第五章 結論與未來研究工作
5.4 未來研究工作
在壓力實驗上，除了以相同尺寸的試樣來執行壓力實驗外，嘗試改變 立方體試樣之尺寸，探討受壓力學行為是否會因為試樣尺寸的改變而造成 力學行為的不同。除了切割成立方體外，改變試樣的高度，試樣外觀改變 為長方體，同樣探討力學行為是否會有差異。在數值模擬中，二維化的數 值模型計算之相對彈性模數與實驗數值存在明顯差異，並無法代表為封閉 式泡沫鋁之合理數值模型，因此建議未來發展數值模型以三維幾何作為考 量。
參考文獻
[1] M. Vural and G. Ravichandran, "Dynamic response and energy dissipation characteristics of balsa wood: experiment and analysis,"
International Journal of Solids and Structures, vol. 40, pp. 2147-2170,
2003.[2] M. Yamashita and M. Gotoh, "Impact behavior of honeycomb structures with various cell specifications—numerical simulation and experiment,"
International Journal of Impact Engineering, vol. 32, pp. 618-630, 2005.
[3] W.-Y. Jang and S. Kyriakides, "On the crushing of aluminum open-cell foams: Part I. Experiments," International Journal of Solids and
Structures, vol. 46, pp. 617-634, 2009.
[4] T. Miyoshi, et al., "ALPORAS Aluminum Foam: Production Process, Properties, and Applications," Advanced Engineering Materials, vol. 2, pp.
179-183, 2000.
[5] J. Banhart and J. Baumeister, "Deformation characteristics of metal foams," Journal of Materials Science, vol. 33, pp. 1431-1440, 1998.
[6] M. F. Ashby, et al., Metal Foams: A Design Guide Butterworth-Heinemann, 2000.
[7] J. Banhart, "Manufacture, characterisation and application of cellular metals and metal foams," Progress in Materials Science, vol. 46, pp.
559-632, 2001.
[8] J. Banhart, "Aluminium foams for lighter vehicles," International Journal
of Vehicle Design, vol. 37, pp. 114-125, 2005.
[9] H. R. Zarei and M. Kröger, "Optimization of the foam-filled aluminum tubes for crush box application," Thin-Walled Structures, vol. 46, pp.
214-221, 2008.
[10] D. Leitlmeier, et al., "Development of a Foaming Process for Particulate Reinforced Aluminum Melts," Advanced Engineering Materials, vol. 4, pp. 735-740, 2002.
[11] L. J. Gibson and M. F. Ashby, Cellular Solids: Structure and Properties, 2nd ed.: Cambridge University Press, 1997.
[12] Y. Sugimura, et al., "On the mechanical performance of closed cell Al alloy foams," Acta Materialia, vol. 45, pp. 5245-5259, 1997.
[13] T. Miyoshi, et al., "Enhancement of energy absorption in a closed-cell aluminum by the modification of cellular structures," Scripta Materialia, vol. 41, pp. 1055-1060, 1999.
[14] K. Y. G. McCullough, et al., "Uniaxial stress–strain behaviour of
aluminium alloy foams," Acta Materialia, vol. 47, pp. 2323-2330, 1999.
[15] A. Paul and U. Ramamurty, "Strain rate sensitivity of a closed-cell
aluminum foam," Materials Science and Engineering: A, vol. 281, pp. 1-7, 2000.
[16] T. Mukai, et al., "Experimental study of energy absorption in a
close-celled aluminum foam under dynamic loading," Scripta Materialia, vol. 40, pp. 921-927, 1999.
[17] A. E. Markaki and T. W. Clyne, "The effect of cell wall microstructure on the deformation and fracture of aluminium-based foams," Acta Materialia, vol. 49, pp. 1677-1686, 2001.
[18] C. M. Cady, et al., "Compressive properties of a closed-cell aluminum foam as a function of strain rate and temperature," Materials Science and
Engineering: A, vol. 525, pp. 1-6, 2009.
