer part, and the <a href="/wiki/Arthropod_cuticle" class="mw-redirect" title="Arthropod cuticle">endocuticle</a> on the inner part. The exocuticle is denser than the endocuticle; the endocuticle makes up about 90 volume % of the exoskeleton. Both the exocuticle and endocuticle are made with a Bouligand structure.<sup id="cite_ref-:1_14-2" class="reference"><a href="#cite_note-:1-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Crabs">Crabs</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bouligand_structure&action=edit&section=8" title="Edit section: Crabs"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In <a href="/wiki/Crab" title="Crab">crab</a> exoskeletons, <a href="/wiki/Calcite" title="Calcite">calcite</a> and amorphous <a href="/wiki/Calcium_carbonate" title="Calcium carbonate">calcium carbonate</a> are the minerals deposited in the chitin-protein hierarchical matrix.<sup id="cite_ref-:1_14-3" class="reference"><a href="#cite_note-:1-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> The sheep crab (<i><a href="/wiki/Loxorhynchus_grandis" title="Loxorhynchus grandis">Loxorhynchun grandis</a></i>), like other crabs, has a highly anisotropic exoskeleton.<sup id="cite_ref-:1_14-4" class="reference"><a href="#cite_note-:1-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> The spacing between the (x-y) plane Bouligand lamellae in the crab exocuticle is ~3-5μm, whereas the interlamellar spacing in the endocuticle is much greater, about 10-15μm.<sup id="cite_ref-:1_14-5" class="reference"><a href="#cite_note-:1-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> The smaller spacing of the exocuticle results in a higher lamellae density in the exocuticle. There is a higher hardness measurement in the exocuticle than the endocuticle, which is attributed to a higher mineral content in the exocuticle.<sup id="cite_ref-:1_14-6" class="reference"><a href="#cite_note-:1-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> This gives a higher <a href="/wiki/Wear" title="Wear">wear resistance</a> and <a href="/wiki/Hardness" title="Hardness">hardness</a> on the surface of the exoskeleton, thus giving the crab a greater degree of protection. Under stress, the Bouligand planes fail via normal bundle fracture or bundle separation mechanisms.<sup id="cite_ref-:1_14-7" class="reference"><a href="#cite_note-:1-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> The exocuticle-endocuticle interface is the most critical region and typically where failure first occurs, due to the anisotropic structure and discontinuity of Bouligand planes and spacing at this interface.<sup id="cite_ref-:1_14-8" class="reference"><a href="#cite_note-:1-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p><p>In the z-direction, porous tubules exist normal to the Bouligand planes that penetrate the exoskeleton. The function of these tubules is to transport ions and nutrients to the new exoskeleton during the <a href="/wiki/Molding_(process)" title="Molding (process)">molting process</a>. The presence of these tubules, which have a helical structure, results in a ductile <a href="/wiki/Necking_(engineering)" title="Necking (engineering)">necking</a> region during tension. An increased degree of ductility increases the toughness of the crab exoskeleton. </p> <div class="mw-heading mw-heading4"><h4 id="Lobster">Lobster</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bouligand_structure&action=edit&section=9" title="Edit section: Lobster"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <i><a href="/wiki/American_lobster" title="American lobster">Homarus americanus</a></i> (American lobster) is an arthropod with an exoskeleton structure similar to the crabs above, and with similar trends comparing the endo- and exo- cuticles. An important note for the lobster exoskeleton structural/mechanical properties is the impact of the <a href="/wiki/Honeycomb_structure" title="Honeycomb structure">honeycomb structure</a> formed by the Bouligand planes.<sup id="cite_ref-:23_15-0" class="reference"><a href="#cite_note-:23-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> The <a href="/wiki/Stiffness" title="Stiffness">stiffness</a> values for the exocuticle in lobster range from 8.5-9.5 GPa, while the endocuticle ranges from 3–4.5 GPa.<sup id="cite_ref-:23_15-1" class="reference"><a href="#cite_note-:23-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> Gradients in the honeycomb network, especially at the interface between the endo- and exo- cuticle are believed to be the reason for this discrepancy between the structures.<sup id="cite_ref-:23_15-2" class="reference"><a href="#cite_note-:23-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Mantis_Shrimp">Mantis Shrimp</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bouligand_structure&action=edit&section=10" title="Edit section: Mantis Shrimp"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Mantis_shrimp" title="Mantis shrimp">Stomatopods</a> have thoracic appendages that are used to hunt prey. The appendages can either be spear-like or club-like, depending on the species.<sup id="cite_ref-:53_13-3" class="reference"><a href="#cite_note-:53-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> Mantis shrimp with a club-like appendage, or "dactyl club", uses it to smash the shell of prey such as mollusks or crabs.