非線性彈性固體微孔變形特性

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姓名

蔡瑞騏(Jui-chi Tsai) 查詢紙本館藏

畢業系所

土木工程學系

論文名稱

非線性彈性固體微孔變形特性

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摘要(中)

宏觀的角度下，材料可使用連體力學來進行分析。然而，對於宏觀的材料弱化行為，分析時宜加入微觀的損傷行為計算以加深了解。
本研究延續連體力學之基礎概念，並且以有限元素軟體(ABAQUS)來進行分析材料微孔之變形特性。相較於文獻中所得到的解析解以及Hou和Abeyaratne對於圓形孔洞三軸變形之近似解(HAF)，此篇用數值模型對橡膠微孔的幾何形狀、外部應力邊界條件做更廣泛的探討。藉以了解肉眼看不到的微孔的形狀與材料在受力後微孔擴張到目測能辨別時之形狀之關聯。此外，本篇所使用的橡膠材料包含neo-Hooken材料模型及Ogden材料模型。由數值分析之結果顯示，可藉由目測觀察到之孔洞幾何形狀，推測出未受力前之微孔幾何及其受力方式。

摘要(英)

In macroscopic scale,we usually use the concept of the continuum mechanics to analysis the behavior of the material.However,in order to analyze the weakening of materials,damages in micro scale must be taken into account.
In this thesis,we will analysis the behavior of a micro void in a rubber block by using continuum mechanics and the finite element software(ABAQUS). For the deformations of a spherical micro-void,exact solutions and analytical approximate solution(the Hau-Abeyarantne field)had beed obtained.And we focus on the behavior of non-spherical micro-void in this thesis.we try to build up the relations between the visible shapes of an expanded micro-void and the invisible shape of the undeformed micro-void.Using these results we can infer about the shape of a undeformed micro-void from the observations of the expanded micro-void.The neo-Hookean model and the Ogden model are adopted in our study.

關鍵字(中)

★ 有限元素
★ 橡膠材料
★ HAF

關鍵字(英)

★ finite element
★ rubber
★ Hau-Abeyarantne field

論文目次

摘要 I
ABSTRACT II
誌謝 III
目錄 V
表目錄 VII
圖目錄 VIII
符號表 XIII
第一章緒論 1
第二章基礎理論 3
2-1 控制方程式 3
2-2 材料模型 5
2-2-1 Ogden材料應變能密度函數[23-26] 5
2-2-2 neo-Hookean材料應變能密度函數 6
2-3 HAF 7
第三章橡膠承受非等軸拉伸下圓形微孔之變形 9
3-1 有限元素模型,邊界條件及收斂分析 9
3-2 數值結果及HAF的誤差分析 17
第四章橡膠承受等軸拉伸下非圓形微孔之變形 28
4-1有限元素模型,邊界條件及收斂分析 28
4-2數值結果 39
第五章橡膠承受非等軸拉伸下非圓形微孔之變形 58
5-1有限元素模型及邊界條件 58
5-2數值結果 58
第六章結論 63
參考文獻 66

參考文獻

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指導教授

李顯智(Hin-Chi Lei)

審核日期

2014-7-15

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