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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳俊杉 | zh_TW |
| dc.contributor.advisor | Chuin-Shan Chen | en |
| dc.contributor.author | 蔣斯柏 | zh_TW |
| dc.contributor.author | Jimmy Gaspard Jean | en |
| dc.date.accessioned | 2023-10-03T16:29:28Z | - |
| dc.date.available | 2023-11-09 | - |
| dc.date.copyright | 2023-10-03 | - |
| dc.date.issued | 2023 | - |
| dc.date.submitted | 2023-07-13 | - |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/90527 | - |
| dc.description.abstract | 近年來，工業應用逐漸從鋼、鋁等傳統材料轉向纖維增強聚合物等複合材料。 人們對複合材料日益增長的興趣源自於其優於傳統材料的性能。 為了模擬這些複雜材料的行為並優化其設計，基於有限元方法 (FEM) 以及基於快速傅立葉變換 (FFT) 的多尺度模擬長期以來一直被視為重要工具。 然而成本昂貴這一缺點促使人們使用基於機器學習 (ML) 的代理模型來加速材料的多尺度建模。 其中深層材料網路（DMN）表現較為突出，因為它一方面能夠將微觀結構的表示(representation)壓縮到幾個自由度。 另一方面，它只需要在線彈性數據上進行訓練，即可用於預測複雜的非線性材料行為。 然而，DMN 受到一次只能對單個代表性體積元素 (RVE) 進行建模的限制。 一些過去的研究考慮了通過利用 RVE 的微觀描述符來減輕這種限制的各種方法。 但是，他們只解決了部分問題。 在本研究中，我們希望從根本上解決這個問題。 我們通過利用 RVE 中的全部微觀結構細節來做到這一點。 我們提出了一種混合圖神經網絡（GNN）-DMN 模型，它可以單獨處理多個微觀結構並生成它們的小規模 DMN 表示(representation)。 我們通過考慮顆粒增強複合材料的兩個 RVE 系列來證明我們的概念：circular inclusions 與 ellipse-shaped inclusions 。 研究結果表明不同微觀結構的建模皆可以在本研究提出的模型得到良好的表現。 本研究為進一步研究將具有複雜微觀結構信息泛化(generalization)的大型多尺度模型打開了大門，類似於自然語言處理領域的大型語言模型（LLM）。 | zh_TW |
| dc.description.abstract | In recent years, there has been a progressive shift in various industries from traditional materials such as steel, aluminum to composite materials like fiber-reinforced polymers. These industries range from the automotive to the construction industry. Such a growing interest in composites has stemmed from their superior performance over traditional materials. To simulate the behavior of these complex materials and optimize their design, finite-element-method (FEM)-based as well as fast Fourier transform (FFT)-based multiscale modeling have long been used as essential tools. However, they suffer the drawback of being computationally expensive. This limitation has given rise to the use of machine learning (ML)-based surrogate models to accelerate the multiscale modeling of materials. One such model that stands out is the deep material network (DMN) due to its ability, on one hand, to compress into a few degrees of freedom the representation of microstructures. On another hand, it only needs to be trained on linear elastic data and yet can be used to predict complex nonlinear material behaviors. Nevertheless, DMN suffers from the constraint of being able to model a single representative volume element (RVE) at a time. Some works have considered various approaches to alleviate this limitation by leveraging the microscopic descriptors of RVEs. But, they have addressed the issue only in part. In this work, we tackle the issue at its core. We do so by exploiting the entirety of microstructural details in RVEs. We propose a mixed graph neural network (GNN)-DMN model that can single-handedly treat multiple microstructures and generate their small-scale DMN representations. We prove our concept by considering two families of RVEs of particle-reinforced composites: those with circular inclusions and those with ellipse-shaped inclusions. The results show the possibility to unify under one network the modeling of dissimilar microstructures. Our work opens the door for further research towards the development of large multiscale models with generalization capability of microstructural information for heterogeneous material systems, akin to large language models (LLM) in the field of natural language processing. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2023-10-03T16:29:28Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2023-10-03T16:29:28Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | Acknowledgements i
摘要 iii Abstract v Contents vii List of Figures xi List of Tables xv Chapter 1 Introduction 1 1.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Research Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Structure of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Chapter 2 Literature Review 5 2.1 Multiscale Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.1 Composite Materials . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.2 The Multiscale Modeling Process . . . . . . . . . . . . . . . . . . . 7 2.1.3 Homogenization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2 Machine Learning and Multiscale Modeling . . . . . . . . . . . . . . 11 2.2.1 Feed-forward Neural Network . . . . . . . . . . . . . . . . . . . . 12 2.2.2 Recurrent Neural Network . . . . . . . . . . . . . . . . . . . . . . 12 2.2.3 Convolutional Neural Network . . . . . . . . . . . . . . . . . . . . 13 2.2.4 Graph Neural Network . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2.5 Deep Material Network . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3 Key Insights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Chapter 3 Deep Material Network 21 3.1 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.2 Building Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.3 Network Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.4 Data Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.5 Model Training . