(1) 牧正志, 田村今男, “動的再結晶の組織的特徴および静的再結晶との比較”, 鉄と鋼, Vol. 70, No. 15 (1984), pp. 2073–2080.
(2) Valiev, R.Z., Krasilnikov, N.A. and Tsenev, N.K., “Plastic deformation of alloys with submicron- grained structure”, Materials Science and Engineering: A, Vol. 137, (1991), pp. 35 – 40.
(3) Valiev, R.Z., “Structure and mechanical properties of ultrafine-grained metals”, Materials Science and Engineering: A, Vol. 234-236, (1997), pp. 59 – 66.
(4) Gleiter, H., “Nanostructured materials”, Advanced Materials, Vol. 4, (1992), pp. 474 – 481.
(5) Gleiter, H., “Nanostructured materials: basic concepts and microstructure”, Acta Materialia, Vol. 48, No. 1 (2000), pp. 1 – 29.
(6) Zehtbauer, M.J. and Zhu, Y.T., Bulk Nanostructured Materials, (2009), Wiley-VCH.
(7) Tsuji, N., Ogata, S., Inui, H., Tanaka, I., Kishida, K., Gao, S., Mao, W., Bai, Y., Zheng, R. and Du, J.P., “Strategy for managing both high strength and large ductility in structural materials – sequential nucleation of different deformation modes based on a concept of plaston”, Scripta Materialia, Vol. 181, (2020), pp. 35 – 42.
(8) Humphreys, F.J., “Modelling microstructural evolution during annealing”, Modelling and Simula- tion in Materials Science and Engineering, Vol. 8, No. 6 (2000), pp. 893–910.
(9) 高木節雄, 津崎兼彰, 材料組織学, (2000), 朝倉書店.
(10) Luton, M.J. and Sellars, C.M., “Dynamic recrystallization in nickel and nickel-iron alloys during high temperature deformation”, Acta Metallurgica, Vol. 17, No. 8 (1969), pp. 1033 – 1043.
(11) Humphreys, F.J., Rohrer, G.S. and Rollett, A., Recrystallization and Related Annealing Phenomena, third edition, (2017), Elsevier.
(12) Doherty, R.D., Hughes, D.A., Humphreys, F.J., Jonas, J.J., Juul Jensen, D., Kassner, M.E., King, W.E., McNelley, T.R., McQueen, H.J. and Rollett, A.D., “Current issues in recrystallization: a review”, Materials Science and Engineering: A, Vol. 238, No. 2 (1997), pp. 219 – 274.
(13) Li, J.C.M., “Possibility of subgrain rotation during recrystallization”, Journal of Applied Physics, Vol. 33, No. 10 (1962), pp. 2958–2965.
(14) Segal, V.M., “Materials processing by simple shear”, Materials Science and Engineering: A, Vol. 197, No. 2 (1995), pp. 157 – 164.
(15) Horita, Z., Smith, D.J., Furukawa, M., Nemoto, M., Valiev, R.Z. and Langdon, T.G., “An investiga- tion of grain boundaries in submicrometer-grained Al-Mg solid solution alloys using high-resolution electron microscopy”, Journal of Materials Research, Vol. 11, (1996), pp. 1880–1890.
(16) Saito, Y., Tsuji, N., Utsunomiya, H., Sakai, T. and Hong, R.G., “Ultra-fine grained bulk aluminum produced by accumulative roll-bonding (ARB) process”, Scripta Materialia, Vol. 39, No. 9 (1998), pp. 1221 – 1227.
(17) Tsuji, N., Kamikawa, N., Ueji, R., Takata, N., Koyama, H., and Terada, D., “Managing Both Strength and Ductility in Ultrafine Grained Steels”, ISIJ International, Vol. 48, No. 8 (2008), pp. 1114–1121.
(18) Somani, M.C., Juntunen, P., Karjalainen, L.P., Misra, R.D.K. and Kyröläinen, A., “Enhanced Me- chanical Properties through Reversion in Metastable Austenitic Stainless Steels”, Metallurgical and Materials Transactions A, Vol. 40, No. 3 (2009), pp. 729–744.
(19) Gao, S., Bai, Y., Zheng, R., Tian, Y., Mao, W., Shibata, A., and Tsuji, N., “Mechanism of huge Lüders-type deformation in ultrafine grained austenitic stainless steel”, Scripta Materialia, Vol. 159, (2019), pp. 28 – 32.
