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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 舒貽忠(Yi-Chung Shu) | |
| dc.contributor.author | Kai-Yang Wang | en |
| dc.contributor.author | 王凱陽 | zh_TW |
| dc.date.accessioned | 2021-06-16T10:53:32Z | - |
| dc.date.available | 2015-08-14 | |
| dc.date.copyright | 2013-08-14 | |
| dc.date.issued | 2013 | |
| dc.date.submitted | 2013-08-09 | |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/61213 | - |
| dc.description.abstract | 本文主要使用COMSOL Multiphysics有限元素軟體來進行相場架構模擬，並建立一套標準的計算流程，有助於日後建立相場模型上更快速有效率。有別於過去的快速傅立葉演算法在理論相場法中，須假設均質情況來求解，COMSOL解決了此問題，成功地在非均質假設下模擬出晶域排列。此外COMSOL在數學模型建構上簡單明瞭，大幅降低建立相場模型時間。
本團隊依據Eshelby等效理論及Hashin-Shtrikman變分理論推導出另一種能量表示式，進而建構出等效型相場架構。在本文中，首先簡化等效相場架構，在不考慮極化情形下模擬麻田散鐵來驗證此架構正確性，發現微結構排列確實符合諧和條件與許多實驗上的成果。接著延伸到非均質鐵電材料上來模擬正方晶與菱方晶，等效型確實可以演化出正確晶域排列並且成功算出材料等效係數，提供了更精準的材料性質，也證實使用有限元素軟體COMSOL來建立等效相場架構與計算材料等效係數是可行的。 | zh_TW |
| dc.description.abstract | The thesis aims to develop numerical algorithms implemented in COMSOL finite element software for phase-field simulations. The conventional phase-field simulations adopt algorithms based on the fast Fourier transform. However, such a method is not suitable for the case with material inhomogeneity. Instead, the algorithms developed here are suitable for both cases with material homogeneity and inhomogeneity. In addition, the algorithms based on COMSOL are much simpler than those implemented in programming languages.
The framework is based on the equivalent phase-field models developed by the previous team efforts. It is established by involving the spirit of Eshelby equivalent principle and Hashin-Shtrikman variational formulation. The results are first validated by simulating microstructure patterns in martensitic thin films. Next, the developed algorithms are extended to the case of tetragonal and rhombohedral ferroelectric domain simulations. The results show that many more electromechanical self-accommodation patterns as well as engineered domains are simulated and are consistent with experimental observations. Finally, the effective constants of several engineered domains are calculated and compared with those based on micromechanics calculations. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T10:53:32Z (GMT). No. of bitstreams: 1 ntu-102-R00543060-1.pdf: 28846274 bytes, checksum: a6397d9e995aeb3424b807c1180cd95c (MD5) Previous issue date: 2013 | en |
| dc.description.tableofcontents | 誌謝 i
中文摘要 ii ABSTRACT iii 目錄 iv 圖目錄 vi 表目錄 x 第一章 導論 1 1.1研究背景與目的 1 1.2鐵電材料(ferroelectric) 1 1.3麻田散鐵(martensites) 3 1.4相場法(phased-field method)介紹 3 1.5COMSOL Multiphysics有限元素軟體 4 1.6本文架構 5 第二章 理論架構 6 2.1鐵電材料 6 2.1.1 鐵電材料結構 6 2.1.2 諧和條件 8 2.2理論相場架構 10 2.2.1 鐵電材料內部能量 10 2.2.2 熱力學驅動力與演化方程式 11 2.3非均質等效相場法 14 2.3.1 非均質彈性材料 14 2.3.2 非均質鐵電材料 16 第三章 數值計算 19 3.1演化方程式無因次化 19 3.1.1 理論型相場法無因次化之演化方程式 19 3.1.2 非均質等效相場法無因次化之演化方程式 20 3.1.3 等效數值 21 3.2COMSOL Multiphysics有限元素分析軟體 22 3.2.1 COMSOL PDE介紹 22 3.2.2 相場模型建立 23 3.2.3 COMSOL 等效係數計算 30 3.2.4 模型建構流程 34 第四章 非均質相場模型驗證 35 4.1(001) 晶向薄膜 36 4.2(110) 晶向薄膜 37 4.3(111) 晶向薄膜 40 4.4忽略(△C)-1/μ演化方程式 41 第五章 鐵電材料相場模擬 45 5.1正方晶微結構模擬 45 5.1.1 理論型態數學模型演化結果 47 5.1.2 等效型態數學模型演化結果 50 5.1.3 理論型與等效型相場比較 55 5.2菱方晶微結構模擬 56 5.2.1 理論型態數學模型演化結果 58 5.2.2 等效型態數學模型演化結果 61 第六章 結論與未來展望 66 6.1結論 66 6.2未來展望 67 參考文獻 70 附錄A COMSOL操作補充說明 74 附錄B COMSOL平行運算 82 附錄C 本文COMSOL中各項定義 85 附錄D 微結構演化過程 88 附錄E 模擬中各項材料係數 90 | |
| dc.language.iso | zh-TW | |
| dc.subject | 多重耦合有限元素軟體 | zh_TW |
| dc.subject | 相場法 | zh_TW |
| dc.subject | 鐵電材料 | zh_TW |
| dc.subject | 麻田散鐵 | zh_TW |
| dc.subject | martensite | en |
| dc.subject | ferroelectrics | en |
| dc.subject | phase-field models | en |
| dc.subject | COMSOL Multiphysics | en |
| dc.title | 多重耦合有限元素軟體模擬非均質鐵電材料之相場法應用 | zh_TW |
| dc.title | Phase-Field simulation of ferroelectric domains with material inhomogeneity – A finite element approach | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 101-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 周逸儒(Yi-Ju Chou),鄒年棣(Nien-Ti Tsou) | |
| dc.subject.keyword | 麻田散鐵,鐵電材料,相場法,多重耦合有限元素軟體, | zh_TW |
| dc.subject.keyword | martensite,ferroelectrics,phase-field models,COMSOL Multiphysics, | en |
| dc.relation.page | 93 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2013-08-09 | |
| dc.contributor.author-college | 工學院 | zh_TW |
| dc.contributor.author-dept | 應用力學研究所 | zh_TW |
| 顯示於系所單位： | 應用力學研究所 | |
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