泡沫材料具有高孔隙率、低密度、優良隔音及隔熱與高吸能特性，於相同單位重條件下能提供較高勁度與強度，所以，泡沫材料已廣泛運用於各項輕質結構工程中，其中，球殼泡沫材能改善傳統連通型泡沫材與封閉型泡沫材，於製作過程易產生微結構缺陷之問題，由於球殼泡沫材料較易掌握其孔洞尺寸，而且泡沫堆疊方式具規則性，所以，此類泡沫材料之力學行為較能準確加以預估。本文探討單尺寸球殼堆疊之泡沫材，以及由雙尺寸球殼所堆疊製成泡沫材之力學性質，希望採用雙尺寸堆疊方式以提高原先單尺寸堆疊製成泡沫材料之力學性質，選用有限元素套裝軟體ABAQUS，針對不同堆疊模型進行數值模擬與分析，施加一均佈載重以計算分析其楊氏模數，進而求得不同堆疊泡沫材料其楊氏模數與相對密度之關係回歸式，根據數值分析結果，發現雙尺寸簡單立方堆疊所構成泡沫材料，其楊氏模數產生明顯改善，至於體心立方堆疊方式，若由單尺寸增為雙尺寸，所製成泡沫材料於相對密度偏低時，其楊氏模數確可增加，但此加勁成效卻隨相對密度增加而下降，最後，面心立方堆疊方式已相當緻密，所以，若由單尺寸增為雙尺寸，所製成泡沫材料之楊氏模數變化不大。

Foam materials has properties of high porosity, low density, high energy absorption and well absorption of heat and sound. Besides, the foam material can provide higher strength under the condition of same unit weight. As the result, foams material is widely used in lightweight construction. Hollow sphere foams can solve the problem of traditional foams with microstructure defects which produce during manufacturing. On account of regularly stacking and controllable hollow sphere size, hollow sphere foam materials may avoid most part of microstructure defects and their mechanical behavior would be more predictable. This study revolves in the elastic constants of foams made from single-sized and dual-sized hollow spheres. Using dual-sized hollow spheres stacking to strengthen the original structure of single-sized hollow sphere foams under same relative density. Selecting finite element software ABAQUS to do simulation analysis including different stacking models. Applying a given force on hollow sphere foam model to calculate Young’s modulus and poison ratio from simulation results. Arranging simulation data of hollow sphere foam models from different stacking to get numerical relationship function between Young’s modulus and relative density. According to numerical analysis result, Young’s modulus of dual-sized hollow sphere foams obviously larger than single-sized sphere foams under simple cubic stack structure. Under body-center cubic stacking structure, Young’s modulus of dual-sized hollow sphere foams is higher than single-sized at low relative density. For face-center cubic stacking, Young’s modulus do not change much from single-sized to dual-sized hollow sphere foams.

[1]　Lorna J, Gibson LJ. “Biomechanics of cellular solids.” Journal of biomechanics, 38 377-399 (2005)
[2]　Li ZW, Wang HW, Wei ZJ, Wang YG. “Fabrication and compressive properties of K405 alloy hollow sphere foams.” Rare Metal Mater. Eng. 37(1), 135-138 (2008)
[3]　Sanders WS, Gibson LJ. “ Mechanics of hollow sphere foams,” Materials Science and Engineering: A, Vol. 347, pp. 70-85 (2003).
[4]　Sanders WS, Gibson LJ. “ Mechanics of BCC and FCC hollow-sphere foams,” Materials Science and Engineering: A. Vol. 352, pp. 150-161 (2003).
[5]　Gibson LJ, Ashby MF, Cellular Solids: Structure and properties (2nd ed.), Cambridge University Press (1997).
[6]　Simone AE, Gibson LJ. “Aluminum foams produced by liquid-state processes.” Acta mater. Vol.46, No. 9, pp. 3109-3123 (1998)
[7]　Kang YA, Zhang JY, Tan TC, “Effect of relative density on the compressive property and energy absorption capacity of aluminum foams,” Journal of Functional Materials: Vol. 37 pp.247-254(2006)

[8]　何博文,”泡沫鋁之三軸力學行為,”國立成功大學工程研究所碩士論文(2001)
[9]　陳婷容,”蜂巢與泡沫材料之潛變斷裂與潛變挫曲,”國立成功大學工程研究所博士論文(2008)
[10]　Simone AE, Gibson LJ. “Effects of solid distribution on the stiffness and strength of metallic foam,” Acta mater. Vol. 46, No. 6, pp. 2139-2150 (1998).
[11]　Lin TC. “In-plane and out-of plane Mechanical properties and microstructural efficiency of elliptical cell honeycombs,” Ph.D. dissertation, Department of Civil Engineering, National Cheng Kung University, Tainan, Taiwan (2013).
[12]　Fiedler T, Ochsner A. “On the anisotropy of adhesively bonded metallic hollow sphere structures,” Science Direct: Scripta Materialia 58, pp.695-698 (2008).
[13]　Gasser S, Paun F, Cayzeele A, Brechet Y. “Uniaxial tensile elastic properties of a regular stacking of brazed hollow spheres.” Scripta Materialia 48 pp. 1617-1623 (2003)