請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/98898完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 劉立偉 | zh_TW |
| dc.contributor.advisor | Li-Wei Liu | en |
| dc.contributor.author | 盂冠廷 | zh_TW |
| dc.contributor.author | Guan-Ting Yu | en |
| dc.date.accessioned | 2025-08-20T16:12:12Z | - |
| dc.date.available | 2025-08-21 | - |
| dc.date.copyright | 2025-08-20 | - |
| dc.date.issued | 2025 | - |
| dc.date.submitted | 2025-08-13 | - |
| dc.identifier.citation | [1] M. Alkhader, W. Abuzaid, M. Elyoussef, and S. Al-Adaileh. Localized strain fields in honeycomb materials with convex and concaved cells. European Journal of Mechanics - A/Solids, 80:103890, 2020.
[2] M. Alkhader and M. Vural. Mechanical response of cellular solids: Role of cellular topology and microstructural irregularity. International Journal of Engineering Science, 46(10):1035–1051, 2008. [3] P. J. Armstrong, C. O. Frederick, et al. A mathematical representation of the multiaxial Bauschinger effect, volume 731. Berkeley Nuclear Laboratories Berkeley, CA, 1966. [4] R. S. Ayyagari and M. Vural. Multiaxial yield surface of transversely isotropic foams: Part I—Modeling. Journal of the Mechanics and Physics of Solids, 74:49–67, 2015. [5] S. Balawi and J. Abot. The effect of honeycomb relative density on its effective inplane elastic moduli: An experimental study. Composite Structures, 84(4):293–299, 2008. [6] J. Banhart, H. Stanzick, L. Helfen, and T. Baumbach. Metal foam evolution studied by synchrotron radioscopy. Applied Physics Letters, 78(8):1152–1154, 2001. [7] R. Bengtsson, M. Mousavi, R. Afshar, and E. K. Gamstedt. Viscoelastic behavior of softwood based on a multiscale computational homogenization. Mechanics of Materials, 179:104586, 2023. [8] J. R. Cahoon, W. H. Broughton, and A. R. Kutzak. The determination of yield strength from hardness measurements. Metallurgical Transactions, 2(7):1979–1983, 1971. [9] B. G. Christoff, H. Brito-Santana, R. Talreja, and V. Tita. Multiscale embedded models to determine effective mechanical properties of composite materials: Asymptotic homogenization method combined to finite element method. Composites Part C: Open Access, 9:100303, 2022. [10] S. Demiray, W. Becker, and J. Hohe. Numerical determination of initial and subsequent yield surfaces of open-celled model foams. International Journal of Solids and Structures, 44(7–8):2093–2108, 2007. [11] C. O. Frederick and P. J. Armstrong. A mathematical representation of the multiaxial bauschinger effect. Materials at high temperatures, 24(1):1–26, 2007. [12] S. Gaitanaros and S. Kyriakides. On the effect of relative density on the crushing and energy absorption of open-cell foams under impact. International Journal of Impact Engineering, 82:3–13, 2015. [13] L. J. Gibson and M. F. Ashby. Cellular solids: Structure and properties. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 382(1782):25–42, 1982. [14] L. J. Gibson and M. F. Ashby. Cellular Solids: Structure and Properties. Cambridge University Press, 1997. [15] I. Guha, X. Zhang, C. S. Rajapakse, G. Chang, and P. K. Saha. Finite element analysis of trabecular bone microstructure using ct imaging and continuum mechanical modeling. Medical Physics, 49(6):3886–3899, 2022. [16] H.-K. Hong and C.-S. Liu. Internal symmetry in bilinear elastoplasticity. International Journal of Non-Linear Mechanics, 34(2):279–288, 1999. [17] H.-K. Hong and C.-S. Liu. Internal symmetry in the constitutive model of perfect elastoplasticity. International Journal of Non-Linear Mechanics, 35(3):447–466, 2000. [18] Z. Hu, K. Thiyagarajan, A. Bhusal, T. Letcher, Q. H. Fan, Q. Liu, and D. Salem. Design of ultra-lightweight and high-strength cellular structural composites inspired by biomimetics. Composites Part B: Engineering, 121:108–121, 2017. [19] R. Hutchinson and N. Fleck. The structural performance of the periodic truss. Journal of the Mechanics and Physics of Solids, 54(4):756–782, 2006. [20] A. Ingrole, A. Hao, and R. Liang. Design and modeling of auxetic and hybrid honeycomb structures for in-plane property enhancement. Materials & Design, 117:72–83, 2017. [21] M. Khan, T. Baig, and S. Mirza. Experimental investigation of in-plane and out-ofplane crushing of aluminum honeycomb. Materials Science and Engineering: A, 539:135–142, 2012. [22] R. Lakes. Foam structures with a negative poisson＇s ratio. Science, 235(4792):1038–1040, 1987. [23] X. Li, Z. Lu, Z. Yang, Q. Wang, and Y. Zhang. Yield surfaces of periodic honeycombs with tunable poisson＇s ratio. International Journal of Mechanical Sciences, 141:290–302, 2018. [24] C.