(20) Tian, Y.Z., Bai, Y., Zhao, L.J., Gao, S., Yang, H.K., Shibata, A., Zhang, Z.F., and Tsuji, N., “A novel ultrafine-grained Fe22Mn0.6C TWIP steel with superior strength and ductility”, Materials Characterization, Vol. 126, (2017), pp. 74 – 80.
(21) Nishiyama, Z., Martensitic Transformation, (1978), Academic Press.
(22) Kurdjumov, G. and Sachs, G., “Über den Mechanismus der Stahlhärtung”, Zeitschrift für Physik, Vol. 64, (1930), pp. 325–343.
(23) Nishiyama, Z., “X-ray investigation of the mechanism of the transformation from face centered cubic lattice to body centered cubic”, The science reports of the Tohoku University, Vol. 23, (1934), pp. 637–664.
(24) 大塚和弘 [著], 堂山昌男, 小川恵一, 北田正弘 [監修], 合金のマルテンサイト変態と形状記憶効果, (2012), 内田老鶴圃.
(25) Bowles, J.S. and Mackenzie, J.K., “The crystallography of martensite transformations I”, Acta Met- allurgica, Vol. 2, No. 1 (1954), pp. 129 – 137.
(26) Mackenzie, J.K. and Bowles, J.S., “The crystallography of martensite transformations II”, Acta Metallurgica, Vol. 2, No. 1 (1954), pp. 138 – 147.
(27) Bowles, J.S. and Mackenzie, J.K., “The crystallography of martensite transformations III. Face- centred cubic to body-centred tetragonal transformations”, Acta Metallurgica, Vol. 2, No. 2 (1954), pp. 224 – 234.
(28) Mackenzie, J.K. and Bowles, J.S., “The crystallography of martensite transformations IV. Body- centred cubic to orthorhombic transformations”, Acta Metallurgica, Vol. 5, No. 3 (1957), pp. 137 – 149.
(29) Wechsler, M.S., Lieberman, D.S. and Read, T.A., “On the theory of the formation of martensite”, Transactions AIME, Vol. 197, (1953), pp. 1503–1515.
(30) Lieberman, D.S., Wechsler, M.S. and Read, T.A., “Cubic to Orthorhombic Diffusionless Phase Change - Experimental and Theoretical Studies of AuCd”, Journal of Applied Physics, Vol. 26, No. 4 (1955), pp. 473–484.
(31) 松原英一郎, 田中功, 大谷博司, 安田秀幸, 沼倉宏, 古原忠, 辻伸泰, 金属材料組織学, (2011), 朝倉書店.
(32) Peirce, D., Asaro, R.J. and Needleman, A., “Material rate dependence and localized deformation in crystalline solids”, Acta Metallurgica, Vol. 31, No. 12 (1983), pp. 1951 – 1976.
(33) Asaro, R.J. and Needleman, A., “Texture development and strain hardening in rate dependent poly- crystals”, Acta Metallurgica, Vol. 33, No. 6 (1985), pp. 923 – 953.
(34) Wheeler, A.A., Boettinger, W.J. and McFadden, G.B., “Phase-field model for isothermal phase transitions in binary alloys”, Physical Review A, Vol. 45, (1992), pp. 7424–7439.
(35) Kobayashi, R., “Modeling and numerical simulations of dendritic crystal growth”, Physica D: Non- linear Phenomena, Vol. 63, No. 3 (1993), pp. 410 – 423.
(36) Taylor, G.I., “Plastic Strain in Metals”, Journal of the Institute of Metals, Vol. 62, (1938), pp. 307–324.
(37) Peirce, D., Asaro, R.J. and Needleman, A., “An analysis of nonuniform and localized deformation in ductile single crystals”, Acta Metallurgica, Vol. 30, No. 6 (1982), pp. 1087 – 1119.
(38) Kondo, K., “Non-Riemannian geometry of imperfect crystals from a macroscopic viewpoint”, Memoirs of the unifying study of the basic problems in engineering science by means of geome- try, Vol. 1, (1955), pp. 458–469.
(39) Bilby, B.A., Bullough, R. and Smith, E., “Continuous distributions of dislocations: a new appli- cation of the methods of non-Riemannian geometry”, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 231, No. 1185 (1955), pp. 263–273.