<sup id="cite_ref-:4_16-0" class="reference"><a href="#cite_note-:4-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> The <a href="/wiki/Odontodactylus_scyllarus" title="Odontodactylus scyllarus">peacock mantis shrimp</a> is a species of mantis shrimp that has a dactyl club. The clubs are able to withstand fracture under the high stress waves associated with blows against prey. This is possible due to the multi-regional structure of the clubs, which includes a region incorporating a Bouligand structure.<sup id="cite_ref-:53_13-4" class="reference"><a href="#cite_note-:53-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p><p>The outer, top region of the club is called the impact region. The impact region is supported periodic zones and a striated region. The periodic regions are below the impact region, on the inside of the club. The striated region is present on the sides of the club, surrounding the edges of the periodic region.<sup id="cite_ref-:53_13-5" class="reference"><a href="#cite_note-:53-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p><p>The impact region is about 50 to 70 μm thick, and is made with highly crystallized <a href="/wiki/Hydroxyapatite" title="Hydroxyapatite">hydroxyapatite</a>. The periodic region is dominated by an amorphous calcium carbonate phase.<sup id="cite_ref-:5_17-0" class="reference"><a href="#cite_note-:5-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> Surrounded by the amorphous mineral phase are chitin fibrils, which make up a Bouligand structure. The layered arrangement of the periodic region corresponds to a compete 180° rotation of the fibers. The impact region has a similar structure, but with a larger pitch distance (length between compete 180° rotation).<sup id="cite_ref-:53_13-6" class="reference"><a href="#cite_note-:53-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> The striated region is made of highly aligned parallel chitin fiber bundles.<sup id="cite_ref-:5_17-1" class="reference"><a href="#cite_note-:5-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p><p>The club appendage can sustain high intensity load by shear wave filtering because of the periodicity and chirality of its Bouligand structure.<sup id="cite_ref-:53_13-7" class="reference"><a href="#cite_note-:53-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> Catastrophic crack growth is hindered in two ways. When crack growth follows the helicoidal structure between layers of chitin fibers, a large surface area per crack length is produced. Therefore, there is high total energy dissipated during club impact and crack propagation. When cracks propagate through neighboring layers, growth is hampered because of modulus oscillation. The Bouligand structure has anisotropic stiffness, resulting in an elastic modulus oscillation through the layers. Overall damage tolerance is improved, with crack propagation depending on growth direction in relation to chitin fiber orientation.<sup id="cite_ref-:5_17-2" class="reference"><a href="#cite_note-:5-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Fish">Fish</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bouligand_structure&action=edit&section=11" title="Edit section: Fish"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Arapaima">Arapaima</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bouligand_structure&action=edit&section=12" title="Edit section: Arapaima"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Arapaima" title="Arapaima">Arapaima</a> fish's outer scales are designed to resist piranha bites. This is achieved through the scales' hierarchical architecture. The thinness of the scales and their overlapping arrangement allow for flexibility during movement. This also influences how much a single scale will bend when a predator attacks.<sup id="cite_ref-:32_9-8" class="reference"><a href="#cite_note-:32-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>In the species <i><a href="/wiki/Arapaima_gigas" title="Arapaima gigas">Arapaima gigas</a></i>, each scale has two distinct structural regions which results in a scale that is resistant to puncture and bending. The outer layer is about 0.5 mm thick and is highly <a href="/wiki/Mineralization_(biology)" class="mw-redirect" title="Mineralization (biology)">mineralized</a>, which makes it hard, promoting predator tooth fracture. The inner layer is about 1 mm thick and is made of mineralized collagen fibrils arranged in a Bouligand structure.<sup id="cite_ref-:32_9-9" class="reference"><a href="#cite_note-:32-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> In the fibrils, collagen molecules are embedded with hydroxyapatite mineral nanocrystals. Collagen fibrils align in the same direction to make a layer of collagen lamella, of about 50 μm in thickness. Lamellae are stacked with a misalignment in orientation, creating a Bouligand structure.<sup id="cite_ref-:32_9-10" class="reference"><a href="#cite_note-:32-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>When the scales bend during an attack, stress is distributed due to the corrugated morphology. The largest deformation is designed to occur in the inner core layer. The inner layer can support more plastic deformation than the brittle outer layer. This is because the Bouligand structure can adjust its lamellar layers to adapt to applied forces.