臺灣博碩士論文加值系統

本研究提出之三維等效單軸應變組成模型，目的是用來模擬材料多軸非線性行為，並引用Darwin和Pecknold所提出之等效單軸應變概念分離材料多軸受力之柏松效應；本模型數值計算過程中皆以全量應變形式而非傳統塑性力學分為彈性應變與塑性應變兩部分，且將材料多軸行為以單軸實驗結果預測，跳脫傳統塑性力學繁瑣之數學推導。除此之外，本研究將此組成模型應用範圍由混凝土材料延伸至岩石材料以及金屬材料，進一步驗證本研究理論之正確性以及廣義性。
本研究於混凝土及岩石材料中，提出軟化模型(Softening model)與動態帽蓋模型(Kinematic cap model)之理論，解決了先前Darwin 和 Pecknold與Elwi和Murray模型中軟化段下降過快，以及無法探討應力路徑有變動之問題。而金屬材料中以硬化模型(Hardening model)之理論，定義出金屬材料通過降伏點後塑性硬化之程度，且將此金屬硬化模型結合循環加卸載(Cyclic loading)，可模擬塑性力學中定義之動態硬化(Kinematic hardening)、等向硬化(Isotropic hardening)以及獨立硬化(Independent hardening)等現象，且包辛格效應(Bauschinger effect)將透過硬化模型於硬化過程中是否有形變產生來定義。
本研究以不同時刻下之應力狀態於材料破壞模型上定義當前時刻之極限強度參數(Ultimate strength parameters)，藉由此極限強度參數調整單軸應力-應變模型來預測多軸情況下真實之材料參數如：材料勁度模數(Stiffness modulus)與泊松比(Poisson’s ratio)。本研究所開發之模型維持一貫之數值計算流程，只需修改對應之材料破壞模型以及描述材料單軸行為之單軸應力-應變模型即可，混凝土材料使用Menetrey和Willam所提出之三參數破壞準則、岩石材料使用Drucker-Prager破壞準則、金屬材料則使用von-Mises破壞準則。

This research presents a three-dimensional constitutive model of material based on the concept of equivalent uniaxial strain in order to decouple Poisson’s effect in multiaxial loading condition. The equivalent uniaxial strain is a fictitious material index which is invented to compute the parameters such as material stiffness modulus and Poisson’s ratio. The characteristics of uniaxial stress-strain model which defined by the ultimate strength parameters are obtain from material failure surface and the ultimate strength parameters varies with current stress or strain state.
This research contains not only concrete material but also rock material and metal material, exerted by monotonic loading, proportional loading non-proportional loading and cyclic loading. A hypothesis of kinematic cap model is proposed to reflect the influence of the non-proportional loading path. Further, a hypothesis of softening model is applied on concrete and rock material not only to simulate post-peak branch behavior but to reflect the transition between brittle softening and ductile softening under different confining pressure.
In concrete material established closed Menetrey-Willam (CMW) failure model which combined with Menetrey-Willam meridian and the cap model in concrete material and replaced Menetrey-Willam meridian with Drucker-Prager criterion in rock material. Saenz stress-strain model is applied and adjusted by the ultimate strength parameters from material failure model to reflect the latest stress or strain condition in both concrete and rock material. von-Mises criterion is applied to build material failure model for metal material as well. Correlation studies with available experimental tests are presented to valid the performance of proposed three d constitutive of materials.