(40) Kröner, E., “Die spannungsfunktionen der dreidimensionalen isotropen elastizitätstheorie”, Zeitschrift für Physik, Vol. 139, No. 2 (1954), pp. 175–188.
(41) 近藤一夫, “連続転位分布理論”, 日本金属学会会報, Vol. 10, No. 12 (1971), pp. 787–793.
(42) Fleck, N.A., Muller, G.M., Ashby, M.F. and Hutchinson, J.W., “Strain gradient plasticity: Theory and experiment”, Acta Metallurgica et Materialia, Vol. 42, No. 2 (1994), pp. 475 – 487.
(43) Evers, L.P., Brekelmans, W.A.M. and Geers, M.G.D., “Non-local crystal plasticity model with in- trinsic SSD and GND effects”, Journal of the Mechanics and Physics of Solids, Vol. 52, No. 10 (2004), pp. 2379 – 2401.
(44) Ohashi, T., “Crystal plasticity analysis of dislocation emission from micro voids”, International Journal of Plasticity, Vol. 21, No. 11 (2005), pp. 2071 – 2088.
(45) Aoyagi, Y. and Shizawa, K., “Multiscale crystal plasticity modeling based on geometrically nec- essary crystal defects and simulation on fine-graining for polycrystal”, International Journal of Plasticity, Vol. 23, No. 6 (2007), pp. 1022 – 1040.
(46) Lee, E.H., “Elastic-plastic deformation at finite strains”, Journal of applied mechanics, Vol. 36, No. 1 (1969), pp. 1–6.
(47) Forest, S., Cailletaud, G. and Sievert, R., “A cosserat theory for elastoviscoplastic single crystals at finite deformation”, Archives of Mechanics, Vol. 49, (1997), pp. 705–736.
(48) Shizawa, K. and Zbib, H.M., “A thermodynamical theory of gradient elastoplasticity with disloca- tion density tensor. I: Fundamentals”, International Journal of Plasticity, Vol. 15, No. 9 (1999), pp. 899 – 938.
(49) Kratochvil, J. “Finite strain theory of inelastic behavior of crystalline solids”. In Sawczuk, A., editor, Foundations of Plasticity, pp. 401–415. Noordhoff, Leyden, (1972).
(50) 高木知弘, 山中晃徳, フェーズフィールド法 - 数値シミュレーションによる材料組織設計, (2012), 養賢堂.
(51) Kobayashi, R., Warren, J.A. and Carter, W.C., “Vector-valued phase field model for crystallization and grain boundary formation”, Physica D: Nonlinear Phenomena, Vol. 119, No. 3 (1998), pp. 415 – 423.
(52) Kobayashi, R., Warren, J.A. and Carter, W.C., “A continuum model of grain boundaries”, Physica D: Nonlinear Phenomena, Vol. 140, No. 1 (2000), pp. 141 – 150.
(53) Warren, J.A., Kobayashi, R., Lobkovsky, A.E. and Carter, W.C., “Extending phase field models of solidification to polycrystalline materials”, Acta Materialia, Vol. 51, No. 20 (2003), pp. 6035 – 6058.
(54) Steinbach, I., Pezzolla, F., Nestler, B., Seesselberg, M., Prieler, R., Schmitz, G.J. and Rezende, J.L.L., “A phase field concept for multiphase systems”, Physica D: Nonlinear Phenomena, Vol. 94, No. 3 (1996), pp. 135 – 147.
(55) Steinbach, I. and Pezzolla, F., “A generalized field method for multiphase transformations using interface fields”, Physica D: Nonlinear Phenomena, Vol. 134, No. 4 (1999), pp. 385 – 393.
(56) Ding, R. and Guo, Z.X., “Microstructural evolution of a Ti–6Al–4V alloy during 𝛽-phase process- ing: experimental and simulative investigations”, Materials Science and Engineering: A, Vol. 365, No. 1 (2004), pp. 172 – 179.
(57) Bernacki, M., Chastel, Y., Coupez, T. and Logé, R.E., “Level set framework for the numerical modelling of primary recrystallization in polycrystalline materials”, Scripta Materialia, Vol. 58, No. 12 (2008), pp. 1129 – 1132.