[19] L. J. Gibson, et al., "The Mechanics of Two-Dimensional Cellular
Materials," Proceedings of the Royal Society of London. A. Mathematical
and Physical Sciences, vol. 382, pp. 25-42, July 8, 1982 1982.
[20] M. J. Silva, et al., "The effects of non-periodic microstructure on the elastic properties of two-dimensional cellular solids," International
Journal of Mechanical Sciences, vol. 37, pp. 1161-1177, 1995.
[21] S. D. Papka and S. Kyriakides, "Experiments and full-scale numerical simulations of in-plane crushing of a honeycomb," Acta Materialia, vol.
46, pp. 2765-2776, 1998.
[22] K. Li, et al., "Micromechanics model for three-dimensional open-cell foams using a tetrakaidecahedral unit cell and Castigliano's second theorem," Composites Science and Technology, vol. 63, pp. 1769-1781, 2003.
[23] L. Gong, et al., "Compressive response of open-cell foams. Part I:
Morphology and elastic properties," International Journal of Solids and
Structures, vol. 42, pp. 1355-1379, 2005.
[24] W.-Y. Jang, et al., "On the microstructure of open-cell foams and its effect on elastic properties," International Journal of Solids and Structures, vol.
45, pp. 1845-1875, 2008.
[25] D. Weaire and R. Phelan, "A counter-example to Kelvin's conjecture on minimal surfaces," Philosophical Magazine Letters, vol. 69, pp. 107-110, 1994/02/01 1994.
[26] W.-Y. Jang and S. Kyriakides, "On the crushing of aluminum open-cell foams: Part II analysis," International Journal of Solids and Structures, vol. 46, pp. 635-650, 2009.
[27] S. Santosa and T. Wierzbicki, "On the modeling of crush behavior of a closed-cell aluminum foam structure," Journal of the Mechanics and
Physics of Solids, vol. 46, pp. 645-669, 1998.
[28] S. A. Meguid, et al., "FE modelling of deformation localization in metallic foams," Finite Elements in Analysis and Design, vol. 38, pp.
631-643, 2002.
[29] A. E. Simone and L. J. Gibson, "Effects of solid distribution on the stiffness and strength of metallic foams," Acta Materialia, vol. 46, pp.
2139-2150, 1998.
[30] I. C. Konstantinidis, et al., "Model for determining mechanical properties of aluminum closed-cell foams," Theoretical and Applied Fracture
Mechanics, vol. 43, pp. 157-167, 2005.
[31] I. Jeon, et al., "Finite element simulation of the plastic collapse of closed-cell aluminum foams with X-ray computed tomography,"
Mechanics of Materials, vol. 42, pp. 227-236, 2010.
[32] S. D. Papka and S. Kyriakides, "In-plane crushing of a polycarbonate honeycomb," International Journal of Solids and Structures, vol. 35, pp.
239-267, 1998.
[33] E. W. Andrews, et al., "Size effects in ductile cellular solids. Part II:
experimental results," International Journal of Mechanical Sciences, vol.
43, pp. 701-713, 2001.
[34] L. J. Gibson and M. F. Ashby, "The Mechanics of Three-Dimensional Cellular Materials," Proceedings of the Royal Society of London. A.
Mathematical and Physical Sciences, vol. 382, pp. 43-59, July 8, 1982
1982.[35] C. Tekoğlu, et al., "Size effects in foams: Experiments and modeling,"
Progress in Materials Science, vol. 56, pp. 109-138, 2011.
[36] J.-b. Sha, et al., "FEM modelling of single-core sandwich and 2-core multilayer beams containing foam aluminum core and metallic face sheets under monolithic bending," Progress in Natural Science: Materials
International, vol. 21, pp. 127-138, 2011.
[37] R. T. DeHoff and F. N. Rhines, Quantitative Microscopy. New York:
McGraw-Hill, 1968.
[38] Y. Mu, et al., "Effect of cell shape anisotropy on the compressive behavior of closed-cell aluminum foams," Materials & Design, vol. 31, pp.