-S. Liu, L.-W. Liu, and H.-K. Hong. A scheme of automatic stress-updating on yield surfaces for a class of elastoplastic models. International Journal of NonLinear Mechanics, 85:6–22, 2016. [25] L.-W. Liu, P.-H. Chen, and G.-T. Yu. Return-free integrations for mixed control of stress and strain states. prepared. [26] L.-W. Liu, Z.-C. Ciou, and P.-H. Chen. A return-free integration for anisotropichardening elastoplastic models. Computers & Structures, 301:107423, 2024. [27] L.-W. Liu, C.-Y. Yang, and H.-G. Chen. Finite element analysis on yield surface evolution of cellular materials. International Journal of Mechanical Sciences, 246:108123, 2023. [28] S. Malek and L. Gibson. Effective elastic properties of periodic hexagonal honeycombs. Mechanics of Materials, 91:226–240, 2015. [29] L. R. Meza, G. P. Phlipot, C. M. Portela, A. Maggi, L. C. Montemayor, A. Comella, D. M. Kochmann, and J. R. Greer. Reexamining the mechanical property space of three-dimensional lattice architectures. Acta Materialia, 140:424–432, 2017. [30] H. Qing and L. Mishnaevsky. Moisture-related mechanical properties of softwood: 3d micromechanical modeling. Computational Materials Science, 46(2):310–320, 2009. [31] D. Sharma and S. S. Hiremath. In-plane and out-plane flexural properties of the bird feather-inspired panels: Experimental, digital image correlation, and finite element study. Aerospace Science and Technology, 127:107731, 2022. [32] S.-J. Sung, L.-W. Liu, H.-K. Hong, and H.-C. Wu. Evolution of yield surface in the 2d and 3d stress spaces. International Journal of Solids and Structures, 48(6):1054–1069, 2011. [33] B. van Rietbergen, G. von Ingersleben, C. Chesnut, B. MacDonald, H. K. Genant, D. C. Newitt, S. Majumdar, S. T. Harris, and P. Garnero. In vivo assessment of architecture and micro-finite element analysis derived indices of mechanical properties of trabecular bone in the radius. Osteoporosis International, 13(1):6–17, 2002. [34] S. P. Väänänen, L. Grassi, M. S. Venäläinen, H. Matikka, Y. Zheng, J. S. Jurvelin, and H. Isaksson. Automated segmentation of cortical and trabecular bone to generate finite element models for femoral bone mechanics. Medical Engineering & Physics, 70:19–28, 2019. [35] A.-J. Wang and D. L. McDowell. In-plane stiffness and yield strength of periodic metal honeycombs. Journal of Engineering Materials and Technology, 126(2):137–156, 2004. [36] S. Wang, C. Deng, O. Ojo, B. Akinrinlola, J. Kozub, and N. Wu. Design and modeling of a novel three dimensional auxetic reentrant honeycomb structure for energy absorption. Composite Structures, 280:114882, 2022. [37] B. Wonsiewicz and R. Hart. Finite strain and the 0.01 percent offset yield strength. Journal of Testing and Evaluation, 1(5):412–415, 1973. [38] H. C. Wu and W. C. Yeh. On the experimental determination of yield surfaces and some results of annealed 304 stainless steel. International Journal of Plasticity, 7(8):803–826, 1991. [39] L. Yue, H. Liu, Z. Cheng, Q. Kan, and G. Kang. Yield surface of multidirectional gradient lattices with octet architectures. International Journal of Plasticity, 182:104140, 2024. [40] H. Zhong, T. Song, C. Li, R. Das, J. Gu, and M. Qian. The gibson-ashby model for additively manufactured metal lattice materials: Its theoretical basis, limitations and new insights from remedies. Current Opinion in Solid State and Materials Science, 27(3):101081, 2023. [41] H. Zhu and C. Chen. Combined effects of relative density and material distribution on the mechanical properties of metallic honeycombs. Mechanics of Materials, 43(5):276–286, 2011. | - |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/98898 | - |