(58) Bernacki, M., Logé, R.E. and Coupez, T., “Level set framework for the finite-element modelling of recrystallization and grain growth in polycrystalline materials”, Scripta Materialia, Vol. 64, No. 6 (2011), pp. 525 – 528.
(59) Takaki, T., Hirouchi, T., Hisakuni, T., Yamanaka, A. and Tomita, Y., “Multi-phase-field model to simulate microstructure evolutions during dynamic recrystallization”, Materials Transactions, Vol. 49, No. 11 (2008), pp. 2559–2565.
(60) Takaki, T., Yoshimoto, C., Yamanaka, A. and Tomita, Y., “Multiscale modeling of hot-working with dynamic recrystallization by coupling microstructure evolution and macroscopic mechanical behavior”, International Journal of Plasticity, Vol. 52, (2014), pp. 105 – 116.
(61) Muramatsu, M. and Shizawa, K., “A dynamic recrystallization simulation based on phase-field and dislocation-crystal plasticity models”, Young Investigators Conferences 2012 (YIC2012) Book of Abstracts, (2012), pp. 587–593.
(62) Levitas, V.I., Idesman, A.V. and Olson, G.B., “Continuum modeling of strain-induced martensitic transformation at shear-band intersections”, Acta Materialia, Vol. 47, No. 1 (1998), pp. 219 – 233.
(63) Iwamoto, T. and Tsuta, T., “Finite element simulation of martensitic transformation in single-crystal TRIP steel based on crystal plasticity theory with cellular automata approach”, Key Engineering Materials, Vol. 274, (2004), pp. 679–684.
(64) Tjahjanto, D.D., Turteltaub, S. and Suiker, A.S.J., “Crystallographically based model for transformation-induced plasticity in multiphase carbon steels”, Continuum Mechanics and Ther- modynamics, Vol. 19, (2008), pp. 399 – 422.
(65) Lee, M.G., Kim, S.J. and Han, H.N., “Crystal plasticity finite element modeling of mechanically induced martensitic transformation (MIMT) in metastable austenite”, International Journal of Plas- ticity, Vol. 26, No. 5 (2010), pp. 688 – 710.
(66) Olson, G.B. and Cohen, M., “Kinetics of strain-induced martensitic nucleation”, Metallurgical Transactions A, Vol. 6, (1975), pp. 791 – 795.
(67) Olson, G.B. and Cohen, M., “Stress-assisted isothermal martensitic transformation: Application to TRIP steels”, Metallurgical Transactions A, Vol. 13, (1982), pp. 1907 – 1914.
(68) Yamanaka, A., Takaki, T. and Tomita, Y., “Elastoplastic phase-field simulation of martensitic trans- formation with plastic deformation in polycrystal”, International Journal of Mechanical Sciences, Vol. 52, No. 2 (2010), pp. 245 – 250.
(69) Levitas, V.I., “Phase field approach to martensitic phase transformations with large strains and in- terface stresses”, Journal of the Mechanics and Physics of Solids, Vol. 70, (2014), pp. 154 – 189.
(70) Wang, Y. and Khachaturyan, A.G., “Three-dimensional field model and computer modeling of martensitic transformations”, Acta Materialia, Vol. 45, No. 2 (1997), pp. 759 – 773.
(71) Guo, X.H., Shi, S.Q. and Ma, X.Q., “Elastoplastic phase field model for microstructure evolution”, Applied Physics Letters, Vol. 87, No. 22 (2005), p. 221910.
(72) Guedes, J.M. and Kikuchi, N., “Preprocessing and postprocessing for materials based on the homog- enization method with adaptive finite element methods”, Computer Methods in Applied Mechanics and Engineering, Vol. 83, No. 2 (1990), pp. 143 – 198.
(73) 寺田賢二郎, 菊地昇, 均質化法入門, (2003), 丸善.
(74) Terada, K. and Kikuchi, N., “A class of general algorithms for multi-scale analyses of heterogeneous media”, Computer Methods in Applied Mechanics and Engineering, Vol. 190, No. 40 (2001), pp. 5427 – 5464.
(75) Hill, R., “Elastic properties of reinforced solids: Some theoretical principles”, Journal of the Me- chanics and Physics of Solids, Vol. 11, No. 5 (1963), pp. 357 – 372.