第一章、前言 1
1.1 研究動機與目的 1
1.2 文獻回顧 2
1.3 研究方法與內容 3
第二章、三維等效單軸應變與應力組成模型 4
2.1 三維增量組成關係 4
2.2 等效單軸應變 5
2.3 單軸應力-應變關係模型 7
2.4 材料破壞準則 9
2.4.1 Haigh-Westergaard坐標系統 10
2.4.2 極限強度參數定義 14
2.5 動態材料破壞模型 16
2.5.1 軟化模型與硬化模型 18
2.5.2 動態帽蓋模型 24
第三章、普通強度混凝土三維等效單軸應變模型 29
3.1 普通強度混凝土材料單軸應力-應變關係 29
3.2 普通強度混凝土三參數破壞準則 31
3.3 普通強度混凝土破壞模型修正 35
第四章、高強度混凝土三維等效單軸應變模型 51
4.1 高強度混凝土單軸應力-應變關係 53
4.2 高強度混凝土三參數破壞準則 55
4.3 高強度混凝土破壞模型修正 58
4.4 高強度混凝土軟化模型理論 76
4.5 高強度混凝土動態帽蓋模型理論 83
第五章、岩石材料三維等效單軸應變模型 94
5.1 岩石材料單軸應力-應變關係模型 96
5.2 岩石材料Drucker-Prager 破壞準則 98
5.3 岩石材料破壞模型修正： 100
5.4 岩石材料動態帽蓋模型理論： 117
5.5 岩石材料非等向性假設 123
5.6 岩石材料帽蓋模型斜率之修正 127
第六章、金屬材料三維等效單軸應變模型 136
6.1 金屬材料 von-Mises 破壞準則 137
6.2 金屬材料單軸應力-應變模型 140
6.3 金屬材料極限強度參數定義修正 141
6.4 金屬材料硬化模型理論 143
第七章、數值算例與實驗比對 149
7.1 普通強度混凝土雙軸等比例加載 149
7.2 普通強度混凝土三軸等比例加載 152
7.3 高強度混凝土三軸不等比例加載 154
7.4 岩石三軸不等比例加載 161
7.5 鋁合金雙軸拉力實驗 169
7.6 鋼材雙軸拉力實驗 173
7.7 金屬三軸加卸載 175
結論與建議 182
參考文獻 184

〔1〕 Lekhnitskii, SG. In: Brandstatter JJ, editor. Theory of elasticity of an anisotropic elastic body. San Francisco, CA: Holden-Day.
〔2〕 Saenz, IP. Discussion of ‘equation for the stress–strain curve of concrete, by P. Desay and S. Krishan’. (1964). ACI Journal, 61(9):1229–35.
〔3〕 Kupfer, HB. Hilsdorf HK. Ru¨sch H. (1969). Behavior of concrete under biaxial stresses. ACI Journal, 66(8):656–66.
〔4〕 William, K.J. Warnke, E.P. (1974).Constitutive model for the triaxial behavior of concrete. International Association for Bridges and Structural Engineering, Bergamo, Italy.
〔5〕 Darwin, David. David A. Pecknold, ASCE. (1976). Analysis of RC Shear Panels Under Cyclic Loading. Journal of the Structural Division, 1976, Vol. 102, Issue 2, Pg. 355-369.
〔6〕 Linse, D. H. Aschl. (1976). Versuche zum Verhalten von Beton unter mehrachsiger Beanspruchung. In München durchgeführtes Teilprojekt eines internationalen Vergleichsprogrammes. Versuchsbericht, Lehrstuhl für Massivbau, Technische Universität München.
〔7〕 Elwi, Alaa A. David W. Murray. (1979). A 3D Hypoelastic Concrete Constitutive Relationship. Journal of the Engineering Mechanics Division, Vol. 105, Issue 4, Pg. 623-641
〔8〕 Bazant, Zdenek P. Tatsuya Tsubaki. (1980). Total Strain Theory and Path-Dependence of Concrete. Journal of the Engineer Mechanics Division, pp. 1151-1173
〔9〕 Klisinski, M. (1985). Degradation and Plastic Deformation of Concrete. IFTR Report 38, Ph.D. thesis, Polish Academy of Sciences.
〔10〕 Chen, W. F. Han, D. J. (1988). Plasticity for Structural Engineers, Springer-Verlag, New York, N.Y.
〔11〕 Kolymbas, D. (1991). An outline of hypo-plasticity. Archive of Applied Mechanics, Volume 61, Issue 3, pp 143–151.
〔12〕 Labbane, Mondher. Nripendra K. Saha. Edward C. Ting. (1993). Yield criterion and loading function for concrete plasticity. International Journal of Solids and Structures, Volume 30, Issue 9, Pages 1269-1288.
〔13〕 Menetrey, P. K. J. Willam. (1995). Triaxial Failure Criterion for Concrete and Its Generalization. ACI Structural Journal, Title no. 92-S30.