1567-1569, 2010.
表 2.1 各區域試樣之相對密度 （a）TOP（b）MID（c）BOT
（c）
Specimen No. ρ* ρs(%) Specimen No. ρ* ρs(%)
L01 12.57 R01 12.35
L02 12.36 R02 12.36
L03 12.34 R03 12.38
L04 12.28 R04 11.91
L05 11.78 R05 11.75
L06 11.60 R06 11.75
L07 11.69 R07 10.83
L08 11.62 R08 10.85
L09 11.27 R09 10.65
L10 10.91
L11 10.61
L12 11.05
Average (L) 11.67 Average (R) 11.65
表 2.2 沿著方向 3 各區域之相對密度比較（a）TOP（b）MID（c）BOT
TOP_Part1 9.32 8.28-10.18
TOP_Part2 8.81 8.37-9.29
TOP_Part3 7.89 7.64-8.21
（b）
MID_Part1 7.84 7.77-7.96
MID_Part2 8.37 8.28-8.45
MID_Part3 9.22 8.74-9.87
（c）
BOT_Part1 12.38 12.28-12.57
BOT_Part2 11.73 11.60-11.91
BOT_Part3 10.89 10.61-11.27
表 2.3 表面細胞寬高比
K12 K13 K23 K12min−max K13min−max K23min−max
TOP 0.891 0.856 0.991 0.802-1.098 0.755-1.038 0.844-1.203 MID 1.082 1.099 1.004 1.020-1.145 1.020-1.182 0.965-1.069 BOT 1.144 1.130 0.995 1.031-1.235 1.014-1.248 0.956-1.044
表 3.1 D1實驗材料機械性質（a）BOT（b）MID（c）TOP
（a）
Specimen No. ρ* ρs(%) *1 (%) E
E σI1 MPa σP1MPa ∆εP1(%)
BOT_L03 12.34 1.603 3.32 3.56 48.85
BOT_R04 11.91 1.494 3.07 3.34 48.78
BOT_R07 10.83 1.293 2.53 2.73 46.93
（b）
Specimen No. ρ* ρs(%) *1 (%) E
E σI1 MPa σP1MPa ∆εP1(%)
MID_L09 9.87 1.071 2.05 2.10 52.92
MID_R04 8.35 0.918 1.82 1.78 58.41
MID_L02 7.82 0.895 1.72 1.60 60.16
（c）
Specimen No. ρ* ρs (%) *1 (%) E
E σI1 MPa σP1MPa ∆εP1(%)
TOP_R03 9.53 0.306 1.09 1.19 43.96
TOP_L08 8.75 0.359 1.02 1.10 46.49
TOP_R09 7.85 0.511 1.23 1.27 52.96
表 3.2 D2實驗材料機械性質（a）BOT（b）MID（c）TOP
（a）
Specimen No. ρ* ρs(%) *2 (%) E
E σI2 MPa σP2 MPa ∆εP2(%)
BOT_R02 12.36 1.197 2.70 2.87 46.31
BOT_R05 11.75 1.147 2.55 2.57 47.96
BOT_L12 11.05 1.107 2.37 2.51 48.27
（b）
Specimen No. ρ* ρs(%) *2 (%) E
E σI2 MPa σP2 MPa ∆εP2(%)
MID_L10 9.75 0.847 1.77 1.85 50.36
MID_L06 8.45 0.586 1.69 1.66 56.28
MID_R02 7.77 0.787 1.62 1.50 61.10
（c）
Specimen No. ρ* ρs(%) *2 (%) E
E σI2 MPa σP2 MPa ∆εP2(%)
TOP_L02 9.10 0.777 1.90 1.74 61.73
TOP_R04 8.97 0.819 1.76 1.65 59.81