(76) Luo, Z.P. and Zhang, S.Q., “High-resolution electron microscopy on the X-Mg12ZnY phase in a high strength Mg-Zn-Zr-Y magnesium alloy”, Journal of Materials Science Letters, Vol. 19, No. 9 (2000), pp. 813–815.
(77) Kawamura, Y., Hayashi, K., Inoue, A. and Masumoto, T., “Rapidly solidified powder metallurgy Mg97Zn1Y2alloys with excellent tensile yield strength above 600 MPa”, Materials Transactions, Vol. 42, No. 7 (2001), pp. 1172–1176.
(78) Kawamura, Y. and Yamasaki, M., “Formation and mechanical properties of Mg97Zn1RE2 alloys with long-period stacking ordered structure”, Materials Transactions, Vol. 48, No. 11 (2007), pp. 2986–2992.
(79) Marsden, J.E. and Hughes. T.J.R., Mathematical foundations of elasticity, (1982), Prentice Hall.
(80) Toupin, R.A., “Theories of elasticity with couple-stress”, Archive for Rational Mechanics and Anal- ysis, Vol. 17, No. 2 (1964), pp. 85–112.
(81) Clayton, J.D., Nonlinear Mechanics of Crystals, (2011), Springer.
(82) Mandel, J., CISM Courses and Lectures No. 97, (1971), Springer-Verlag.
(83) Kratochvil, J., “Finite-strain theory of crystalline elastic-inelastic materials”, Journal of Applied Physics, Vol. 42, No. 3 (1971), pp. 1104–1108.
(84) Ashby, M.F., “The deformation of plastically non-homogeneous materials”, The Philosophical Magazine: A, Vol. 21, No. 170 (1970), pp. 399–424.
(85) Schouten, J.A., Ricci-Calculus, (1954), Springer-Verlag Berlin Heidelbert.
(86) Clayton, J.D., Bammann, D.J. and McDowell, D.L., “Anholonomic configuration spaces and metric tensors in finite elastoplasticity”, International Journal of Non-Linear Mechanics, Vol. 39, No. 6 (2004), pp. 1039 – 1049.
(87) Cheong, K.S., Busso, E.P. and Arsenlis, A., “A study of microstructural length scale effects on the behaviour of FCC polycrystals using strain gradient concepts”, International Journal of Plasticity, Vol. 21, No. 9 (2005), pp. 1797 – 1814.
(88) Gurtin, M.E., “The burgers vector and the flow of screw and edge dislocations in finite-deformation single-crystal plasticity”, Journal of the Mechanics and Physics of Solids, Vol. 54, No. 9 (2006), pp. 1882 – 1898.
(89) Ohashi, T., “Numerical modelling of plastic multislip in metal crystals of f.c.c. type”, Philosophical Magazine A, Vol. 70, No. 5 (1994), pp. 793–803.
(90) Maugin, G.A. and Muschik, W., “Thermodynamics with internal variables, part I. general concepts. part II. applications.”, Journal of Non-Equilibrium Thermodynamics, Vol. 19, (1994), pp. 217–249; 250–289.
(91) 棚橋隆彦, 連続体の力学 (3) –物質の構成方程式–, (1986), 理工図書.
(92) Eringen, A.C., Nonlinear Theory of Continuous Media, (1962), McGraw-Hill.
(93) 棚橋隆彦, 連続体の力学 (2) –一般原理とその応用–, (1986), 理工図書.
(94) 久田俊明, 非線形有限要素法のためのテンソル解析の基礎, (1992), 丸善.
(95) Allen, S.M. and Cahn, J.W., “A microscopic theory for antiphase boundary motion and its applica- tion to antiphase domain coarsening”, Acta Metallurgica, Vol. 27, No. 6 (1979), pp. 1085 – 1095.
(96) 村上澄男, 連続体損傷力学, (2008), 森北出版.
(97) Hutchinson, J.W., “Bounds and self-consistent estimates for creep of polycrystalline materials”, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, Vol. 348, No. 1652 (1976), pp. 101–127.
(98) Pan, J. and Rice, J.R., “Rate sensitivity of plastic flow and implications for yield-surface vertices”, International Journal of Solids and Structures, Vol. 19, No. 11 (1983), pp. 973 – 987.
