本論文主要分成兩主軸，分別為”模擬技術的建構”以及”應力模擬應用於積層製造”。
模擬技術的建構包括將實心樣品的拉伸試驗結果利用有限元素分析軟體進行重現，驗證模擬中楊氏係數的準確性以及探討模擬中拉伸樣品有無倒角對樣品拉伸時所產生的應力集中現象與變形量有何影響。應力模擬應用於積層製造則是針對不同的單元孔洞結構進行多種不同之機械性質測試，包括拉伸、壓縮、剪切、撓曲等。並將其中表現最適合應用於人工髖關節之Diagonal孔洞結構排入人工髖關節並進行ISO 7206-4試驗模擬受到最大下壓力值時的應力分布情形。
針對具有孔洞結構的模擬則是與文獻結果、實驗結果交互比對，包括模擬驗證圓形規則孔洞鋁樣品壓縮文獻，探討不同的相對密度與楊氏係數之間的關係，本論文成功利用方程式歸納出規則孔洞與楊氏係數之經驗關係式，且得到與文獻相同的趨勢，即在孔洞結構中相對密度愈大，材料的楊氏係數亦會越大。與文獻的比對結果亦包括將蜂巢狀結構拉伸實驗文獻利用模擬重現並比較模擬與文獻之楊氏係數，比對後得到相近之結果，文獻與本論文之結果分別為0.48MPa與0.46MPa。
與實驗結果比對則是包括將CNC製程製備之不同孔洞結構之片狀5052鋁試片與EBM製程製備之孔洞結構棒狀Ti6Al4V試片之拉伸試驗結果利用模擬重現，並比較模擬結果，比較的項目包括楊氏係數、應力集中的位置與應力集中的數值。根據結果顯示與5052鋁片在孔洞數少、相對密度高的時候楊氏係數與模擬結果相近，而實際實驗中隨著孔洞數增多楊氏係數減少的趨勢於模擬中亦有發生。EBM製備之孔洞結構棒狀Ti6Al4V試片楊氏係數與模擬之比較結果亦相近，實際實驗與模擬之楊氏係數分別為11.8 GPa與14.8 GPa。而無論是CNC與EBM製程製備試片的破裂處，均與模擬的應力集中處位置相同，且模擬中應力集中處的數值亦大於材料的降伏強度，說明本模擬系統可以判斷材料受力超過彈性區後可能發生塑性變形的位置。
本論文亦將模擬技術應用與髖關節應力模擬中，並參考ISO 7206-4規範，髖關節所受到的最大下壓力值2300 N進行模擬，首先確認實心髖關節結構受力之後的von-Mises應力分布與文獻結果相同均為250MPa左右。以此模擬驗證作為基準並進行延伸實驗，將髖關節受到不同下壓力值、插入不同楊氏係數之底座以模仿插入不同人骨之模擬結果進行統整，得到下壓力值越大，髖關節之應力集中數值越大，與插入楊氏係數越大之底座，髖關節的應力集中數值越小之結果。最後將Diagonal孔洞結構匯入髖關節應力模擬中，以探討孔洞結構對髖關節應力模擬會造成之影響。

For patients recovering from total hip replacement surgery, the stress shielding effect, which is caused by a difference in Young’s modulus between the hip prosthesis and human bone, can lead to prosthesis loosening or dislocation. Additive manufacturing technology, such as electron beam melting (EBM), is mature enough to fabricate porous structures made of Ti6Al4V alloy.
This thesis studies the mechanical properties of porous structures and their application to artificial hip prostheses using the finite element method. The study is divided into two parts. The first part establishes the simulation method and the second part discusses the application of the simulation results to hip prostheses.
The simulation and experimental results of the Young’s modulus of carbon steel show a very small deviation of about 0.7%. Porous samples with various pore geometries show the trend that higher relative density is accompanied by higher Young’s modulus in both simulation and experiments. Several unit cell structures were chosen for further mechanical simulation. The diagonal unit cell was found to be the most stable. Various compression load, Young’s modulus of cement, hip prosthesis outlook were simulated based on ISO 7206-4. The results show that when the porous structures were applied in a hip prosthesis, the stress concentration value decreased.

[1] MatWeb, "Mechanical properties of Titanium Ti-6Al-4V (Grade 5)," 2017.
[2] A. O’CONNOR, "The Claim: After Being Broken, Bones Can Become Even Stronger," New York Times. Retrieved, pp. 10-19, 2010.
[3] J. Biemond, G. Hannink, N. Verdonschot, and P. Buma, "Bone ingrowth potential of electron beam and selective laser melting produced trabecular-like implant surfaces with and without a biomimetic coating," Journal of Materials Science: Materials in Medicine, vol. 24, no. 3, pp. 745-753, 2013.
[4] 林國權, "由 RAPID 2015 看全球 3D 列印在醫療產業之應用發展趨勢," 材料世界網, 2015.
[5] J. Y. Rho, R. B. Ashman, and C. H. Turner, "Young's modulus of trabecular and cortical bone material: ultrasonic and microtensile measurements," Journal of biomechanics, vol. 26, no. 2, pp. 111-119, 1993.