TOP_R07 8.21 0.682 1.51 1.47 59.37
表 3.3 D3實驗材料機械性質（a）BOT（b）MID（c）TOP
（a）
Specimen No. ρ* ρs(%) *3 (%) E
E σI3 MPa σP3 MPa ∆εP3(%)
BOT_L02 12.36 1.143 2.58 2.79 44.69
BOT_R06 11.75 1.160 2.57 2.71 47.61
BOT_R09 10.65 1.050 2.38 2.48 50.46
（b）
Specimen No. ρ* ρs(%) *3 (%) E
E σI3 MPa σP3 MPa ∆εP3(%)
MID_L11 9.26 0.847 1.77 1.85 50.36
MID_L07 8.40 0.791 1.63 1.68 54.39
MID_R03 7.80 0.723 1.42 1.46 58.57
（c）
Specimen No. ρ* ρs(%) *3 (%) E
E σI3 MPa σP3 MPa ∆εP3(%)
TOP_R05 8.68 0.858 1.94 1.78 59.51
TOP_L01 8.33 0.831 1.56 1.63 55.08
TOP_R08 7.65 0.566 1.22 1.27 55.79
表 3.4 不同方向下機械性質比較（a）BOT（b）MID（c）TOP
（a）
Specimen No. ρ* ρs(%) E* E(%) σI MPa σP MPa ∆εP(%) Exp.1
BOT_L03_D1 12.34 1.603 3.32 3.56 48.85
BOT_L04_D2 12.28 1.213 2.60 2.82 45.48
BOT_L02_D3 12.36 1.143 2.58 2.79 44.69
Exp.2
BOT_L09_D1 11.27 1.095 2.41 2.66 48.01
BOT_L12_D2 11.05 1.107 2.37 2.51 48.27
BOT_L10_D3 10.61 1.202 2.47 2.50 49.23
Exp.3
BOT_L05_D1 11.78 1.523 3.17 3.38 49.38
BOT_L08_D2 11.62 1.160 2.47 2.64 47.28
BOT_L06_D3 11.60 1.127 2.54 2.69 47.52
Exp.4
BOT_R01_D1 12.35 1.515 3.38 3.61 48.85
BOT_R02_D2 12.36 1.197 2.70 2.87 46.31
BOT_R03_D3 12.38 1.258 2.68 2.89 46.21
Exp.5
BOT_R04_D1 11.91 1.494 3.07 3.34 48.78
BOT_R05_D2 11.75 1.147 2.55 2.57 47.96
BOT_R06_D3 11.75 1.160 2.57 2.71 47.61
Exp.6
BOT_R07_D1 10.83 1.293 2.53 2.73 46.93
BOT_R08_D2 10.85 1.111 2.40 2.47 50.06
BOT_R09_D3 10.65 1.050 2.38 2.48 50.46
（b）
Specimen No. ρ* ρs(%) E* E(%) σI MPa σP MPa ∆εP（%）
Exp.1
MID_L09_D1 9.87 1.071 2.05 2.10 52.92
MID_L10_D2 9.75 0.847 1.77 1.85 50.36
MID_L11_D3 9.26 0.848 1.61 1.76 49.40
Exp.2
MID_L02_D1 7.82 0.895 1.72 1.60 60.16
MID_L01_D2 7.83 0.662 1.38 1.38 56.40
MID_L04_D3 7.88 0.656 1.29 1.41 51.88
Exp.3
MID_L05_D1 8.39 0.934 1.81 1.77 57.92
MID_L06_D2 8.45 0.586 1.69 1.66 56.28
MID_L07_D3 8.40 0.791 1.63 1.68 54.39
Exp.4
MID_R01_D1 7.82 0.888 1.75 1.60 62.24
MID_R02_D2 7.77 0.787 1.62 1.50 61.10