(99) Bailey, J.E. and Hirsch, P.B., “The dislocation distribution, flow stress, and stored energy in cold- worked polycrystalline silver”, The Philosophical Magazine A, Vol. 5, No. 53 (1960), pp. 485–497.
(100) Hill, R., “Generalized constitutive relations for incremental deformation of metal crystals by mul-tislip”, Journal of the Mechanics and Physics of Solids, Vol. 14, No. 2 (1966), pp. 95 – 102.
(101) Kondo, R., Tadano, Y. and Shizawa, K., “A phase-field model of twinning and detwinning cou-pled with dislocation-based crystal plasticity for HCP metals”, Computational Materials Science, Vol. 95, (2014), pp. 672 – 683.
(102) Weertman, J., “Anomalous work hardening, non-redundant screw dislocations in a circular bar de- formed in torsion, and non-redundant edge dislocations in a bent foil”, Acta Materialia, Vol. 50, No. 4 (2002), pp. 673 – 689.
(103) Peirce, D., Shih, C.F. and Needleman, A., “A tangent modulus method for rate dependent solids”, Computers & Structures, Vol. 18, No. 5 (1984), pp. 875 – 887.
(104) Bensousson, A., Lions, J.L., Papanicolaou, G., Asymptotic Analysis for Periodic Structures, (1978), North-Holland.
(105) Sanchez-Palencia, E., Non-Homogeneous Media and Vibration Theory, (1980), Springer.
(106) Nakamachi, E., Tam, N.N. and Morimoto, H., “Multi-scale finite element analyses of sheet metals by using SEM-EBSD measured crystallographic RVE models”, International Journal of Plasticity, Vol. 23, No. 3 (2007), pp. 450 – 489.
(107) 仲町英治, 飯星真治, 陳貽平, 上田整, 上辻靖智, 藤田宏平, “結晶均質化有限要素法によるマルチスケール塑性変形解析”, 日本機械学会論文集A 編, Vol. 70, No. 690 (2004), pp. 191 – 197.
(108) Ohno, N., Okumura, D. and Noguchi, H., “Microscopic symmetric bifurcation condition of cellular solids based on a homogenization theory of finite deformation”, Journal of the Mechanics and Physics of Solids, Vol. 50, No. 5 (2002), pp. 1125 – 1153.
(109) Yuan, X., Tomita, Y. and Andou, T., “A micromechanical approach of nonlocal modeling for media with periodic microstructures”, Mechanics Research Communications, Vol. 35, No. 1 (2008), pp. 126 – 133.
(110) Kouznetsova, V.G., Geers, M.G.D. and Brekelmans, W.A.M., “Multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme”, In- ternational Journal for Numerical Methods in Engineering, Vol. 54, No. 8 (2002), pp. 1235 – 1260.
(111) 内田真, 多田直哉, “巨視的なひずみ勾配に対する特性変位関数を導入した 2 次均質化法に基づく有限要素法による変形解析法の構築”, 日本機械学会論文集Ａ編, Vol. 79, No. 806 (2013), pp. 1486–1503.
(112) Suquet, P.M., Elements of homogenization theory for inelastic solid mechanics, (1987), Springer.
(113) 大橋正幸, 遠藤孝雄, 酒井拓, “ニッケルの動的再結晶におよぼす初期結晶粒径の影響”, 日本金属学会誌, Vol. 54, No. 4 (1990), pp. 435–441.
(114) Björklund, S. and Hillert, M., “An analysis of the relation between grain growth and recrystallization based on experimental boundary mobilities”, Metal Science, Vol. 9, No. 1 (1975), pp. 127–134.
(115) Roberts, W. and Ahlblom, B., “A nucleation criterion for dynamic recrystallization during hot work-ing”, Acta Metallurgica, Vol. 26, No. 5 (1978), pp. 801 – 813.
(116) Kim, S.G., Kim, D.I., Kim, W.T. and Park, Y.B., “Computer simulations of two-dimensional and three-dimensional ideal grain growth”, Physical Review E, Vol. 74, (2006), p. 061605.
(117) 三浦誠司, 落合鍾一, 大矢義博, 三島良直, 鈴木朝夫, “Ni3(Al, Ti) 単結晶の流動応力におよぼす歪速度の影響”, 日本金属学会誌, Vol. 51, No. 5 (1987), pp. 400–406.