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.6 Prerequisite for Nonlinear Prediction . . . . . . . . . . . . . . . . . 31 3.6.1 The Newton-Raphson Method . . . . . . . . . . . . . . . . . . . . 31 3.6.2 Newton-Raphson applied to DMN . . . . . . . . . . . . . . . . . . 32 3.7 Nonlinear Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.7.1 Upscaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.7.2 Application of Boundary Conditions . . . . . . . . . . . . . . . . . 35 3.7.3 Downscaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.7.4 Evaluation of constitutive laws at bottom layer . . . . . . . . . . . . 36 3.7.5 Convergence Check . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.8 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.8.1 Training . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.8.2 Learned Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.8.3 Nonlinear Prediction . . . . . . . . . . . . . . . . . . . . . . . . . 40 Chapter 4 A hybrid graph neural network-deep material network model 43 4.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.2 Model Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.3 Graph-based Feature Extraction . . . . . . . . . . . . . . . . . . . . 46 4.3.1 Graph Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 4.3.2 Meshes as graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.3.3 Treatment of graph data . . . . . . . . . . . . . . . . . . . . . . . . 51 4.3.3.1 Multi Layer Perceptron . . . . . . . . . . . . . . . . . 51 4.3.3.2 Message Passing in Graph Neural Networks . . . . . . 51 4.3.3.3 Graph Features . . . . . . . . . . . . . . . . . . . . . . 53 4.4 Microstructure-informed Transformation . . . . . . . . . . . . . . . 54 4.5 Model Training . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.6 Generation of Microstructures . . . . . . . . . . . . . . . . . . . . . 58 Chapter 5 Examples 59 5.1 Example 1: Microstructures with circular inclusions . . . . . . . . . 59 5.1.1 Data Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 5.1.2 Offline Training . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 5.1.3 Online Prediction: Elastic Properties . . . . . . . . . . . . . . . . . 63 5.1.4 Online Prediction: Nonlinear Responses . . . . . . . . . . . . . . . 65 5.2 Example 2: Microstructures with elliptic inclusions . . . . . . . . . . 67 5.2.1 Data Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 5.2.2 Offline Training . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5.2.3 Online Prediction: Elastic Properties . . . . . . . . . . . . . . . . . 70 5.2.4 Online Prediction: Nonlinear Responses . . . . . . . . . . . . . . . 71 Chapter 6 Conclusions and Future Work 75 References 79 Appendix A — Derivations 87 A.1 Localization functions . . . . . . . . . . . . . . . . . . . . . . . . . 87 A.1.1 Derivation of Stress Concentration Matrix . . . . . . . . . . . . . . 87 A.1.2 Derivation of Strain Concentration Matrix . . . . . . . . . . . . . . 89 A.2 Homogenization functions . . . . . . . . . . . . . . . . . . . . . . . 91 A.2.1 Homogenized Compliance Matrix . . . . . . . . . . . . . . . . . . 91 A.2.2 Homogenized Stiffness Matrix . . . . . . . . . . . . . . . . . . . . 91 Appendix B — Algorithms 93 B.1 Nonlinear Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . 93 B.2 Microstructure Generation . . . . . . . . . . . . . . . . . . . . . . . 99 | - |
| dc.language.iso | en | - |
| dc.subject | 計算力學 | zh_TW |
| dc.subject | 多尺度建模 | zh_TW |
| dc.subject | 深層材料網絡 | zh_TW |
| dc.subject | 複合材料 | zh_TW |
| dc.subject | 圖神經網絡 | zh_TW |
| dc.subject | 基於圖的力學深度學習 | zh_TW |
| dc.subject | Graph-based mechanistic deep learning | en |
| dc.subject | Graph neural network | en |
| dc.subject | Deep material network | en |
| dc.subject | Multiscale modeling | en |
| dc.subject | Computational mechanics | en |
| dc.subject | Composite materials | en |
| dc.title | 圖增強的深層材料網絡：泛用微結構的多尺度材料模擬 | zh_TW |
| dc.title | Graph-enhanced Deep Material Network: Multiscale Materials Modeling with Microstructural Generalization | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 111-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 張書瑋;C T Wu | zh_TW |
| dc.contributor.oralexamcommittee | Shu-Wei Chang;C T Wu | en |
| dc.subject.keyword | 計算力學,多尺度建模,複合材料,圖神經網絡,深層材料網絡,基於圖的力學深度學習, | zh_TW |
| dc.subject.keyword | Computational mechanics,Multiscale modeling,Composite materials,Graph neural network,Deep material network,Graph-based mechanistic deep learning, | en |
| dc.relation.page | 100 | - |
| dc.identifier.doi | 10.6342/NTU202301463 | - |
| dc.rights.note | 同意授權(全球公開) | - |
| dc.date.accepted | 2023-07-13 | - |
| dc.contributor.author-college | 工學院 | - |
| dc.contributor.author-dept | 土木工程學系 | - |
| dc.date.embargo-lift | 2025-07-31 | - |
| 顯示於系所單位： | 土木工程學系 | |
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