MID_R03_D3 7.80 0.723 1.42 1.46 58.57
Exp.5
MID_R04_D1 8.35 0.918 1.82 1.78 58.41
MID_R05_D2 8.28 0.888 1.75 1.70 57.71
MID_R06_D3 8.38 0.877 1.72 1.72 57.74
Exp.6
MID_R07_D1 9.21 0.938 1.90 1.95 54.62
MID_R08_D2 8.79 0.870 1.76 1.76 55.45
MID_R09_D3 8.74 0.810 1.68 1.76 53.20
（c）
Specimen No. ρ* ρs(%) E* E(%) σI MPa σP MPa ∆εP（%）
Exp.1
TOP_L04_D1 9.18 0.368 1.11 1.21 45.97
TOP_L02_D2 9.10 0.777 1.90 1.74 61.73
TOP_L01_D3 8.83 0.831 1.56 1.63 55.08
Exp.2
TOP_L12_D1 8.01 0.500 1.26 1.32 54.64
TOP_L11_D2 7.95 0.730 1.55 1.44 60.90
TOP_L09_D3 7.88 0.567 1.30 1.30 58.47
Exp.3
TOP_L08_D1 8.75 0.359 1.02 1.10 46.49
TOP_L06_D2 8.60 0.767 1.66 1.55 60.84
TOP_L05_D3 8.68 0.803 1.71 1.65 60.03
Exp.4
TOP_R06_D1 9.03 0.431 1.14 1.22 48.18
TOP_R04_D2 8.97 0.819 1.76 1.65 59.81
TOP_R05_D3 9.29 0.858 1.94 1.78 59.51
Exp.5
TOP_R09_D1 7.85 0.511 1.23 1.27 52.96
TOP_R07_D2 8.21 0.682 1.51 1.47 59.37
TOP_R08_D3 7.65 0.566 1.22 1.27 55.79
Exp.6
TOP_R03_D1 9.53 0.306 1.09 1.19 43.96
TOP_R01_D2 10.18 0.843 1.94 1.94 56.80
TOP_R02_D3 10.13 1.012 2.28 2.05 60.15
表 3.5 試樣寬高比（a）BOT（b）MID（c）TOP
（a）
Specimen No. ρ* ρs (%) i ,j ,k Kij K ik Exp.1
BOT_L03_D1 12.34 1, 2, 3 1.190 1.202
BOT_L04_D2 12.28 2, 1, 3 0.894 0.956
BOT_L02_D3 12.36 3, 1, 2 0.878 0.992
Exp.2
BOT_L09_D1 11.27 1, 2, 3 1.093 1.014
BOT_L12_D2 11.05 2, 1, 3 0.914 0.991
BOT_L10_D3 10.61 3, 1, 2 0.948 0.985
Exp.3
BOT_L05_D1 11.78 1, 2, 3 1.184 1.248
BOT_L08_D2 11.62 2, 1, 3 0.882 0.980
BOT_L06_D3 11.60 3, 1, 2 0.834 1.017
Exp.4
BOT_R01_D1 12.35 1, 2, 3 1.143 1.134
BOT_R02_D2 12.36 2, 1, 3 0.828 0.993
BOT_R03_D3 12.38 3, 1, 2 0.842 1.010
Exp.5
BOT_R04_D1 11.91 1, 2, 3 1.126 1.176
BOT_R05_D2 11.75 2, 1, 3 0.879 0.964
BOT_R06_D3 11.75 3, 1, 2 0.876 1.006
Exp.6
BOT_R07_D1 10.83 1, 2, 3 1.126 1.050
BOT_R08_D2 10.85 2, 1, 3 0.879 0.994
BOT_R09_D3 10.65 3, 1, 2 0.946 0.988
（b）
Specimen No. ρ* ρs (%) i ,j ,k Kij K ik Exp.1