| dc.description.abstract | 本研究針對蜂巢狀複合材料在多軸載重條件下之降伏面演化行為進行有限元素模擬與量化分析，系統探討不同幾何設計參數對降伏面形貌之影響。模擬架構採用一套具材料異向性、拉壓不對稱及非線性異向性硬化行為之彈塑性組成模型，並搭配前人為處理混合控制問題所建立之免映射數值積分方法，以使用者材料副程式（UMAT）形式實作於商用有限元素分析軟體 ABAQUS 中。為確認該模組之數值正確性與穩定性，本研究設計五種複雜載重歷程進行單元素模擬，並與理論解析解比較，同時進行網格收斂分析與時間增量敏感性測試，並參考前人對邊界效應與尺寸影響之討論，補充本研究模型所需之前處理驗證工作。降伏面分析方面，採用等效塑性應變增量作為降伏點判定準則，結合探測與預加載路徑設計，針對兩類幾何變化條件──剛性基材體積佔比與單元格構型──進行降伏面演化分析，並引入面積比、長寬比與包辛格效應等三項量化指標，對不同條件下之降伏面幾何變化與方向性行為進行比較。模擬結果證實所建構之 UMAT 模組具備高度準確性與穩定性，等效塑性應變增量準則亦能有效捕捉接續降伏點與硬化行為；整體而言，本研究建立一套可應用於蜂巢狀複合材料降伏面分析之模擬流程，對未來仿生結構與功能性複合材料之塑性行為預測具有實用潛力。 | zh_TW |
| dc.description.abstract | This study conducts finite element simulations and quantitative analysis to investigate the yield surface evolution of cellular composites under multiaxial loading, focusing on the influence of geometric design parameters on the shape and behavior of yield surfaces. The simulation framework adopts an elastoplastic constitutive model incorporating material anisotropy, tension–compression asymmetry, and nonlinear anisotropic hardening, combined with a previously developed return-free numerical integration method for mixed control problems. The model is implemented into the commercial finite element software ABAQUS via a user-defined material subroutine (UMAT). To verify the numerical stability and accuracy of the implementation, five representative complex loading paths are simulated using a single-element model and compared against analytical solutions. Mesh convergence analysis, time increment sensitivity tests, and preprocessing validations—such as boundary and size effects—are also conducted to ensure model reliability. Yield surfaces are evaluated using the equivalent plastic strain increment (EPSI) criterion, combined with a series of probing and pre-loading paths. Two geometric design variations—the volume fraction of the stiff matrix and the unit cell configuration (hexagonal vs. auxetic)—are analyzed in relation to the evolution of yield surfaces. Additionally, three quantitative indicators—area ratio, aspect ratio, and the Bauschinger effect—are introduced to compare directional behavior and geometric changes of the yield surfaces under different conditions. Simulation results confirm the high accuracy and stability of the implemented UMAT model and demonstrate the effectiveness of the EPSI criterion in capturing successive yield points and hardening evolution. Overall, this study establishes a simulation framework for yield surface analysis of cellular composites, offering practical potential for future applications in bio-inspired structures and functional composite materials. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2025-08-20T16:12:12Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2025-08-20T16:12:12Z (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 Notations and Conventions xvii Chapter 1 Introduction 1 1.1 Mechanical behavior of cellular materials . . . . . . . . . . . . . . . 1 1.1.1 Influence of relative density . . . . . . . . . . . . . . . . . . . . . 2 1.1.2 Auxetic cellular materials . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Yield point determination . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Finite element modeling of cellular structures . . . . . . . . . . . . . 5 1.4 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Chapter 2 Elastoplastic model and return-free integration for UMAT 9 2.1 Anisotropic elastoplastic model with A–F hardening . . . . . . . . . 9 2.1.1 Flow rule and yield function for strain-controlled loading . . . . . . 10 2.1.2 Mixed-control formulation of stress–strain states . . . . . . . . . . . 12 2.1.3 Armstrong–Frederick hardening model under mixed control . . . . 14 2.2 Return-free integration method . . . . . . . . . . . . . . . . . . . . 17 2.2.1 Concept of internal symmetry . . . . . . . . . . . . . . . . . . . . . 17 2.2.2 Lie-group based evolution of internal variables . . . . . . . . . . . 18 2.2.3 Pull-back operation and numerical framework . . . . . . . . . . . . 19 2.3 UMAT implementation of the return-free method . . . . . . . . . . . 20 2.3.1 Derivation of consistent tangent modulus . . . . . . . . . . . . . . 21 2.3.2 Flow chart of user-defined material (UMAT) . . . . . . . . . . . . . 22 2.4 Model verification under benchmark cases . . . . . . . . . . . . . . 