: force experienced by fibers parallel to load ：平行于负载 的纤维所承受的力
Mechanically, less-mineralized helical structures provide THREE principal structural attributes: 在机械上，矿化程度较低的螺旋结构提供三个主要结构属性：
i) increased isotropy in multiple directions along the fiber plane by stacking layers of fibers or fibrils at varying angles. i） 通过以不同角度堆叠纤维或原纤维层，沿纤维平面在多个方向上增加各向同性。
ii) increased toughness as the misaligned fiber planes can distract crack advance, forcing it to propagate in multiple planes. ii） 由于未对准的纤维平面会分散裂纹的前进，迫使其在多个平面上扩展，因此韧性增加。
iii) significant increase in the compressive strength and stiffness over fibrous structures, despite consisting of the same constituents. iii） 尽管由相同的成分组成，但纤维结构的抗压强度和刚度显着增加。
Examples of the mechanical advantages of helical structures 螺旋结构的机械优势示例
(crack deflection -> improved toughness) （裂纹偏转 - >韧性提高）
Gradient structures: materials and interfaces that accommodate property mismatch (e.g. strength, modulus) through a gradual transition in order to avoid interfacial mismatch stress buildup, resulting in an increased toughness 梯度结构：通过逐渐过渡来适应性能错配（例如强度、模量）的材料和界面，以避免界面错配应力积累，从而提高韧性
Gradient 梯度
Biological gradient structures from nature 来自自然界的生物梯度结构
is the initial value of the property is the distance from interface 是属性 的初始值是与接口的距离 is non-dimensional exponent 是无量纲指数 is material constant 是材料常数
Mechanically, gradient structures provide stress relief at the interfaces between dissimilar materials, which are characterized through a smooth transition in properties. 在机械上，梯度结构在不同材料之间的界面处提供应力消除，其特点是性能的平滑过渡。
Gradient structures can serve to avoid interfacial stresses that exist between similar materials with significantly different mechanical (or thermal, optical, electromagnetic) properties. 梯度结构可以避免在机械（或热、光学、电磁）特性明显不同的相似材料之间存在的界面应力。
For example, the well-bonded interface to arrest cracks propagating from the stiff enamel to the tough dentin due to the elastic modulus mismatch. 例如，由于弹性模量不匹配，粘合良好的界面可以防止裂纹从坚硬的牙釉质蔓延到坚韧的牙本质。
4)Layered structures: complex composites that increase the toughness of (most commonly) brittle materials through the introduction of interfaces 4）层状结构：通过引入界面来增加（最常见的）脆性材料的韧性的复杂复合材料
Biological layered structures from nature 来自自然界的生物分层结构
All materials contain flaws (defects), material's actual strength is much lower than theoretical values. 所有材料都包含缺陷（缺陷），材料的实际强度远低于理论值。
Griffith equation: Griffith 方程：
Maximum stress that material can withstand 材料可以承受的最大应力 is the length of a crack or void in material mode 1 critical fracture toughness 是材料 模态 1 临界断裂韧性中裂纹或空隙的长度 is increased by a layered structure: 通过分层结构增加：
First, by deflecting or twisting a crack, the applied stress is taken out of the preferred Mode I (opening) orientation, resulting in a more-tortuous crack path. 首先，通过偏转或扭曲裂纹，将施加的应力从首选的模式 I（开口）方向带走，从而产生更加曲折的裂纹路径。
Second, any deflection of the crack will result in an inherently longer crack path over a straight crack thus increasing the work required to propagate a crack. 其次，裂纹的任何偏转都会导致在直线裂纹上产生固有更长的裂纹路径，从而增加扩展裂纹所需的功。
5)Tubular structures: long aligned pores (a.k.a. tubules) that allow for energy absorption and crack deflection 5） 管状结构：排列成序的长孔（又名小管），允许能量吸收和裂纹偏转
Biological tubular structures from nature 来自自然界的生物管状结构
(e) （五）