MID_L09_D1 9.87 1, 2, 3 1.111 1.172
MID_L10_D2 9.75 2, 1, 3 0.884 1.041
MID_L11_D3 9.26 3, 1, 2 0.882 0.972
Exp.2
MID_L02_D1 7.82 1, 2, 3 1.143 1.120
MID_L01_D2 7.83 2, 1, 3 0.874 0.991
MID_L04_D3 7.88 3, 1, 2 0.912 0.993
Exp.3
MID_L05_D1 8.39 1, 2, 3 1.128 1.118
MID_L06_D2 8.45 2, 1, 3 0.879 1.021
MID_L07_D3 8.40 3, 1, 2 0.915 0.999
Exp.4
MID_R01_D1 7.82 1, 2, 3 1.058 1.061
MID_R02_D2 7.77 2, 1, 3 0.940 1.002
MID_R03_D3 7.80 3, 1, 2 0.938 0.992
Exp.5
MID_R04_D1 8.35 1, 2, 3 1.045 1.072
MID_R05_D2 8.28 2, 1, 3 0.965 1.003
MID_R06_D3 8.38 3, 1, 2 0.907 1.009
Exp.6
MID_R07_D1 9.21 1, 2, 3 1.045 1.075
MID_R08_D2 8.79 2, 1, 3 0.967 1.006
MID_R09_D3 8.74 3, 1, 2 0.941 1.008
（c）
Specimen No. ρ* ρs (%) i ,j ,k Kij K ik Exp.1
TOP_L04_D1 9.18 1, 2, 3 0.834 0.825
TOP_L02_D2 9.10 2, 1, 3 1.199 0.944
TOP_L01_D3 8.83 3, 1, 2 1.289 1.034
Exp.2
TOP_L12_D1 8.01 1, 2, 3 0.893 0.937
TOP_L11_D2 7.95 2, 1, 3 1.034 1.050
TOP_L09_D3 7.88 3, 1, 2 1.082 0.965
Exp.3
TOP_L08_D1 8.75 1, 2, 3 0.833 0.821
TOP_L06_D2 8.60 2, 1, 3 1.195 0.965
TOP_L05_D3 8.68 3, 1, 2 1.235 0.949
Exp.4
TOP_R06_D1 9.03 1, 2, 3 0.851 0.843
TOP_R04_D2 8.97 2, 1, 3 1.146 0.938
TOP_R05_D3 9.29 3, 1, 2 1.189 1.024
Exp.5
TOP_R09_D1 7.85 1, 2, 3 0.964 1.019
TOP_R07_D2 8.21 2, 1, 3 1.023 0.984
TOP_R08_D3 7.65 3, 1, 2 1.007 1.021
Exp.6
TOP_R03_D1 9.53 1, 2, 3 0.842 0.784
TOP_R01_D2 10.18 2, 1, 3 1.188 0.954
TOP_R02_D3 10.13 3, 1, 2 1.262 1.058
表 4.1 二維蜂巢狀模型解析解與數值模型之彈性模數比較
* (%) ρs
ρ 解析解 平面應力元素 誤差 (%)
10.65 0.3043% 0.3069% 0.85
10.85 0.3223% 0.3250% 0.85
10.91 0.3281% 0.3309% 0.86
11.05 0.3417% 0.3447% 0.87
11.6 0.3975% 0.4012% 0.93
11.62 0.3997% 0.4034% 0.93
11.75 0.4144% 0.4184% 0.96
12 0.4421% 0.4464% 0.97
12.36 0.4849% 0.4899% 1.01
12.38 0.4869% 0.4918% 1.02
（a） （b）
（c） （d）
圖 1.1 不同形式的細胞狀材料（a）巴爾莎木（SEM 圖）（b）鋁製的蜂巢 狀材料（c）Duocel®開口式泡沫鋁（電腦斷層掃描圖）（d）ALPORAS™封
閉式泡沫鋁
圖 1.2 ALPORAS™封閉式泡沫鋁之受壓力學行為 0
200 400 600 800 1000