<sup id="cite_ref-:32_9-11" class="reference"><a href="#cite_note-:32-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>Adjustment of the Bouligand structure during loading has been measured using small angle X-ray scattering (<a href="/wiki/Small-angle_X-ray_scattering" title="Small-angle X-ray scattering">SAXS</a>). The four mechanisms through which adjustments occur are fibril rotation, collagen fibril stretching, tensile opening between fibrils, and sympathetic lamella rotation.<sup id="cite_ref-:32_9-12" class="reference"><a href="#cite_note-:32-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>Fibrils adapting to the loading environment enhance the flexibility of the lamellae. This contributes resistance to scale bending, and therefore increases fracture resistance. As a whole, the outer scale layer is <a href="/wiki/Hardness" title="Hardness">hard</a> and <a href="/wiki/Brittleness" title="Brittleness">brittle</a>, while the inner layer is <a href="/wiki/Ductility" title="Ductility">ductile</a> and <a href="/wiki/Toughness" title="Toughness">tough</a>.<sup id="cite_ref-:32_9-13" class="reference"><a href="#cite_note-:32-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Carp">Carp</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bouligand_structure&action=edit&section=13" title="Edit section: Carp"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A similar Bouligand structure was found in the scales of the <a href="/wiki/Common_carp" title="Common carp">common carp</a> (<i><a href="/wiki/Common_carp" title="Common carp">Cyprinus carpio</a></i>).<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> Compared to the arapaima, the mineral content in carp scales is lower, while exhibiting higher total energy dissipation in tensile testing as well as higher fibril extensibility. </p> <div class="mw-heading mw-heading2"><h2 id="Biomimicry">Biomimicry</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bouligand_structure&action=edit&section=14" title="Edit section: Biomimicry"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Additive_Manufacturing">Additive Manufacturing</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bouligand_structure&action=edit&section=15" title="Edit section: Additive Manufacturing"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/3D_printing" title="3D printing">Additive manufacturing</a> is a popular upcoming form of industry which allows for complex geometries and unique performance characteristics for AM parts.<sup id="cite_ref-:42_19-0" class="reference"><a href="#cite_note-:42-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> The main issue with mechanical properties of AM parts is the introduction of <a href="/wiki/Microstructure" title="Microstructure">microstructural</a> heterogeneities within layers of deposited material. These defects, including <a href="/wiki/Porosity" title="Porosity">porosity</a> and unique interfaces, result in anisotropy of the <a href="/wiki/Mechanical_properties" class="mw-redirect" title="Mechanical properties">mechanical response</a> of the workpiece, which is undesirable. To combat this <a href="/wiki/Anisotropy" title="Anisotropy">anisotropic</a> mechanical response, a Bouligand-inspired tool path is used to deposit the material in a twisted Bouligand structure.<sup id="cite_ref-:42_19-1" class="reference"><a href="#cite_note-:42-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> This results in a stress transfer mechanism which uses interlayer heterogeneities as stress deflection points, thus <a href="/wiki/Strengthening_mechanisms_of_materials" title="Strengthening mechanisms of materials">strengthening</a> the workpiece at these points. Bouligand tool paths are used specifically in cement/ceramic deposition AM. Bouligand-inspired AM parts have been observed to behave better than cast elements under mechanical stress.<sup id="cite_ref-:42_19-2" class="reference"><a href="#cite_note-:42-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Pitch_Angle">Pitch Angle</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bouligand_structure&action=edit&section=16" title="Edit section: Pitch Angle"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A critical parameter in the development of the Bouligand-inspired tool path is the pitch angle. The pitch angle γ is the angle at which the helicoidal structure is formed.<sup id="cite_ref-:02_7-6" class="reference"><a href="#cite_note-:02-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> The relative size of the pitch angle is critical for the mechanical response of a Bouligand-inspired AM tool piece. For γ < 45° (small angle), interfacial crack growth and interfacial microcracking is observed. For 45° < γ < 90° (large pitch angle), dominant crack growth through the solid is observed.