以電腦模擬計算骨骼微結構為啟發的高韌性複合材料

Abstract

隨著工業技術的推移與發展，材料設計對於產業需求與日俱增。現今材料追求兼顧強度與韌性，並且具備輕量化的特性，然而人工材料的發展限制導致無法因應此需求。因此，藉由效仿自然界中來自不同生物所帶來的特殊結構與優異的力學特性，使得仿生材料成為眾多研究者設法突破人工材料劣勢的設計對象。為了生存於特殊的環境，不同生活習性的生物體內中演化出不同的骨骼結構，也發展出相異的機械性能。來自不同物種的骨骼提供了多樣化的結構材料設計參考，擴展材料設計空間，因此本研究啟發自骨骼的微結構，透過微結構的拓樸排列所形成複合材料，探討此複合材料具備的高韌性材料性質。 本研究的骨骼微結構來自袋鼠科及偶蹄目兩種分群，共四個物種的股骨。股骨屬於後肢的大腿骨之一，本研究微觀上特別關注骨小樑結構。袋鼠科與偶蹄目具有不同的運動行為，前者常以後肢帶動大幅度的跳躍，前肢不參與跳躍，後者則在奔跑前後肢以同等力量著地，該兩者分群的運動行為是否能夠為啟發自骨骼微結構的複合材料帶來高韌性的力學優勢，以及該高韌性分群所具備的幾何性質，是本研究的探討對象之一。本研究利用電腦斷層掃描影像以及圖像處理演算法，取得骨骼的微結構單元。在幾何特徵方面，藉由提取圖像特徵的計算方法，可得骨骼微結構的孔隙率、骨小樑厚度、孔洞大小等。在力學行為上，使用二維三角晶格彈簧模型預測參考骨骼微結構拓樸形式的複合材料的破壞力學行為，探討高韌性的複合材料。 本研究發現不同分群或物種的骨骼微結構皆具有廣闊的幾何特徵分布，帶來廣大的設計空間，也反映在力學性質的多樣性。在力學性質上，來自紅頸袋鼠(袋鼠科)骨頭微結構的複合材料具有最高的楊氏模數、極限強度和韌性，而偶蹄目並未發現擁有較高的力學性質。以機器學習模型輔助進行分群及物種的分類，對於幾何特徵，騮毛小羚羊(偶蹄目)和紅頸袋鼠(袋鼠科)最能夠展現幾何特徵上的差異，對於具最高韌性的紅頸袋鼠(袋鼠科)，具備較低骨小樑角度和較高平均骨小樑厚度。除此之外，亦運用主成分分析將幾何特徵進行正交轉換，再以相同方式進行分類，結果也是騮毛小羚羊(偶蹄目)和紅頸袋鼠(袋鼠科)最能夠在主成分的分布上觀察到此差異。本研究亦使用機器學習模型釐清幾何特徵與力學性質的關係。平均骨小樑角度會同時顯著影響楊氏模數、極限強度和韌性，而平均孔洞大小和孔隙率主要影響楊氏模數，極限強度和韌性主要受骨小樑角度和孔洞凸殼面積的標準差影響。針對韌性，三者最為有影響力的幾何特徵與韌性皆呈中度負相關。透過上述方法，可幫助了解以骨骼微結構為啟發複合材料的設計空間，以及從中發掘優異的力學性質。

Modern materials are now expected to balance strength and toughness while being lightweight. However, the development of artificial materials faces limitations that hinder meeting these requirements. Thus, researchers are seeking to biomimetic materials, which exhibit excellent mechanical properties found in unique structures. Different animals have evolved different skeletal structures to survive in different environments, providing design insights for structural material. Therefore, this thesis explores composite materials inspired by bone microstructures. This study focuses on the microstructures of femurs from four species within Macropodiformes and Atiodactyla. These two clades exhibit different locomotion behaviors: Macropodiformes primarily use hindlimbs for hopping, with forelimbs not involved in hopping, while Artiodactyla distribute their loading evenly on both forelimbs and hindlimbs. This study investigates whether the locomotive behaviors of these two groups can inspire the design of composite materials with high toughness derived from bone microstructure, and examines the geometric features that characterize the high toughness in these groups. Bone microstructures were obtained using X-ray microtomographic imaging and image processing algorithms. Geometric features such as porosity, trabecular thickness, and pore size were calculated using image feature extraction methods. The mechanical behavior and failure mechanisms of composite materials, based on the topology of bone microstructures, were predicted using a lattice spring model. In this study, we found that the bone microstructures of different clades or species exhibit a wide range of geometric features, providing extensive design space and reflecting a diversity of mechanical properties. Bennetts wallaby showed the highest Young's modulus, ultimate strength, and toughness, while Artiodactyla did not exhibit higher mechanical properties. Machine learning models were employed to classify clades and species based on geometric features. Bay duiker (Artiodactyla) and Bennetts wallaby (Macropodiformes) showed the most significant differences in average trabecular angle and thickness. For the group of Bennetts wallaby, which exhibits the highest toughness, a lower trabecular angle and a higher average trabecular thickness are observed. Principal component analysis was also used to orthogonally transform geometric features, with similar classification results showing differences in the distribution of principal components between the two species. Machine learning models were also used to evaluate the relationship between geometric features and mechanical properties. The average trabecular angle strongly influenced Young's modulus, ultimate strength, and toughness. For toughness, the three most influential geometric features and toughness were moderately negatively correlated. This approach allows us to be able to understand the design space inspired by bone microstructures and identify excellent mechanical properties.