0 1 2 3 4 5 6
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 σ
(psi)
δ / h
σ (MPa)
ALPORAS Aluminum Foams BOT_L03_D1
ρs= ρ*
12.34%
（a）
（b）
圖 1.3 泡沫鋁三明治結構應用（a）以泡沫鋁為芯材製成之三明治結構（b）
由泡沫鋁三明治結構製成之起重臂
圖 1.4 空心管內填滿泡沫鋁之能量吸收裝置
圖 1.5 西門子 COMBINO 列車之能量吸收裝置
圖 1.6 BMW 引擎支撐座之樣品
圖 1.7 Kelvin cell 十四面體
○
1○
2○
3圖 2.1 封閉式泡沫鋁之表面及表面局部放大
○ 1
○
2○
35 mm G
（a）
（a）
（b）
圖 2.3 封閉式泡沫鋁表面（a）試樣切面（b）表面細胞壁之放大
5 mm
（a）
（b）
圖 2.4 表面細胞壁量測（a）表面細胞壁之照片與厚度量測位置（b）細胞 壁勾勒圖與壁面長度定義
1 2 3
4 5 6 7 1 2 3 4 5 6
7
圖 2.5 壁面厚度變化
圖 2.6 表面細胞狀結構以多邊形近似示意圖
0 1 2 3 4
-0.5 0 0.5
ξ (=x / ) t(ξ)
t
of(ξ) = 22ξ4 + 6ξ2 + 1
圖 2.7 表面多邊形出現頻率
圖 2.8 沿方向 3 分組示意圖
0 100 200
2 3 4 5 6 7 8 9 10 11
N
Number of Edges
1(G)
2 Part 1 3
Part 2 Part 3
L R
（a）
（b）
（c）
圖 2.9 試樣切面比較（a）TOP（b）MID（c）BOT
5 mm
5 mm
5 mm
2 1
1 3
2 3 2
1
1 3
2 3 2
1
1 3
2 3
圖 2.10 寬高比量測示意
1 3
（a） （b）
ALPORAS Aluminum Foams
BOT_L03_D1 ρ
s
（a）
ALPORAS Aluminum Foams BOT_D1
ALPORAS Aluminum Foams MID_D1
MID_L09 MID_R04 MID_L02
δ / h
（c）
圖 3.3 D1實驗之受壓應力─位移關係圖（a）BOT（b）MID（c）TOP 0
200 400
0 1 2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 σ
(psi)
σ (MPa)
7.85%
9.53%
8.75%
ρs
ρ*
ALPORAS Aluminum Foams TOP_D1
δ / h
TOP_R03 TOP_L08 TOP_R09
圖 3.4 D1實驗之機械性質（a）軸向彈性模數E*1 E（b）局部極大應力值σI1
（a）
ALPORAS Aluminum Foams BOT_D2
ALPORAS Aluminum Foams MID_D2
MID_L10 MID_L06 MID_R02
δ / h
（c）
圖 3.5 D2實驗之受壓應力─位移關係圖（a）BOT（b）MID（c）TOP 0
200 400 600
0 1 2 3 4
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 σ
(psi)
σ (MPa)
9.10%
8.97%
8.21%
ρs
ρ*
ALPORAS Aluminum Foams TOP_D2
TOP_L02 TOP_R04 TOP_R07
δ / h
（a）
ALPORAS Aluminum Foams BOT_D3
ALPORAS Aluminum Foams MID_D3
MID_L11 MID_L07 MID_R03
（c）
圖 3.6 D3實驗之受壓應力─位移關係圖（a）BOT（b）MID（c）TOP 0
200 400
0 1 2 3
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 σ
(psi)
σ (MPa)
8.68%
8.33%
7.65%
ρs
ρ*
ALPORAS Aluminum Foams TOP_D3
δ / h
TOP_R05 TOP_L01 TOP_R08
圖 3.7 D2實驗之機械性質（a）軸向彈性模數E*2 E（b）局部極大應力σI2及
圖 3.8 D3實驗之機械性質（a）軸向彈性模數E*3 E（b）局部極大應力σI3及
