Application of Fracture Mechanics Concepts to Hierarchical Biomechanics of Bone and Bone-like Materials
Application of Fracture Mechanics Concepts to Hierarchical Biomechanics of Bone and Bone-like Materials
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DOI：
10.1007/978-1-4020-5423-5_8
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发表时间：
2006-03
影响因子：
2.5
通讯作者：
Huajian Gao
中科院分区：
文献类型：
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作者：
Huajian Gao
断裂力学的概念，以获得一些理解的层次纳米复合结构的硬生物组织，如骨，牙齿和贝壳。在结构层次的最基本水平，骨和骨样材料表现出纳米长度尺度上的一般结构，其由在软蛋白质基质中以平行交错图案排列的硬矿物血小板组成。本文围绕以下问题展开讨论：（1）长度尺度问题：为什么纳米尺度对生物材料很重要？(2)刚性问题：大自然是如何创造一种含有高体积分数软材料的刚性复合材料的？(3)韧性问题：大自然是如何构建一个含有高体积分数脆性材料的坚韧复合材料的？(4)强度问题：大自然如何平衡蛋白质和矿物质的广泛不同强度？(5)优化问题：从结构优化的角度能否理解骨和骨样材料的通用纳米结构？如果是，优化的是什么？目标函数是什么？(6)屈曲问题：大自然是如何防止骨骼中的细长矿物质血小板在压缩下屈曲的？(7)层次问题：为什么自然界总是设计层次结构？结构层次的作用是什么？考虑到生物学的复杂性，对这些问题的全面分析远远超出了本文的范围。这里的目的只是使用简单的分析和数值模型来说明类骨材料的一些基本机械设计原理。考虑到这一目标，长度尺度的问题是解决的基础上的原则，缺陷公差，在类比断裂力学的相关概念，表明纳米尺寸使通常脆性矿物晶体不敏感的裂纹样缺陷。在纳米长度尺度上的临界尺寸以下，矿物晶体不再通过预先存在的裂纹的扩展而失效，而是通过在其极限强度附近均匀破裂而失效。抗脆性断裂的类骨材料的稳健设计提供了达尔文生存力竞争与缺口不敏感性工程设计之间的有趣类比。对生物纳米结构的刚度、强度、韧性、稳定性和优化等问题进行了跟踪分析，进一步揭示了骨和类骨材料的基本设计原理。交错的纳米结构被证明是一个优化的结构与硬矿物晶体提供结构刚度和软蛋白质基体耗散断裂能。最后，通过模拟骨纳米结构的多层自相似复合结构的模型分层材料，讨论了结构分层问题。我们表明，由此产生的“分形骨”，模型分层材料，在不同的长度尺度具有不同的属性，可以被设计为容忍多个长度尺度的裂纹样缺陷。
Fracture mechanics concepts are applied to gain some understanding of the hierarchical nanocomposite structures of hard biological tissues such as bone, tooth and shells. At the most elementary level of structural hierarchy, bone and bone-like materials exhibit a generic structure on the nanometer length scale consisting of hard mineral platelets arranged in a parallel staggered pattern in a soft protein matrix. The discussions in this paper are organized around the following questions: (1) The length scale question: why is nanoscale important to biological materials? (2) The stiffness question: how does nature create a stiff composite containing a high volume fraction of a soft material? (3) The toughness question: how does nature build a tough composite containing a high volume fraction of a brittle material? (4) The strength question: how does nature balance the widely different strengths of protein and mineral? (5) The optimization question: Can the generic nanostructure of bone and bone-like materials be understood from a structural optimization point of view? If so, what is being optimized? What is the objective function? (6) The buckling question: how does nature prevent the slender mineral platelets in bone from buckling under compression? (7) The hierarchy question: why does nature always design hierarchical structures? What is the role of structural hierarchy? A complete analysis of these questions taking into account the full biological complexities is far beyond the scope of this paper. The intention here is only to illustrate some of the basic mechanical design principles of bone-like materials using simple analytical and numerical models. With this objective in mind, the length scale question is addressed based on the principle of flaw tolerance which, in analogy with related concepts in fracture mechanics, indicates that the nanometer size makes the normally brittle mineral crystals insensitive to cracks-like flaws. Below a critical size on the nanometer length scale, the mineral crystals fail no longer by propagation of pre-existing cracks, but by uniform rupture near their limiting strength. The robust design of bone-like materials against brittle fracture provides an interesting analogy between Darwinian competition for survivability and engineering design for notch insensitivity. The follow-up analysis with respect to the questions on stiffness, strength, toughness, stability and optimization of the biological nanostructure provides further insights into the basic design principles of bone and bone-like materials. The staggered nanostructure is shown to be an optimized structure with the hard mineral crystals providing structural rigidity and the soft protein matrix dissipating fracture energy. Finally, the question on structural hierarchy is discussed via a model hierarchical material consisting of multiple levels of self-similar composite structures mimicking the nanostructure of bone. We show that the resulting “fractal bone”, a model hierarchical material with different properties at different length scales, can be designed to tolerate crack-like flaws of multiple length scales.