以數據驅動的計算彈性固體力學及其應用

Data-Driven Computational Elastic Solid Mechanics and its Applications

蘇東垣(Tung-Huan Su)

指導教授 ： 陳俊杉

國立臺灣大學/工學院/土木工程學研究所/博士(2022年)

https://doi.org/10.6342/NTU202200014

摘要

數據驅動計算力學(data-driven computational mechanics, DDCM)顛覆傳統的計算力學架構，賦予計算力學在材料大數據時代的重大轉變。透過直接使用應力應變數據資料暨材料數據庫於計算力學架構中，材料組成律的建模需求得以緩解。承襲無材料模型的精神，數據驅動鑑定(data-driven identification, DDI)法為數據驅動計算架構提供了大量的材料數據。DDCM和DDI在許多應用中都展現出相當看好的前景，例如材料數據獲取法、使用全域應力應變測量法於材料特性分析以及以數據驅動的多尺度模擬計算方法。在本論文中，我們致力於以數據驅動無組成律模型的方法來擴展上述應用之範疇。
關於材料數據獲取法方面，我們將流形學習技術中的局部凸空間重建法融入到DDI方法中，建立了局部凸形數據驅動鑑定(Local-convexity data-driven identification, LCDDI)法。並透過線彈性、複合彈性材料與彈塑性材料的三個數值案例來驗證LCDDI方法的有效性。與DDI方法相比，LCDDI可以減少一個數量級的機械應力誤差以及減少60%以上的材料數據誤差。
在材料特性分析方面，我們首次將DDI方法應用於銅基形狀記憶合金以研究其超彈性行為。在第一個應用DDI於銅鋁錳單晶形狀記憶合金的案例，我們結合DDI方法與數位影像相關法(digital image correlation, DIC)來鑑定銅鋁錳單金形狀記憶合金的局部能量耗散特性；關於第二個應用DDI於銅鋁錳雙晶形狀記憶合金的案例，我們首次使用DIC+DDI方法探討兩個不同晶粒方向的雙晶，在循環負載次數增加下，非均勻的轉變應力場與應變場的變化；以及造成轉變應力下降即功能性疲勞的可能原因。
在多尺度模擬方面，我們呈現局部凸形數據驅動（LCDD）多尺度模擬法在準確性和效率方面的潛力。與其他的數據驅動多尺度有限元素法相比，結果顯示，LCDD多尺度法可以大幅降低準備離線數據庫的計算成本，這是因為該方法只需要相對少的材料數據點的數據庫即可達到相同的精度。
本研究展現了無組成律的計算方法在許多方面的潛力，例如高品質材料數據獲取法、全域應力應變測量法(DIC+DDI)於超彈性材料的特性分析以及高效率數據驅動多尺度模擬法。最後，在這項研究工作，我們討論並給出關於上述方面的結果總結以及未來展望

關鍵字

數據驅動計算力學 ； 數據驅動鑑定法 ； 材料數據獲取 ； 材料數據庫品質 ； 流形學習法 ； 局部凸空間數據驅動鑑定法 ； 全域非接觸式應力應變測量法 ； 數位影像相關法 ； 銅鋁錳形狀記憶合金 ； 超彈性力學行為, ； 能量消散 ； 轉變應力 ； 功能性疲勞 ； 數據驅動多尺度有限元素法

並列摘要

Data-driven computational mechanics (DDCM) revolutionizes computational mechanics framework, giving computational mechanics a major shift in the era of materials big data. By directly employing stress-strain data pairs (i.e., material database) in the framework, the need for material constitutive modeling is relaxed. Following the model-free concept, data-driven identification (DDI) can provides abundant material data for data-driven computing framework without constitutive model. Both DDCM and DDI have shown great promising perspectives in many applications, such as material data acquisition, material characterization using full-field stress and strain measurement, and data-driven multiscale simulation. In this thesis, we devoted our efforts to expand the boundaries of the applications with the data-driven model-free methods.
As for methodologies for material data acquisition, we incorporate locally convex reconstruction method, which is one of manifold learning techniques, into the DDI approach to establish the local convexity data-driven identification (LCDDI) method. The effectiveness of the LCDDI method is illustrated through three numerical examples focused on linear elastic materials, composite elastic materials and elastoplastic matrials. Compared with the DDI approach, LCDDI results in an order of magnitude reduction in error in mechanical stresses and over 60% error reduction in the material database.
Regarding material characterization, it is first time that we apply the DDI method to Cu-based shape memory alloys (SMAs) to study their superelastic behaviors. For first application of DDI to Cu-Al-Mn single crystal SMAs, we apply the DDI method combined with digital image correlation (DIC) measurement to reveal the local energy dissipation characteristics of Cu-Al-Mn single crystal SMAs. For second application of DDI to Cu-Al-Mn bicrystal SMAs, the evolution of the inhomogeneous distribution of the transformation stress and strain fields with an increasing number of cycles in two differently orientated grains is investigated for the first time using a combined technique of DIC and DDI. Possible factors that cause decrease in transformation stress, i.e., functional fatigue, are investigated and discussed.
As for multiscale simulation, we demonstrate potentials of the local convexity data-driven (LCDD) multiscale simulation in terms of accuracy and efficiency. The results show that LCDD multiscale can significantly reduce computational cost for offline database preparation because the method only requires database with relatively small density of data points to achieve same level, comparing to other data-driven multiscale finite element method (Data-driven FE2).
This thesis demonstrates the potentials of the constitutive model-free methods (i.e., DDCM and DDI) in many aspects such as high-quality material data acquisition, full-field stress and strain measurements (i.e., DIC + DDI techniques) for characterization of superelastic materials, and high-efficiency data-driven multiscale simulation. Results summary and future perspectives with respect to the above aspects are discussed and given.

並列關鍵字

Data-driven computational mechanics (DDCM) ； Data-driven identification (DDI) ； Material data acquisition ； Material database quality ； Manifold learning ； Local convexity data-driven identification (LCDDI) ； Full-field non-contact stress and strain measurements ； Digital image correlation (DIC) ； Cu-Al-Mn shape memory alloys (SMA) ； Superelasticity ； Energy dissipation ； Transformation stress ； Functional fatigue ； Data-driven multiscale finite element method (Data-driven FE2)

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