圖 3.9 BOT 區域試樣以不同施力方向之受壓應力─位移關係圖 ALPORAS Aluminum Foams
BOT_Exp.1
ALPORAS Aluminum Foams BOT_Exp.2
圖 3.10 MID 區域試樣以不同施力方向之受壓應力─位移關係圖
ALPORAS Aluminum Foams MID_Exp.1
ALPORAS Aluminum Foams MID_Exp.2
圖 3.11 TOP 區域試樣以不同施力方向之受壓應力─位移關係圖
ALPORAS Aluminum Foams TOP_Exp.1
ALPORAS Aluminum Foams TOP_Exp.5
圖 3.12 試樣 BOT_L05 受壓應力─位移關係圖（D1實驗）
ALPORAS Aluminum Foams BOT_L05_D1
ρs= ρ*
11.78%
□2 □5
□1 □4
□0 □3
圖 3.13 對應於圖 3.12 狀態□0 至狀態□5 的表面變形情況
圖 3.14 試樣 BOT_L08 受壓應力─位移關係圖（D2實驗）
0 200 400 600 800
0 1 2 3 4 5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 σ
(psi)
σ (MPa)
0
2
3
4
5
1
δ / h
ALPORAS Aluminum Foams BOT_L08_D2
ρs
ρ*=
11.62%
□2 □5
□1 □4
□0 □3
圖 3.15 對應於圖 3.14 狀態□0 至狀態□5 的表面變形情況
圖 3.16 試樣 TOP_L08 受壓應力─位移關係圖（D1實驗）
0 200 400
0 1 2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 σ
(psi)
σ (MPa)
0
2 3
4
5
1
δ / h
ALPORAS Aluminum Foams TOP_L08_D1
ρs= ρ*
8.75%
□2 □5
□1 □4
□0 □3
圖 3.17 對應於圖 3.16 狀態□0 至狀態□5 的表面變形情況
圖 3.18 試樣 TOP_L06 受壓應力─位移關係圖（D2實驗）
0 200 400
0 1 2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 σ
(psi)
σ (MPa)
0
2
3 4
5
1
δ / h
ALPORAS Aluminum Foams TOP_L06_D2
ρs= ρ*
8.60%
□2 □5
□1 □4
□0 □3
圖 3.19 對應於圖 3.18 狀態□0 至狀態□5 的表面變形情況
圖 4.1 二維蜂巢狀結構
圖 4.2 邊之幾何定義
1 2
0.5 0.5
A
A
A-A
圖 4.3 二維蜂巢狀結構之特徵單元
1 2
（a）
⇓
（b）
圖 4.4 結點修正（a）結點處材料重疊情形（b）扣除重複材料部分
60∘
- 4 ×
（a）
（b） （c）
圖 4.5 二維蜂巢狀結構自由體圖（a）特徵單元自由體圖（b）斜向邊自由 體圖（c）直向邊自由體圖
圖 4.6 使用平面應力元素建立之二維蜂巢狀模型（ρ* ρs =12%）
A
iB
iC
jD
j圖 4.7 實驗與蜂巢狀數值模型之相對彈性模數比較
0 0.6 1.2
10 11 12 13
Experiments Plane Stress Analytical Sol.
E
*E (%)
ρ
*/ ρ
s
(%)
圖 4.8 Voronoi 幾何產生方式
圖 4.9 Voronoi 數值模型之幾何
d
2d
1圖 4.10 蜂巢狀數值模型與 Voronoi 數值模型之彈性模數比較（a）與實驗試 樣相同之相對密度（b）相對密度極小
0.1 0.2 0.3
10 11 12 13
Honeycombs Voronoi
E* E (%)
ρ*/ ρ
s (%)
0 5E-8 1E-7 1.5E-7
0 0.05 0.1
Honeycombs Voronoi
E* E (%)
ρ*/ ρ
s (%)
(a)
(b)
附錄 二維蜂巢狀模型幾何參數產生流程圖
選擇
將代入t0 =0.124−1.019+0.04713
求出t0
由式子(4.2)至(4.4) 求出
ρs
ρ*
ρs
ρ* 是否正確？
結束 是 否
決定所需
ρs
ρ*