[6] B. Chang et al., "Influence of pore size of porous titanium fabricated by vacuum diffusion bonding of titanium meshes on cell penetration and bone ingrowth," Acta biomaterialia, vol. 33, pp. 311-321, 2016.
[7] S. Van Bael et al., "The effect of pore geometry on the in vitro biological behavior of human periosteum-derived cells seeded on selective laser-melted Ti6Al4V bone scaffolds," Acta biomaterialia, vol. 8, no. 7, pp. 2824-2834, 2012.
[8] J. Wieding, A. Wolf, and R. Bader, "Numerical optimization of open-porous bone scaffold structures to match the elastic properties of human cortical bone," Journal of the mechanical behavior of biomedical materials, vol. 37, pp. 56-68, 2014.
[9] M. F. Ashby and R. M. Medalist, "The mechanical properties of cellular solids," Metallurgical Transactions A, vol. 14, no. 9, pp. 1755-1769, 1983.
[10] 蔡依珊, 翁嘉蓴, 粘永堂, "積層製造與鍛造生醫陶瓷用途之鈦合金的結晶構造及機械性質比較," 台灣陶瓷研究學會年會, 2017.
[11] Z. Y. Fan, H. J. Niu, A. P. Miodownik, T. Saito, and B. Cantor, "Microstructure and mechanical properties of in situ Ti/TiB MMCs produced by a blended elemental powder metallurgy method," in Key Engineering Materials, vol. 127, pp. 423-430: Trans Tech Pub, 1997.
[12] H. Hasib, O. L. Harrysson, and H. A. West, "Powder removal from Ti-6Al-4V cellular structures fabricated via electron beam melting," Jom, vol. 67, no. 3, pp. 639-646, 2015.
[13] C. Yan, L. Hao, A. Hussein, and P. Young, "Ti–6Al–4V triply periodic minimal surface structures for bone implants fabricated via selective laser melting," journal of the mechanical behavior of biomedical materials, vol. 51, pp. 61-73, 2015.
[14] M. Larner and L. P. Dávila, "The mechanical properties of porous aluminum using finite element method simulations and compression experiments," MRS Online Proceedings Library Archive, vol. 1580, 2013.
[15] C.-T. Yang, H.-W. Wei, H.-C. Kao, and C.-K. Cheng, "Design and test of hip stem for medullary revascularization," Medical Engineering and Physics, vol. 31, no. 8, pp. 994-1001, 2009.
[16] I. D. Learmonth, C. Young, and C. Rorabeck, "The operation of the century: total hip replacement," The Lancet, vol. 370, no. 9597, pp. 1508-1519, 2007.
[17] J. Charnley, "Arthroplasty of the hip: a new operation," The Lancet, vol. 277, no. 7187, pp. 1129-1132, 1961.
[18] J. J. Callaghan, J. C. Albright, D. D. Goetz, J. P. Olejniczak, and R. C. Johnston, "Charnley total hip arthroplasty with cement: minimum twenty-five-year follow-up," Jbjs, vol. 82, no. 4, pp. 487-497, 2000.
[19] J. Charnley, "Fracture of femoral prostheses in total hip replacement. A clinical study," Clinical Orthopaedics and Related Research, no. 111, pp. 105-120, 1975.
[20] J. Charnley, "Detachment and reattachment of the great trochanter," in Low friction arthroplasty of the hip: Springer, 1979, pp. 140-151.
[21] B. Wroblewski, "Direction and rate of socket wear in Charnley low-friction arthroplasty," Bone & Joint Journal, vol. 67, no. 5, pp. 757-761, 1985.
[22] R. Y. Woo and B. F. Morrey, "Dislocations after total hip arthroplasty," The Journal of bone and joint surgery. American volume, vol. 64, no. 9, pp. 1295-1306, 1982.
[23] M. Ridzwan, S. Shuib, A. Hassan, A. Shokri, and M. M. Ibrahim, "Problem of stress shielding and improvement to the hip implant designs: a review," J. Med. Sci, vol. 7, no. 3, pp. 460-467, 2007.
[24] R. v. Mises, "Mechanik der festen Körper im plastisch-deformablen Zustand," Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, vol. 1913, no. 4, pp. 582-592, 1913.
[25] Wiki, "Cauchy stress tensor," 2018.
[26] 蔡依珊, "碩士論文," 虎尾科技大學, 2018.
[27] A. Standard, "E8," Standard Test Methods for Tension Testing of Metallic Materials," Annual book of ASTM standards, vol. 3, pp. 57-72, 2004.
[28] J. Lee, Y. Kim, H. Jang, and W. Chung, "Cr2O3 sealing of anodized aluminum alloy by heat treatment," Surface and Coatings Technology, vol. 243, pp. 34-38, 2014.
[29] 成功大學, "微奈米中心奈微拉伸試驗機介紹," 2018.
[30] 成功大學, "微奈米中心X光繞射儀介紹," 2018.