〔14〕 Imran, I. S. J. Pantazopoulou. (1996). Experimental Study of Plain Concrete under Triaxial Stress. ACI Materials Journal, no. 93-M67 pp.589-601.
〔15〕 Wu, Wei. Erich Bauerb, Dimitiros Kolymbas. (1996). Hypoplastic constitutive model with critical state for granular materials. Mechanics of Materials, 23 pp. 45-69.
〔16〕 Balan, Toader A. Filip C. Filippou. Egor P. Popov. (1997). Constitutive Model for 3D Cyclic Analysis of Concrete Structures. Journal of Engineering Mechanics, Volume 123 Issue 2.
〔17〕 Pivonka, P. R Lackner, H Mang. (2000). Numerical analyses of concrete subjected to triaxial compressive loading. European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000 Barcelona, 11-14.
〔18〕 Balan, Toader A. Enrico Spacone. Minho Kwon. (2001). A 3D hypoplastic model for cyclic analysis of concrete structures. Engineering Structures, 23 333–342.
〔19〕 Grassl, Peter, Karin Lundgren. Kent Gylltoft. (2002). Concrete in Compression: a plasticity theory with a novel hardening law. International Journal of Solids and Structures, 39,5205–5223.
〔20〕 Malecot, Yann. Laurent Daudeville. Fabrice Dupray. Cédric Poinard, Eric Buzaud. (2002). Strength and damage of concrete under high triaxial loading. European Journal of Environmental and Civil Engineering, Volume 14, 2010 - Issue 6-7 Pages 777-803.
〔21〕 Niels, Saabye Ottosen. Matti Ristinmaa. (2005). The Mechanics of Constitutive Modeling. ELSEVIER, San Diego, CA. ISBN: 0-008-044606-X.
〔22〕 Lu, Xiaobin. (2005). Uniaxial and Triaxial Behavior of High Strength Concrete With and Without Steel Fibers, Doctorate Dissertation, Faculty of New Jersey Institute of Technology.
〔23〕 Andrea, Mordini. (2006). Three-Dimensional Numerical Modeling of Reinforced Concrete Behavior. Doctorate Dissertation, University of Parma, Faculty of Engineering.
〔24〕 Papanikolaou, Vassilis K. Andreas J. Kappo. (2007). Confinement-sensitive plasticity constitutive model for concrete in triaxial compression. International Journal of Solids and Structures, 44 (2007) 7021–7048.
〔25〕 Li, Tianbai. Roger Crouch. (2010). A C2 plasticity model for structural concrete. Computers and Structures, 88 (2010) 1322–1332.
〔26〕 Dede, Tayfun. Yusuf Ayvaz. (2010). Plasticity models for concrete material based on different criteria including Bresler–Pister. Materials and Design, 31 (2010) 278–286.
〔27〕 Pisano, A. A. P. Fuschi, D. De Domenico. (2013). A kinematic approach for peak load evaluation of concrete element. Computers 和 Structures, Volume 119, 1 April 2013, Pages 125–139.
〔28〕 Pisano, A.A. P. Fuschi, D. De Domenico. (2013). Peak loads and failure modes of steel-reinforced concrete beams: Predictions by limit analysis. Engineering Structures, 56 (2013) 477–488.
〔29〕 Lu, Xilin. Jingjing Wang. Fuwen Zhang. (2013). Seismic collapse simulation of spatial RC frame structures. Computers and Structures, 119 (2013) 140–154.
〔30〕 張鈴菀(98)。向量式有限元分析法於鋼筋混凝土結構非線性行為之應用。碩士論文，國立中央大學土木工程學系研究所。
〔31〕 賴昱儒(103)。混凝土結構分析之三維等效單軸組成材料模型。碩士論文，國立中央大學土木工程學系研究所。
〔32〕 李尚達(105)。混凝土之三維等效單軸應變材料組成模型。碩士論文，國立中央大學土木工程學系研究所。
〔33〕 Coox, N. G. W. K. Hodgson. (1965). Some Detailed Stress-Strain Curves for Rock. Journal of Geophysical Research, VOL. 70, NO. 12.
〔34〕 Mogi, Kiyoo. (1967). Effect of the Intermediate Principal Stress on Rock Failure. Journal of Geophysical Research, Volume 72, Issue 20, Pages 5117–5131.
