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姓名

楊頂順(Young Ding Shun) 查詢紙本館藏

畢業系所

土木工程學系

論文名稱

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摘要(中)

含微孔圓球受均佈或三軸拉力的力學問題，與材料損傷研究有關。過去三十年，相關的研究不少，有數值的分析，也有解析解。
本文旨在指出目前仍被忽略的兩個細節。其一是，有限元素法計算圓球受均佈拉力之問題時，在微孔快速擴張的臨界邊界值之計算，與精確解所描述者相當接近，會讓人以為數值解值得信賴，但是，數值解其實並不滿足材料組成律！！其二是，圓球受三軸拉力而變形，可由Hou – Abeyaratne Field 來描述，此近似的解析解推測圓形微孔會變成橢球狀。此與數值計算結果一致，故一般認為此解析解在定性上表現不錯，但本文發現此解析解在定性上與數值解之結果其實相差頗多。

摘要(英)

The micro-void growth problem of an elastic spherical ball subjected to triaxial loading is related to the studies of damages in materials.
A lot of analytical and numerical investigations of this problem had been carried out in the past thirty years.
The theme of this thesis is to point out two misleading facts which had been ignored by the large in the past.
The first is about the precision of the finite element solutions which had been thought to be quite reliable. We found that the numerical solutions do not even satisfy the constitutive law.
The second is about the Hou - Abeyaratne Field, which predicts that the micro-void will be deformed into an elliptical void. The ellipticity of the deformed void had been confirmed many times by numerical computations. However, we found that one important difference between the HAF and the finite element solution still exists.

關鍵字(中)

★ 有限元素法
★ 微孔

關鍵字(英)

★ finite element
★ micro-void

論文目次

摘要………………………………………………………..I
ABSTRACT…………………………………………..…II
目錄……………………………………………………...III
表目錄………………………………………………..…..V
圖目錄………………………………………………...…VI
第一章緒論………………………...……………………1
第二章基礎理論和圓對稱解析解……………………...4
2.1 非線性彈性力學簡介………………………4
2.2 圓對稱解析解………………………………6
第三章有限元素分析……………………………….....10
3.1 模型之建立……………………………….10
3.2 網格收斂性分析………………………......15
3.3開孔曲面之計算…………………………...20
第四章圓對稱數值解與解析解之對比……………….23

第五章三軸變形數值解與解析解之對比.....................32
第六章結論………………………………………….…40
參考文獻……………………………………………...…41

參考文獻

參考文獻
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[2] A. Needleman, Void Growth In An Elastic-Plastic Medium. J. Appl. Mech. 39(1972) 964-970.
[3] A. L. Gurson, Continuum Theory Of Ductile Rupture By Void Nucleation And Growth: Part I—Yield Criteria And Flow Rules For Porous Ductile Media. J. Energ. Matl. Tech. , Trans.Asme,(1977) 2-15.
[4] U. Stigh, Effects Of Interacting Cavities On Damage Parameter. J. Appl. Mech. 53(1986), 485-490.
[5] A. N. Gent ,Cavitation In Rubber: A Cautionary Tale. Rubber Chem. Tech., 63(1990) 49-53.
[6] E. Bayraktar , Et. Al., Damage Mechanisms In Natural (Nr) And Synthetic Rubber (Sbr): Nucleation, Growth And Instability Of The Cavitation. Fatique Fract. Engrg. Mater. Struct. , 31(2008)184-196.
[7] C. Fong, Cavitation Criterion For Rubber Materials: A Review Of Void-Growth Models. J. Polymer Sci.: Part B: Polymer Phys., 39(2001)2081-2096.
[8] A.N. Gent and P. B. Lindley, Internal rupture of bonded rubber cylinders in tensions. Proc. R. Soc. Ser. A, 249(1958)195-205.
[9] J.M.Ball, Discontinous equilibrium solutions and cavitation in nonlinear elasticity. Phil.Trans.R.Soc.Lond, A306 (1982) 557-610.
[10] C.O.Horgan and R.Abeyaratne, A bifurcation problem for a compressible nonlinearly elastic medium: growth of a micro-void. J.Elasticity, 16 (1986) 189-200.
[11] H.S. Hou and R. Abeyaratne, Cavitation in elastic and elastic-plastic solids.. J. Mech. Phys. Solids, 40 (1992) 571-592.

[12]M. Danielsson, D.M. Parks and M.C. Boyce, Constitutive modeling of porous hyperelastic material. Mech. Mater., 36(2004)347-358.
[13] J. Li, D. Mayau and F. Song, A constitutive model for cavitation and cavity growth in rubber-like materials under arbitrary tri-axial loading. Int. J. Solids Struct., 44(2007)6080-6100.
[14] J. Li, D. Mayau and V. Lagarrigue, A constitutive model dealing with damage due to cavity growth and the Mullins effect in rubber-like materials under triaxial loading. J. Mech. Phys. Solids, 56(2008)953-973.
[15] X. Xu and D. Henao , An efficient numerical method for cavition in nonlinear elasticity. Math. Models Methods. Appl. Sci. ,21(2011)1733-1760.
[16] O. Lepez-Pamies , To Nakamura , and M. I. Idiart , Cavition in elastemeric solids : II - Onset -of – cavitation surface for neo-Hookean materials , J. Mech. Phys. Solids , 59(2011)1488-1505.
[17]Liu, Yueting, Finite element modeling of growth of void in rubber-like materials, 2014, Final Year Project Report (Supervised by Prof. Thomas Lok), Bachelor of science in Civil Engineering, University of Macau.

指導教授

李顯智(H.C.Lei)

審核日期

2015-7-28

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