<sup id="cite_ref-:42_19-3" class="reference"><a href="#cite_note-:42-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Battery_Electrodes">Battery Electrodes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bouligand_structure&action=edit&section=17" title="Edit section: Battery Electrodes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Crab shells which already have the Bouligand structure can be used as templates for nanostructured battery electrodes. Crab shells are a low-cost, sustainable alternative to otherwise expensive starting materials and processing methods for nanostructures batteries. The crab shells have a Bouligand structure composed of highly mineralized chitin fibers. The structure can be used as a bio-template to make hollow carbon nanofibers. The desired battery materials, often sulfur and silicon, can be contained in these hollow fibers to create the cathodes and anodes.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Nanocellulose_Films">Nanocellulose Films</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bouligand_structure&action=edit&section=18" title="Edit section: Nanocellulose Films"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Cellulose nanocrystals self assemble into helicoidal thin films, the pitch angle between the layers can then be modified via solvent processing. The resulting nanocellulose films, which have a Bouligand structure, can be manipulated to achieve various effects on the material properties. These nanocellulose films are impact-resistant, sustainable, and multi-functional and can be used in various applications such as stretchable electronics, protective coatings, eyewear, and body armor.<sup id="cite_ref-:02_7-7" class="reference"><a href="#cite_note-:02-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bouligand_structure&action=edit&section=19" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFShermanQuanYangRitchie2017" class="citation journal cs1">Sherman, Vincent R.; Quan, Haocheng; Yang, Wen; Ritchie, Robert O.; Meyers, Marc A. (2017). "A comparative study of piscine defense: The scales of Arapaima gigas, Latimeria chalumnae and Atractosteus spatula". <i>Journal of the Mechanical Behavior of Biomedical Materials</i>. <b>73</b>: <span class="nowrap">1–</span>16. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.jmbbm.2016.10.001">10.1016/j.jmbbm.2016.10.001</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/27816416">27816416</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+the+Mechanical+Behavior+of+Biomedical+Materials&rft.atitle=A+comparative+study+of+piscine+defense%3A+The+scales+of+Arapaima+gigas%2C+Latimeria+chalumnae+and+Atractosteus+spatula&rft.volume=73&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1-%3C%2Fspan%3E16&rft.date=2017&rft_id=info%3Adoi%2F10.1016%2Fj.jmbbm.2016.10.001&rft_id=info%3Apmid%2F27816416&rft.aulast=Sherman&rft.aufirst=Vincent+R.&rft.au=Quan%2C+Haocheng&rft.au=Yang%2C+Wen&rft.au=Ritchie%2C+Robert+O.&rft.au=Meyers%2C+Marc+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABouligand+structure" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBouligand1965" class="citation journal cs1">Bouligand, Y. 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"Crab Shells as Sustainable Templates from Nature for Nanostructured Battery Electrodes". <i>Nano Letters</i>. <b>13</b> (7): <span class="nowrap">3385–</span>3390. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2013NanoL..13.3385Y">2013NanoL..13.3385Y</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1021%2Fnl401729r">10.1021/nl401729r</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1530-6984">1530-6984</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/23758646">23758646</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nano+Letters&rft.atitle=Crab+Shells+as+Sustainable+Templates+from+Nature+for+Nanostructured+Battery+Electrodes&rft.volume=13&rft.issue=7&rft.pages=%3Cspan+class%3D%22nowrap%22%3E3385-%3C%2Fspan%3E3390&rft.date=2013-07-10&rft_id=info%3Adoi%2F10.1021%2Fnl401729r&rft.issn=1530-6984&rft_id=info%3Apmid%2F23758646&rft_id=info%3Abibcode%2F2013NanoL..13.3385Y&rft.aulast=Yao&rft.aufirst=Hongbin&rft.au=Zheng%2C+Guangyuan&rft.au=Li%2C+Weiyang&rft.au=McDowell%2C+Matthew+T.&rft.au=Seh%2C+Zhiwei&rft.au=Liu%2C+Nian&rft.au=Lu%2C+Zhenda&rft.au=Cui%2C+Yi&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABouligand+structure" class="Z3988"></span></span> </li> </ol></div></div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Context plainlinks metadata ambox ambox-style ambox-Context" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/40px-Edit-clear.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/60px-Edit-clear.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/80px-Edit-clear.svg.png 2x" data-file-width="48" data-file-height="48" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">This article <b>provides insufficient context for those unfamiliar with the subject</b>.<span class="hide-when-compact"> Please help <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Bouligand_structure&action=edit">improve the article</a> by <a href="/wiki/Wikipedia:Writing_better_articles#Provide_context_for_the_reader" title="Wikipedia:Writing better articles">providing more context for the reader</a>.</span> <span class="date-container"><i>(<span class="date">December 2016</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; 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