〔35〕 Wawersik, WR. C Fairhurst. (1970). A study of brittle rock fracture in laboratory compression experiments. International Journal of Rock Mechanics and Mining Sciences 和 Geomechanics Abstracts, Volume 7, Issue 5, Pages 561-564, IN7-IN14, 565-575.
〔36〕 Sandler, IS. FL DiMaggio. GY Baladi. (1974). A generalized cap model for geological materials. National Technical Information Service.
〔37〕 Resende, Luis. John B. Martin. (1985) .Formulation of Drucker‐Prager Cap Model. Journal of Engineering Mechanics, Volume 111 Issue 7.
〔38〕 Tsai, L. C. Jeng, F. S. Lin, M. L. (2001). Different Stress Path on the Mechanical Behavior of Mushan Sandstone. Proceedings of 9th Conference on Current Researches in Geotechnical Engineering, Shihman Reservoir, B033.
〔39〕 Evert, Hoek. Carlos Carranza-Torres. Brent Corkum. (2002). Hoek-Brown Failure Criterion -2002 edition. Proceedings of the fifth North American rock mechanics symposium, Toronto, Canada, vol. 1, 2002. p. 267–73.
〔40〕 Hajiabdolmajida, V. P.K. Kaisera. C.D. Martin. (2002). Modeling brittle failure of rock. International Journal of Rock Mechanics 和 Mining Sciences, 39.
〔41〕 HASHIBA, Kimihiro. Xiujun GAO. Seisuke OKUBO. Katsunori FUKUI. (2004). Observation of The Tri-Axial Compressive Creep of Tage Tuff Placed Within a Transparent Vessel. The Mining and Materials Processing Institute of Japan, Vol.120 p. 190 ― 196.
〔42〕 Ivan, S. Sandler. (2005). Review of the development of Cap Models for geomaterials. Shock and Vibration, 12, 67–71.
〔43〕 Deng, Chujian. He, Guojie. Zheng, Yingren. (2006). Studies on Drucker-Prager yield criterions based on M-C yield criterion and application in geotechnical engineering. Chinese Journal of Geotechnical Engineering, Vol. 28, No.6.
〔44〕 Han, L.H.. J.A. Elliott. A.C. Bentham . A. Mills . G.E. Amidon. B.C. Hancock. (2007) A modified Drucker-Prager Cap model for die compaction simulation of pharmaceutical powders. International Journal of Solids and Structures, 45, 3088–3106.
〔45〕 HASHIBA, Kimihiro. Xiujun GAO. Seisuke OKUBO. Katsunori FUKUI. (2007). Triaxial-Compression Testing Method Developed for Small Rock Specimens. Journal of the Society of Materials Science, Japan, Vol. 56, No. 9, pp. 790-795.
〔46〕 You, Mingqing. (2009). True-triaxial strength criteria for rock. International Journal of Rock Mechanics 和 Mining Sciences, 46, 115– 127.
〔47〕 Kwa´sniewski, M. M. Takahashi. (2010). Strain-based failure criteria for rocks: State of the art and recent advances. Rock Mechanics in Civil and Environmental Engineering, ISRM International Symposium - EUROCK 2010, 15-18 June, Lausanne, Switzerland.
〔48〕 Hua, Jiang. Xie, Yongli. (2010). A note on the Mohr–Coulomb and Drucker–Prager strength criteria. Mechanics Research Communications, 38, 309–314.
〔49〕 Zhang, Baosheng. Mukesh Jain. Chenghao Zhao,. Michael Bruhis. Roger Lawcock. Kevin Ly. (2010). Experimental calibration of density-dependent modified Drucker-Prager/Cap model using an instrumented cubic die for powder compact. Powder Technology, 204, 27–41.
〔50〕 Leandro, R. Alejano. Antonio Bobet. (2012). Drucker–Prager Criterion. Rock mechanics and rock engineering, Volume 45, Issue 6, pp 995–999.
〔51〕 Joseph, F. Labuz. Arno Zang. (2012). Mohr–Coulomb Failure Criterion. Rock Mech Rock Eng, 45:975–979.