Nano- & micro-sized tubules 纳米和微型小管
Human (Mammalia) - Dentin Tubules 人（哺乳动物） - 牙本质小管
Tubular 管
is the elastic modulus of the matrix 是基体的弹性模量 is the volume fraction of the pores 是孔隙的体积分数 is the intertubular matrix strain at failure 是失效时的管间基质应变 is the Poisson's ratio of the matrix 是矩阵的泊松比
Mechanically, tubular structures improve fracture toughness and energy absorption by arresting crack growth by removing the stress singularity at the crack tip and/or by collapsing the tubules when compressed. 在机械方面，管状结构通过消除裂纹尖端的应力奇异性和/或在压缩时使小管塌陷来阻止裂纹的扩大，从而提高断裂韧性和能量吸收。
They can also serve as scattering centers that decrease the amplitude of longitudinal stress pulses generated by impact. 它们还可以用作散射中心，降低撞击产生的纵向应力脉冲的振幅。
6) Cellular structures: lightweight porous or foam architectures that provide directed stress distribution and energy absorption (often 6） 蜂窝结构：轻质多孔或泡沫结构，提供定向应力分布和能量吸收（通常
surrounded by dense layers to form sandwich structures) 被致密层包围，形成夹层结构）
Sandwich 三明治
Open-cell structures 开孔结构
Biological cellular structures from nature 来自自然界的生物细胞结构
are modulus, stress & density of cellular scaffold are modulus, stress & density of solid is power component ranging from 1 to 3 是模量，应力和细胞支架 的密度是模量，应力和固体 密度是从1到3的功率分量
Sandwich structure 夹层结构
Constitutive bending: 本构弯曲：
is deflection of the structure is applied load 是结构 的挠度是施加的载荷 loading geometry related constants is the width of the structure & are thickness of dense shell and porous core is shear modulus of the porous core 加载几何相关的常数 是结构 的宽度 & 是致密壳和多孔芯 的厚度是多孔芯的剪切模量
Sandwich structure 夹层结构
Constitutive buckling: 本构屈曲：
are stiffness, thickness, radius, and Poison's ratio of the dense shell 是刚度、厚度、半径和中毒的致密外壳比率 are stiffness and Poisson's ratio of the porous core is wavelength of the instability divided by 是刚度，多孔芯 的泊松比是不稳定性的波长除以
Mechanically, cellular structures provide some strength (compression, shear) while minimizing the weight (light-weight structure). 在机械上，蜂窝结构提供一定的强度（压缩、剪切），同时最大限度地减少重量（轻质结构）。
Cellular structures are brittle under tension. 细胞结构在张力下很脆。
Unique compressive stress-strain behavior with an initial linear region (due to cell-wall bending), an uneven, jagged plateau region (due to cellwall buckling and fracture), and finally a sharp increase in modulus (due to cellular densification). 独特的压缩应力-应变行为，具有初始线性区域（由于细胞壁弯曲）、不均匀、锯齿状的高原区域（由于细胞壁屈曲和断裂），最后模量急剧增加（由于细胞致密化）。
Compressive stress-strain behavior of cellular structures 细胞结构的压缩应力-应变行为
Strain, 应变
Suture structures: interfaces comprising wavy and interdigitating patterns that control strength and flexibility 缝合结构：由控制强度和柔韧性的波浪形和叉指图案组成的界面
Biological suture structures from nature 来自大自然的生物缝合结构
is critical shear stress that would cause shear failure of the interface 是导致界面剪切破坏的临界剪应力 is critical tensile stress that would cause failure of the suture teeth 是导致缝合齿失效的临界拉伸应力
Li, Y., Ortiz, C. and Boyce, M.C., 2011. Stiffness and strength of suture joints in nature. Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, 84(6), p. 062904. Li， Y.， Ortiz， C. 和 Boyce， MC，2011 年。自然界中缝合关节的刚度和强度。物理评论 E—统计、非线性和软物质物理学，84（6），第 062904 页。
Mechanically, suture structures provide strength at the interfaces of rigid biological components while still controlling the flexibility. 在机械上，缝合结构在刚性生物成分的界面处提供强度，同时仍控制柔韧性。
