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研究生: 陳柏維
Chen, Bo-Wei
論文名稱: 生物組織之黏彈性特性實驗與擬合分析
Experiment and Fitting Analysis of Viscoelastic Properties of Biological Tissues
指導教授: 李旺龍
Li, Wang-Long
學位類別: 碩士
Master
系所名稱: 工學院 - 材料科學及工程學系
Department of Materials Science and Engineering
論文出版年: 2021
畢業學年度: 109
語文別: 中文
論文頁數: 116
中文關鍵詞: 生物組織實驗黏彈性材料彈液動潤滑
外文關鍵詞: EHL, Biological Tissue Experiment, Viscoelastic Material
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  • 隨著科技不斷地進步,人類在醫學生物體上的研究也日益更新,生物體的軟組織研究,如皮膚、眼睛、關節、心臟、肺部等等,這些都與人體的健康密不可分,而目前關於人體肺部之慢性疾病影響,例如特發性肺纖維化(IPF)、哮喘(Asthma)、慢性阻塞性肺部疾病(COPD)和2019年爆發的新型冠狀病毒肺炎(COVID-19)這些疾病為主要全球高齡化人口之主要死因。肺組織就像許多生物軟組織一樣,都是具有高度黏彈性的機械性質,且肺部的機械性質與上述的這些疾病有著相當大的關係。因此若能更進一步的了解這些組織特性,研究其性質,並將其數據應用於建立人工模型,則從實驗獲取數據的方式變得非常重要。
    在本研究當中,將會對兩隻豬之新鮮豬肺以圓柱形平端壓頭與圓球形壓頭進行較淺與較深之壓痕試驗與應力鬆弛實驗,將數據以均方根誤差法擬合Generalized Maxwell黏彈性模型獲得參數,並進行建模擬合與實驗比較,最後在加入暫態擠壓彈液動潤滑系統探討是否有助於改善模型,使之更接近真實情況。
    實驗顯示兩種壓頭在不同深度實驗上大致上都擁有相同之趨勢,而在第二次實驗改善初始接觸之問題能使結果更為真實且使再現性提升,並藉由擬合參數與建模方式來重現實驗之趨勢。而以本研究擬合中間深度之黏彈參數,去模擬不同深度並與實驗值比較發現,在壓入淺深度的區域中能與實驗值接近,而在較深的區域加入彈液動潤滑模型能使模擬結果更靠近實驗值。

    With the advance of science and technology,research on medical organisms becoming more and more updated. The soft tissue research of organisms, such as skin、eyes、joints、heart、lungs、etc.. are inseparable from human health. The current impact of chronic diseases in the human lungs, such as Idiopathic pulmonary fibrosis (IPF)、Asthma、Chronic dual lung disease (COPD) and Coronavirus disease 2019 (COVID-19)。These diseases,like many biological soft tissues,have highly viscoelastic mechanical properties,for lung this property has a considerable relationship with the above-mentioned diseases.Therefore,if we can further understand these organizational characteristics,study their properties, and merge their data to build artificial models,the way to obtain data from experiments becomes very important.

    In this study, the fresh pig lungs of two pigs will be subjected to shallower and deeper indentation tests and stress relaxation tests with a cylindrical flat-end indenter and a spherical indenter, and the data will be simulated by the root mean square error method. Integrate the Generalized Maxwell viscoelastic model to obtain the parameters, and carry out the modeling fitting and experiment comparison.Experiments show that the two types of indenters generally have the same trend in different depth experiments. In the second experiment, improving the initial contact problem can make the results more realistic and improve the reproducibility.

    After fitting the simulated value of the experimental result of the intermediate depth, and adding the elastic fluid motion, the result shows that it can be closer to the real situation.

    中文摘要 I Extended Abstract II 致謝 XVI 目錄 XVII 表目錄 XX 圖目錄 XXI 符號總表 XXV 第一章 緒論 1 1.1 前言 1 1.2 文獻回顧 2 1.2.1 生物組織之機械性質測量方法 2 1.2.2 黏彈性材料 3 1.2.3 肺部之黏彈性 4 1.2.4 彈液動潤滑之演變 5 1.2.5 擠壓彈液動之問題 7 1.3 研究動機與目的 9 1.4 論文架構 11 第二章 研究理論 13 2.1 壓痕試驗原理 13 2.1.1 赫茲接觸力學 13 2.1.2 圓柱形平端壓頭 19 2.2 黏彈性材料模型 22 2.2.1 Maxwell模型 26 2.2.2 Voigt模型 28 2.2.3 三參數線性黏彈性模型 29 2.2.4 Generalized Maxwell模型 32 2.2.5 Prony method數學分析方法 33 2.3 彈性變形方程式 34 2.3.1 線彈性材料模型 34 2.4 彈液動潤滑之理論 35 2.4.1 雷諾方程式 35 2.4.2 液膜厚度方程式 39 2.4.3 擠壓之低壓階段-液動潤滑 40 2.4.4 擠壓之高壓階段-彈液動潤滑 41 2.5 負載平衡方程式 42 2.6 von Mises應力準則 43 第三章 材料與方法 47 3.1 實驗材料 47 3.2 實驗方法 47 3.2.1 壓痕試驗 47 3.2.2 應力鬆弛實驗 48 第四章 數值方法 56 4.1 有限元素法 56 4.1.1 幾何建模參數設定 58 4.1.2 Galerkin法 60 4.1.3 離散公式 61 4.1.4 Newton-Raphson法 62 4.2 網格測試 65 4.3 均方根誤差法 66 4.4 模型計算流程 67 第五章 結果與分析 69 5.1 模擬驗證 70 5.2 圓柱形平端壓頭壓痕試驗 75 5.2.1 實驗結果 75 5.2.2 數值模型建立與分析結果 76 5.3 圓柱形平端壓頭應力鬆弛實驗 80 5.3.1 實驗結果 80 5.3.2 數值模型建立與分析結果 84 5.4 圓球形壓頭壓痕試驗 89 5.4.1 實驗結果 90 5.4.2 數值模型建立與分析結果 93 5.5 圓球形壓頭應力鬆弛實驗 96 5.5.1 實驗結果 97 5.5.2 數值模型建立與分析結果 100 第六章 結論與展望 103 6.1結論 103 6.2未來展望 104 參考文獻 105 附錄 A 無因次負載平衡方程式之推導 110 附錄 B 有限應變理論(Finite strain theory)概述 113

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