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研究生： 謝宗穎
hsieh, tsung-ying
論文名稱： 凝膠承受週期振動外力之接觸問題理論分析
Analysis of Gel Indentation by Oscillatory Load
指導教授： 林育芸
Lin, Y. Y.
學位類別： 碩士
Master
系所名稱： 工學院 - 土木工程學系
Department of Civil Engineering
論文出版年： 2006
畢業學年度： 94
語文別： 中文
論文頁數： 71
中文關鍵詞： 滲透係數 、接觸長度 、週期振動外力 、壓痕機 、凝膠
外文關鍵詞： coefficient of permeability, contact length, oscillatory load, gel, Indentation
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    • 凝膠是由連續性的彈性固態網絡與孔隙中的液體所

    組成，因此當凝膠承受外力變形時，部分應力值由孔隙

    流體所承受，流體間則因產生壓力梯度而產生流動。本

    文主要利用Biot廣義三維壓密理論描述凝膠的力學特

    性，分析以週期振動外力施加壓痕機使其與凝膠接觸之

    力學問題，探討當凝膠受壓時，其內部應力場分佈與差

    異沉陷量變化跟振動頻率、接觸長度與凝膠滲透特性之

    關聯性。

    A gel is a continuous network of a solid phase incorporating a continuous liquid phase. When a gel is subjected to a load, it starts to deform and this gives rise to a pressure gradient in the liquid phase, hence liquid will continue to flow out of the gel.In this work, we analyzed the contact problem between gel and an oscillatory rigid indenter based on the general theory of consolidation by Biot.The stress distribution underneath the indenter and displacement on the surface of gel are influenced by oscillatory frequency, contact length,the permeability of gel.

    中英文摘要.........................................................................................I 誌謝...................................................................................................Ⅲ 目錄...................................................................................................Ⅳ 表目錄...............................................................................................Ⅵ 圖目錄...............................................................................................Ⅶ 符號...................................................................................................Ⅸ 第一章 緒論.......................................................................................1 1.1 研究動機與目的..........................................................................1 1.2 本文內容與組織..........................................................................2 第二章 相關理論與文獻回顧...........................................................4 2.1 凝膠分析相關理論......................................................................4 2.2 壓痕接觸試驗有效量測材料參數..............................................5 第三章 凝膠承受週期振動外力理論分析.....................................11 3.1 凝膠與多孔性介質材料之力學行為........................................11 3.2 凝膠與平面壓痕機二維接觸力學問題描述及理論................14 第四章 數值分析方法與結果.........................................................27 4.1 正規化參數及正規化方程式....................................................27 4.2 正規化應力分佈........................................................................28 4.3 沉陷量之計算............................................................................31 4.4 相位差與凝膠應力場之分析....................................................34 第五章 結論.....................................................................................57 參考文獻..........................................................................................61 附錄A...............................................................................................63 附錄B...............................................................................................66 附錄C...............................................................................................70 自述..................................................................................................71

    [1] www.sandia.gov/media/porosity.htm.

    [2] R. A. Stile W. R. Burghardt and K. E. Healy , “Synthesis and characterization of injectable poly(N-isopropylacrylamide)-based hydrogels that support tissue formation invitro”, Macromolecules, Vol.32 pp. 7370-7379 (1999)

    [3] M. A. Biot, “General theory of three-dimensional consolidation”, J. Applied Physics, Vol.12 pp.155-164 (1941)

    [4] M. A. Biot, “Consolidation settlement under a rectangular load distribution”, J.Applied Physics ,Vol.12 pp. 426-430 (1941)

    [5] G. W. Scherer, “Drying gel VI. Viscoelastic plate ”, J.Non-Crystalline Solids, Vol99, pp.324-358 (1988)

    [6] G. W. Scherer, “Mechanics of syneresis”, J. Non-Crystalline Solids, Vol.108, pp. 18-27 (1989)

    [7] G. W. Scherer, “Drying gel VIII. Revision and review”, J. Non- Crystalline Solids, Vol.109, pp. 171-182 (1989)

    [8] G. W. Scherer, “Crack-tip stress in gels”, J. Non-Crystalline Solids, Vol.144, pp.210-216 (1992)

    [9] G. W. Scherer, “Bending of gel beams:method for characterizing elastic properties and permeability”, J. Non-Crystalline Solids, Vol.142, pp. 18-35 (1992)

    [10] J.R. Rice & M.P. Cleary, ‘‘Some Basic Stress Diffusion Solution for
    Fluid-Saturated Elastic PorousMedia With Compressible Constituents’’, Review of Geophysics and Space Physics, Vol.14,pp 227-241, (1976).

    [11] 莊富欽, “建立接觸力學方法以分析凝膠的彈性及滲透性“,國立成功大學土木工程學系碩士論文,(2004)

    [12] C. Y. Hui, Y. Y. Lin, F. C. Chuang, K. R. Shull, W.C. Lin ,“A contact mechanics method for characterizing the elastic properties and permeability of gels”, Journal of Polymer Science,Part B: Polymer Physics, 44 (2), pp. 359-370 (2006)

    [13] 胡寶文,“多孔性凝膠於壓痕實驗下之力學行為模擬“,國立成功大學土木工程學系碩士論文,(2005)

    [14] F. Nelson. Nunalee and Kenneth R. Shull , “Contact Mechanics Studies with the Quartz Crystal Microbalance: Original of the Contrast Factor for Polymer Gels and Solutions”, Langmuir vol.20,pp.7083-7089 (2004)

    [15] Abramnowitz and Stefan “Handbook of Mathematical Functions”, see section on Legendre functions and orthogonal polynomials.In particular see pp.335,775, (1965)

    [16] H.Hochstadt ,Dover, “Special Function of Mathematical Physics”, (1961)

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