在40億年的演化史中，生物利用演化克服生存壓力並繁殖延續。對於生物而言，如何有效地利用少數幾種常見元素於常溫常壓下形成多功能的結構材料以應對多變的挑戰，對於個體乃至於族群存續至關重要。許多生物結構材料具有輕量化、高比強度、高能量吸收、兼具剛性與韌性之優異機械性質，成功克服工程材料短板。這些特性多源於結構設計而非單純的成分組成所致，如: 多孔、多尺度、孔洞排列......等。由於大多數生物材料具有多功能性，因此常可觀察到不同結構設計之間的搭配。
本研究集合一系列自主研發之設計方法，用以系統性地設計多種輕量化仿生結構材料。設計方法涵蓋人工規劃二維/三維空間中的排列、給定條件的密度/幾何梯度變化、基於初始條件的生成式設計、以真實三維生物結構作為依據的新型設計。在仿生結構設計上，本研究提出多種新穎設計，如: 費氏數列、三度週期最小曲面(TPMS)、旋節分解、反應擴散......等結構。這些結構不僅可用以描述生物結構，亦提出數學模型可供計算。本設計流程中所產生的結構設計皆具有統一形式與操作模式，故所有方法皆可彈性地互相結合進而創造新的結構。同時，本研究亦整合先進積層製造技術與有限元模擬所需之相關接口，提供一站式設計整合框架。本研究可應用於工程中需輕量化設計之場域，並可擴展至多數仿生結構設計流程當中。在工程學與材料科學發展上具創新價值與應用潛力。

In the four-billion-year history of life evolution, organisms have overcome the pressure of survival through evolution while reproducing and continuing. For organisms, effectively utilizing a few common elements to form multifunctional structural materials at room temperature and pressure to cope with changing challenges is crucial to the survival of individuals and even groups. Many biological structural materials have excellent mechanical properties such as lightweight, high specific strength, high energy absorption, excellent mechanical properties with rigidity and toughness, and successfully overcome the shortcomings of engineering materials. These characteristics are mostly due to structural design rather than simple composition, such as porous, multi-scale, and pore arrangement. Due to the versatility of most biological materials, the collocation between different structural designs is often observed.
This research systematically integrated a series of self-developed design methods to design various lightweight bio-inspired structural materials. The design methods covered artificial planning of arrangements in 2D/3D space, density/geometric gradient changes for given conditions, generative design based on initial conditions, and the creation of new designs based on actual 3D biological structures. In the design of bio-inspired structures, this study proposed various novel designs, such as the Fibonacci sequence, triply periodic minimal surface, spinodal decomposition, reaction-diffusion structure, etc., to interpret biological structures and propose mathematical models available for calculation. The generated structures in this workflow had a unified form and operation mode, so all methods could be flexibly combined to create new structures. At the same time, this research also integrated the relevant interfaces required by advanced additive manufacturing and simulation to provide a one-stop design integration framework. This study could be applied to lightweight engineering design scenarios and extended to most bio-inspired structure design processes. It had innovative value and application potential in engineering and materials science development.

摘要 iii
Abstract iv
Content ix
Figure Caption xii
Table Caption xxiv
Chapter 1 Introduction 1
Chapter 2 Literature Review 3
2.1 Biological and bio-inspired structural materials 3
2.1.1 Biological materials and structural design elements 3
2.1.2 Bio-inspired structural materials 7
2.1.3 Summary 9
2.2 Lightweight structural designs 10
2.2.1 Cellular solids 10
2.2.2 Pore arrangement 14
2.2.3 Triply periodic minimal surfaces 18
2.2.4 Spinodal decomposition 20
2.2.5 Reaction-diffusion model 22
2.2.6 Summary 23
2.3 Additive manufacturing 24
2.3.1 Fused deposition modeling 25
2.3.2 Stereolithography 26
2.3.3 Digital light processing 27
2.3.4 PolyJet 28
2.3.5 Selective laser melting/sintering 29
2.3.6 Summary 29
2.4 Simulations 30
2.4.1 Finite element methods 30
2.4.2 Particle-based simulations 32
2.4.3 Summary 34
Chapter 3 Methodology 35
3.1 Lightweight structural designs and generation 35
3.1.1 Computer-aided and element-based designs 35
3.1.2 Structural condition designs and generation 38
3.1.3 Mathematical description designs 42
3.1.4 Generative design by phase-field model 44
3.2 Structure operation and storage methods 48
3.2.1 Continuous to discrete transformation 48
3.2.2 Serialize 3D structures into 2D array sequences 51
3.2.3 Structural variation based on 2D-layered changes 52
3.2.4 Existing structure-based designs 54
3.3 Additive manufacturing 57
3.3.1 Fused deposition modeling 58
3.3.2 Stereolithography and digital light processing 60
3.3.4 PolyJet 64
3.3.5 Selective laser melting/sintering 66
3.4 Quasi-static testing by universal testing machines 67
3.5 Material structure analysis 70
3.5.1 Explicit material structure distribution and analysis 70
3.5.2 Implicit material structure distribution and analysis 72
3.6 Simulations 77
3.6.1 Finite element methods 77
3.6.2 Particle-based simulations 79
Chapter 4 Results and Discussion 80
4.1 Lightweight materials inspired by nature patterns 80
4.1.1 Compression-resistant structures from Liquidambar formosana 80
4.1.2 Tensile-resistant structures inspired by natural patterns 88
4.1.3 Related works 95
4.2 Lightweight materials inspired by periodic surfaces and phase-field methods 102
4.2.1 Programmable and systematically generated TPMS structures 102
4.2.2 Phase-field generated lightweight structures 108
4.3 Lightweight materials inspired by biological materials and design elements 112
4.3.1 Lightweight materials generated from biological structure data 112
4.3.2 Related works 117
4.4 Structural design hybrid framework 123
Chapter 5 Conclusions 127
Chapter 6 Future Work 132
6.1 Limitations of this study and potential improvements 132
6.2 Normal vector distribution 133
6.3 Phase-field-driven topology optimization 135
6.4 Bio-inspired structural adapted materials design 136
6.5 Machine learning-aided lightweight structural design 138
6.6 Multi-property coupled structural material design 140
References 141

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