23 Chapter 3 Finite element models of cellular composites and yield surface detection method 31 3.1 Geometry of the cellular composites . . . . . . . . . . . . . . . . . . 31 3.1.1 Choice of structural configuration . . . . . . . . . . . . . . . . . . 32 3.1.2 Definition of unit cell geometry . . . . . . . . . . . . . . . . . . . . 34 3.1.3 Boundary condition . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.1.4 Setup of parametric variations . . . . . . . . . . . . . . . . . . . . 37 3.2 Finite element discretization . . . . . . . . . . . . . . . . . . . . . . 39 3.2.1 Size effect analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.2.2 Boundary effect reduction . . . . . . . . . . . . . . . . . . . . . . . 41 3.2.3 Convergence analysis of mesh generation . . . . . . . . . . . . . . 42 3.2.4 Increment analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.3 Computational detection of yield surfaces . . . . . . . . . . . . . . . 46 3.3.1 Yield point determination . . . . . . . . . . . . . . . . . . . . . . . 46 3.3.2 Design of probing and preloading paths . . . . . . . . . . . . . . . 47 3.4 Summary of material parameters and geometrical configuration . . . 49 Chapter 4 Yield surface evolution of cellular composites 53 4.1 Influence of volume fraction on yield surface evolution . . . . . . . . 53 4.1.1 Yield surface evolution of ϕ = 6.9% honeycomb composites . . . 54 4.1.2 Yield surface evolution of ϕ = 21.4% honeycomb composites . . 56 4.1.3 Yield surface evolution of ϕ = 32.6% honeycomb composites . . 57 4.1.4 Yield surface evolution of ϕ = 40% honeycomb composites . . . . 59 4.1.5 Comparisons of yield surfaces for cellular composite with different volume fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 4.1.6 Yield surface comparison between cellular materials and composites 70 4.1.7 Yield surfaces of cellular composite by different yield point determinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 4.2 Influence of inclined angle of cell wall . . . . . . . . . . . . . . . . . 76 4.2.1 Yield surface evolution of auxetic cellular composites . . . . . . . . 77 4.2.2 Yield surface comparison between hexagonal and auxetic cellular composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.2.3 Yield surface comparison between auxetic cellular materials and composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.2.4 Yield surfaces of auxetic cellular composite by different yield point determinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 Chapter 5 Conclusions and future works 87 5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.2 Future works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 References 91 Appendix A — Matrix formulation 97 | - |
| dc.language.iso | en | - |
| dc.subject | 混合控制 | zh_TW |
| dc.subject | 包辛格效應 | zh_TW |
| dc.subject | UMAT | zh_TW |
| dc.subject | 降伏面演化 | zh_TW |
| dc.subject | 孔隙複合材料 | zh_TW |
| dc.subject | 免映射數值積分法 | zh_TW |
| dc.subject | Return-free integration | en |
| dc.subject | Yield surface evolution | en |
| dc.subject | Cellular composites | en |
| dc.subject | Mixed control | en |
| dc.subject | UMAT | en |
| dc.subject | Bauschinger effect | en |
| dc.title | 有限元素模擬結合免映射積分法探討蜂巢狀複合材料之降伏面演化 | zh_TW |
| dc.title | Finite element simulation on yield surface evolution of cellular composites using return-free integration | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 113-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 黃仲偉;洪宏基;林哲宇 | zh_TW |
| dc.contributor.oralexamcommittee | Chang-Wei Huang;Hong-Ki Hong;Che-Yu Lin | en |
| dc.subject.keyword | 免映射數值積分法,混合控制,孔隙複合材料,降伏面演化,UMAT,包辛格效應, | zh_TW |
| dc.subject.keyword | Return-free integration,Mixed control,Cellular composites,Yield surface evolution,UMAT,Bauschinger effect, | en |
| dc.relation.page | 98 | - |
| dc.identifier.doi | 10.6342/NTU202504164 | - |
| dc.rights.note | 同意授權(全球公開) | - |
| dc.date.accepted | 2025-08-15 | - |
| dc.contributor.author-college | 工學院 | - |
| dc.contributor.author-dept | 土木工程學系 | - |
| dc.date.embargo-lift | 2025-08-21 | - |
| 顯示於系所單位： | 土木工程學系 | |
文件中的檔案：
| 檔案 | 大小 | 格式 | |
|---|---|---|---|
| ntu-113-2.pdf | 24.01 MB | Adobe PDF | 檢視/開啟 |
系統中的文件，除了特別指名其著作權條款之外，均受到著作權保護，並且保留所有的權利。