泡沫材料為一內部含有大量孔洞之輕質材料，依據微觀構件連接方式不同，可分為連通型泡沫材料與封閉型兩大類泡沫材料。由於泡沫材料中之微觀構件，其主要的變形機制為撓曲變位，故本研究採用不同邊界束制之細長梁，作為模擬泡沫材料微觀構件力學性質之簡化模型，探討由應變硬化固體材料所構成細長梁之彈塑性行為，同時，推導不同邊界條件下之外載力與撓曲變位關係式，進而分析比較連通型泡沫材料與封閉型泡沫材料之塑性變位行為，最後，建立一理論應力應變關係式描述不同泡沫材料之彈塑性行為。
本研究採用有限元素分析軟體Abaqus進行細長梁簡化模型之數值分析。首先，以應變硬化固體材料所構成細長梁，模擬連通型泡沫材料中之任一微觀構件，針對簡支梁、固定端梁及懸臂梁等不同端點旋轉束制條件，結合材料塑性變形理論，分析細長梁之外載集中力與其作用處撓曲變位關係，藉由無因次化及正規化處理後，選用一雙指數函數擬合不同邊界條件下細長梁之外力—變位關係式。其次，採用細長梁及其底部接合薄板之複合結構，模擬封閉型泡沫材料中之微觀構件，配合數值分析模型與計算結果，建立外載集中力與其作用處撓曲塑性變位關係式，最後，評估不同應變硬化固體材料，對所構成連通型與封閉型泡沫材料塑性行為之影響。

This study investigates the influence of strain hardening on the plastic behavior of cellular foams through a combination of theoretical derivation and finite element analysis (FEA). Since the deformation of foam materials is governed primarily by the bending of their microscopic cell edges, the mechanical response of these cell edges can be represented by simplified slender beam models. Open-cell foams are modeled using individual slender beams with different end constraints, while closed-cell foams are represented by a composite structure consisting of a slender beam attached to a thin plate. By incorporating strain-hardening material behavior into these simplified structural models, the study establishes theoretical load–displacement capable of describing the elastoplastic response of different foam materials. Numerical simulations performed using a finite element analysis software Abaqus validate the theoretical formulations and demonstrate how strain hardening, geometric constraints, and boundary conditions collectively influence the plastic deformation of both open-cell and closed-cell foams. The proposed formulations provide a simple yet accurate analytical framework for predicting the mechanical behavior of foam materials while significantly reducing computational complexity compared with detailed microstructural simulations.

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