There is an optimum suture tooth angle . 有一个最佳的缝合齿角度 。
A suture structure with a high level of hierarchy will generally have higher stiffness and toughness than a simple suture structure. 具有高层次结构的缝合结构通常比简单的缝合结构具有更高的刚度和韧性。
The design and level of hierarchy can effectively tailor the tensile strength of suture structures. 层次结构的设计和级别可以有效地定制缝合结构的拉伸强度。
Overlapping structures: featuring multiple plates or scales that overlap to form flexible and often armored surfaces 重叠结构：具有多个板或鳞片，它们重叠形成柔性且通常是铠装表面
Plates 板
Biological overlapping structures from nature 来自自然界的生物重叠结构
Alligator Gar (Actinopterygii) - Overlapping Scales 鳄雀鳝 （Actinopterygii） - 重叠的鳞片
Macro-scale flexible coverage 宏观尺度灵活覆盖
Bio-inspired protective armor 仿生防护装甲
Overlapping 重叠
is the angle between the distal ends of two adjacent scales when the body is in a curved state is the normalized curvature due to rotation of the scales at the proximal 是当身体处于弯曲状态 时两个相邻鳞片的远端之间的夹角，是由于鳞片在近端旋转而产生的归一化曲率
Mechanically, overlapping structures are capable of ensuring constant coverage (protection) while allowing flexibility. 在机械上，重叠结构能够确保恒定的覆盖（保护），同时允许灵活性。
Most organisms employ scales that balance the variables/qualities of scale length and spacing between scales, providing high overall flexibility to facilitate natural motion while minimizing the local rotation of scales to resist puncture. 大多数生物体使用的鳞片可以平衡鳞片长度和鳞片之间间距的变量/质量，提供高度的整体灵活性 以促进自然运动，同时最大限度地减少鳞片 的局部旋转以抵抗穿刺。
Characteristic features commonly found in many natural materials: 许多天然材料中常见的特征：
i) Stiff and hard building blocks, i） 坚硬的构建块，
ii) down to nanometer size, delimited by iii) weaker interfaces, and ii） 低至纳米尺寸，由 iii） 较弱的界面分隔，以及
iv) arranged into complex multiscale, hierarchical architectures. iv） 排列成复杂的多尺度、分层架构。
Natural-inspired structural designs 自然风格的结构设计
Synthetic materials (polymers, ceramics, and metals) 合成材料（聚合物、陶瓷和金属）
One or more of the eight structural design elements 八个结构设计元素中的一个或多个
Various materials processing routes and techniques at nano-, micro-, meso- and macroscales (recombinant technologies, biomineralization, layer-by-layer deposition, selfassembly, bio-templating, magnetic manipulation, freeze-casting, vacuum-casting, extrusion, and roll compaction, laser engraving, and 3D printing) 纳米、微观、中观和宏观尺度的各种材料加工路线和技术（重组技术、生物矿化、逐层沉积、自组装、生物模板、磁操作、冷冻铸造、真空铸造、挤出和辊压、激光雕刻和 3D 打印）
With the advent of modern biotechnology and nanoscale manufacturing, hierarchical materials (or composites) composed of ceramics and/or polymers are now becoming viable alternatives to the other dominant class of structural materials like metals. 随着现代生物技术和纳米级制造的出现，由陶瓷和/或聚合物组成的分层材料（或复合材料）现在正在成为金属等其他主要结构材料的可行替代品。
Such ceramic- and polymer-based materials are lightweight and exhibit impressive mechanical properties in spite of their relatively low densities, due to the direct result of including the aforementioned structural design elements. 这种陶瓷和聚合物基材料重量轻，尽管密度相对较低，但由于包含上述结构设计元素的直接结果，它们表现出令人印象深刻的机械性能。
Examples 例子
a) Fibrous recombinant spider silk from mammalian cells; a） 来自哺乳动物细胞的纤维状重组蜘蛛丝;
b) helical fiber reinforced composites that are capable of deflecting crack growth; b） 能够偏转裂纹扩展的螺旋纤维增强复合材料;
