連通型泡沫材料，乃微觀構件間無薄膜之多孔輕質材料，其彈塑性變形機制主要受撓曲變形所影響。因此，本研究藉由不同邊界束制條件之細長梁，模擬泡沫材料中微觀構件之受力與撓曲變位行為，進而探討連通型泡沫材料之彈塑性應力應變關係。首先，使用有限元素套裝軟體ABAQUS，進行數值分析，並透過塑性變形理論推導，分別探討完美塑性材料與應變硬化材料所構成之細長梁，其彈塑性變位行為。經數值分析與理論推導後發現，將不同邊界束制條件下之細長梁，其外載集中力及作用處變位量，除以各自對應之初始降伏點，加以正規化處理後，可獲得一致的正規化彈塑性變形關係，此關係可由一理論變位函數加以描述。此外，當集中力作用處與梁中承受最大彎矩位置重疊時，可忽略不同斷面幾何形狀與加載條件所造成之影響，因此，該理論表示式適用於描述，具有不同邊界轉動束制條件微觀構件之彈塑性變位關係，由此微觀構件之理論彈塑性變位函數，經因次分析後，可進一步求得連通型泡沫材料之彈塑性應力應變關係，並與泡沫鋁單軸壓力試驗結果相互比較，以驗證本研究所建立連通型泡沫材料彈塑性行為理論表示式之適用性。

The dominant deformation mechanism of lightweight open-cell foams, which are composed of an interconnected network of solid struts, is the flexural deflection of each slender cell strut. Thus, a slender beam under different boundary conditions can be employed to analyze the elasto-plastic behavior of open-cell foams. In the study, the elasto-plastic deflection of a rectangular cross-section slender beam, made from either a perfectly plastic or a strain-hardening solid and subjected to a concentrated force, is first analyzed numerically by using a finite element software ABAQUS, and then compared to the theoretical results derived from conjugated beam method. Furthermore, the normalized concentrated force and flexural deflection of the slender beam are defined as the values at any instance divided by those at the outset of initial yielding. It is found that the relationship between the normalized concentrated force and flexural deflection can be described well by a simple function, regardless of the boundary condition of the slender beam. Meanwhile, the effects of boundary condition, concentrated force location and cross-sectional shape on the normalized simple function are insignificant when the concentrated force is loaded at the critical section of the beam. As a result, the normalized simple function of the slender beam can be utilized to analyze the elastic-plastic stress-strain relationship of open-cell foams. Finally, the theoretical elasto-plastic behavior derived here is compared with the experimental results of uniaxial compression test for aluminum alloy foams to verify its validity and accuracy.

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