〔52〕 翁孟嘉(91)。麓山帶砂岩之力學特性及其與微組構關係研究。博士論文，國立台灣大學土木工程學研究所。
〔53〕 Ramberg, W. Osgood WR. (1943). Description of stress-strain curves by three parameters. NASA Scientific and Technical Information Facility, Technical note No. 902.
〔54〕 Brown, MW. KJ. Miller. (1978). Biaxial Cyclic Deformation Behavior of Steels. Fatigue of Engineering Materials and Structures, Vol. 1, pp. 93-106.
〔55〕 Karafillis, A.P. M.C. Boyce. (1993). A general anisotropic yield criterion using bounds and a transformation weighting tensor. Journal of the Mechanics and Physics of Solids, Volume 41, Issue 12, Pages 1859-1886.
〔56〕 Hopperstad, OS. M Langseth. S Remseth. (1995). Cyclic stress-strain behavior of alloy AA6060 T4, part II: Biaxial experiments and modeling. International Journal of Plasticity, Vol. 11, No. 6, pp. 741-762.
〔57〕 Meijer, G. Z. Xia. F. Ellyin. (1996). Biaxial Cyclic Analysis of A1203p-6061 Al Composite. Acta Materialia, Volume 45, Issue 8, August 1997, Pages 3237-3249.
〔58〕 Kuwabara, Toshihiko. Satoshi Ikeda,. Kensuke Kuroda.(1998). Measurement and analysis of differential work hardening in cold-rolled steel sheet under biaxial tension. Journal of Materials Processing Technology, 80 – 81, 517 – 523.
〔59〕 Calloch, Sylvain. Didier Marquis. (1998). Triaxial tension-compression tests for multiaxial cyclic plasticity. International Journal of Plasticity, 15 (1999) pp. 521-549.
〔60〕 Bochera, L. P. Delobellea. P. Robineta. X. Feaugas. (2000). Mechanical and microstructural investigations of an austenitic stainless steel under non-proportional loadings in tension–torsion-internal and external pressure. International Journal of Plasticity, 17, 1491–1530.
〔61〕 Yoshida, Fusahito. Takeshi Uemori. (2001). A model of large-strain cyclic plasticity describing the Bauschinger effect and work hardening stagnation. International Journal of Plasticity, 18, 661–686.
〔62〕 Yoshida, Fusahito. Takeshi Uemori. Kenji Fujiwara. (2001). Elastic–plastic behavior of steel under in-plane cyclic tension–compression at large strain. International Journal of Plasticity, 18, 633–659.
〔63〕 McNaney, J.M. V. Imbeni. Y. Jung. Panayiotis Papadopoulos. R.O. Ritchie. (2002). An experimental study of the superelastic effect in a shape-memory Nitinol alloy under biaxial loading. Mechanics of Materials, 35 969–986.
〔64〕 Yoshida, Fusahito. Takeshi Uemori. (2003). A model of large-strain cyclic plasticity and its application to spring back simulation. International Journal of Mechanical Sciences, 45, 1687 – 1702.
〔65〕 Kim, J.R. Rasmussen. (2003). Full-range stress–strain curves for stainless steel alloys. Journal of Constructional Steel Research, 59, 47–61.
〔66〕 Green, D.E. K.W. Neale. S.R. MacEwen. A. Makinde. R.Perrin. (2004). Experiment investigation of the biaxial behavior of an aluminum sheet. International Journal of Plasticity, 20 (2004) 1677–1706.
〔67〕 Mohr, Dirk. Johan Jacquemin. (2008). Large deformation of anisotropic austenitic stainless steel sheets at room temperature: Multi-axial experiments and phenomenological modeling. Journal of the Mechanics and Physics of Solids, 56, 2935–2956.
〔68〕 Mohr, Dirk. Matthieu Dunand. Keun-Hwan Kim. (2010). Evaluation of associated and non-associated quadratic plasticity models for advanced high strength steel sheets under multi-axial loading. International Journal of Plasticity, 26, 939–956.
〔69〕 Sung, Shin-Jang. Li-Wei Liu. Hong-Ki Hong. Han-Chin Wu.(2011). Evolution of yield surface in the 2D and 3D stress spaces. International Journal of Solids and Structures, 48, 1054–1069.