c) gradient structures formed by applying magnetic fields to a particle-reinforced matrix composite; c） 通过将磁场施加到颗粒增强基复合材料上而形成的梯度结构;
d) layered composites formed from freeze casting; d） 由冷冻铸造形成的层状复合材料;
e) tubules formed from bio-templating; e） 由生物模板形成的小管;
f) 3D-printed cellular structures; f） 3D 打印的细胞结构;
g) sutures employed to toughen glass; g） 用于钢化玻璃的缝合线;
h) overlapping structures for potential robotics. h） 潜在机器人技术的重叠结构。
Summary 总结
Fibrous structures provide high tensile, but effectively no compressive resistance and are employed within a wide variety of silks, muscles and connective tissues (e.g., hagfish slime, spider silk). 纤维结构提供高拉伸性，但实际上没有抗压性，并用于各种丝、肌肉和结缔组织（例如盲鳗粘液、蜘蛛丝）。
Helical structures can be either a twisted ply that provides in-plane isotropy and increased toughness, or reinforcements that provide torsional rigidity. As a result, helical structures are found in a wide variety of structural and protective materials (e.g., crab and insect exoskeletons). 螺旋结构可以是提供面内各向同性和增加韧性的扭曲层，也可以是提供扭转刚度的增强层。因此，螺旋结构存在于各种结构和保护材料（例如，螃蟹和昆虫外骨骼）中。
Gradient structures occur at material interfaces and accommodate property mismatch through a gradual transition. They provide increased toughness and are predominately found linking rigid and compliant materials in teeth, protective scales, and exoskeletons. 梯度结构出现在材料界面处，并通过逐渐过渡来适应属性不匹配。它们提供更高的韧性，主要用于连接牙齿、保护鳞片和外骨骼中的刚性和柔韧性材料。
Layered structures increase the toughness of, most commonly, brittle materials through the introduction of numerous interfaces, and are found through a variety of support structures (e.g., mollusk nacre, sponge spicules). 层状结构通过引入许多界面来增加脆性材料的韧性，最常见的是通过各种支撑结构（例如软体动物珍珠层、海绵针状物）发现的。
Tubular structures employ organized cylindrical porosity in order to increase toughness, through either energy absorption, crack deflection, or wave scattering. They are found in protective materials that are designed to absorb impact, such as hooves, horns, and teeth. 管状结构采用有组织的圆柱形孔隙率，以便通过能量吸收、裂纹偏转或波散射来提高韧性。它们存在于旨在吸收冲击力的保护材料中，例如蹄子、角和牙齿。
Cellular structures consist of porous materials or foams that allow for stress distribution and energy absorption while minimizing weight. They are often surrounded by dense layers in order to form sandwich structures. Cellular structures are found in a wide variety of organisms (e.g., turtle shells, porcupine quills). 蜂窝结构由多孔材料或泡沫组成，允许应力分布和能量吸收，同时最大限度地减轻重量。它们通常被致密的层包围，以形成夹层结构。细胞结构存在于多种生物体中（例如，龟壳、豪猪刺）。
Suture structures are wavy and interdigitating interfaces that provide control of strength and flexibility. They are found in protective structures and can be tailored to either provide more flexibility (e.g., leatherback sea turtles, sticklebacks) or stiffness (e.g., mammalian skulls). 缝合结构是波浪形和叉指状接口，可控制强度和柔韧性。它们存在于保护结构中，可以定制以提供更大的柔韧性（例如棱皮龟、粘背龟）或刚度（例如哺乳动物头骨）。
Overlapping structures provide for flexibility while ensuring complete coverage of the body. They are found in a variety of protective exteriors from the exoskeletons of millipedes to the scales of fish. 重叠结构提供了灵活性，同时确保完全覆盖身体。它们存在于各种保护性外壳中，从千足虫的外骨骼到鱼的鳞片。
Of important note, many biological materials exhibit two or more of these structural elements that cooperate to provide a complex array of multifunctional properties for the organism. 值得注意的是，许多生物材料表现出两个或多个这些结构元件，这些结构元件协同为生物体提供了一系列复杂的多功能特性。