(118) Bordoni, P.G., “Dislocation relaxation at high frequencies”, Il Nuovo Cimento (1955-1965), Vol. 17, No. 1 (1960), pp. 43–91.
(119) 長津輝, 佐藤愼一, 村松眞由, 青柳吉輝, 志澤一之, “Multi-phase-field 理論および転位-結晶塑性論に基づく動的再結晶モデルの構築とそのシミュレーション”, 日本機械学会関東支部第 17 期総会講演会講演論文集, Vol. 2011.17, (2011), pp. 353–354.
(120) Asaro, R.J., “Geometrical effects in the inhomogeneous deformation of ductile single crystals”, Acta Metallurgica, Vol. 27, No. 3 (1979), pp. 445 – 453.
(121) 須藤一, 田村今男, 西澤泰二, 金属組織学, (1972), 丸善.
(122) Yamasaki, M., Hashimoto, K., Hagihara, K. and Kawamura, Y., “Effect of multimodal microstruc- ture evolution on mechanical properties of Mg-Zn-Y extruded alloy”, Acta Materialia, Vol. 59, No. 9 (2011), pp. 3646 – 3658.
(123) Inoue, A., Kishida, K., Inui, H. and Hagihara, K., “Compression of Micro-pillars of a Long Period Stacking Ordered Phase in the Mg-Zn-Y system”, MRS Proceedings, Vol. 1516, (2013), pp. 151 – 156.
(124) Garces, G., Perez, P., Cabeza, S., Lin, H.K., Kim, S., Gan, W. and Adeva, P., “Reverse tension/com- pression asymmetry of a Mg-Y-Zn alloys containing LPSO phases”, Materials Science and Engi- neering: A, Vol. 647, (2015), pp. 287 – 293.
(125) Shao, X.H., Yang, Z.Q. and Ma, X.L., “Strengthening and toughening mechanisms in Mg-Zn-Y alloy with a long period stacking ordered structure”, Acta Materialia, Vol. 58, No. 14 (2010), pp. 4760 – 4771.
(126) Hagihara, K., Yokotani, N. and Umakoshi, Y., “Plastic deformation behavior of Mg12YZn with 18R long-period stacking ordered structure”, Intermetallics, Vol. 18, No. 2 (2010), pp. 267 – 276.
(127) Hagihara, K., Kinoshita, A., Sugino, Y., Yamasaki, M., Kawamura, Y., Yasuda, H.Y. and Umakoshi, Y., “Plastic deformation behavior of Mg97Zn1Y2 extruded alloys”, Transactions of Nonferrous Metals Society of China, Vol. 20, No. 7 (2010), pp. 1259 – 1268.
(128) Hagihara, K., Kinoshita, A., Fukusumi, Y., Yamasaki, M. and Kawamura, Y., “High-temperature compressive deformation behavior of Mg97Zn1Y2 extruded alloy containing a long-period stacking ordered (LPSO) phase”, Materials Science and Engineering: A, Vol. 560, (2013), pp. 71 – 79.
(129) Slutsky, L.J. and Garland, C.W., “Elastic constants of magnesium from 4.2 K to 300 K”, Physical Review, Vol. 107, No. 4 (1957), pp. 972 – 976.
(130) Tane, M., Nagai, Y., Kimizuka, H., Hagihara, K. and Kawamura, Y., “Elastic properties of an Mg- Zn-Y alloy single crystal with a long-period stacking-ordered structure”, Acta Materialia, Vol. 61, No. 17 (2013), pp. 6338 – 6351.
(131) 木村祐一, 上田亮, 志澤一之, “高次応力モデルを用いた Mg 基 LPSO 相の寸法効果に対する転位-結晶塑性 FEM 解析”, 材料, Vol. 68, No. 11 (2019), pp. 825 – 832.
(132) Han, H.N., Lee, C.G., Oh, C.S., Lee, T.H. and Kim, S.G., “A model for deformation behavior and mechanically induced martensitic transformation of metastable austenitic steel”, Acta Materialia, Vol. 52, No. 17 (2004), pp. 5203 – 5214.
(133) Iwamoto, T., “Multiscale computational simulation of deformation behavior of TRIP steel with growth of martensitic particles in unit cell by asymptotic homogenization method”, International Journal of Plasticity, Vol. 20, No. 4 (2004), pp. 841 – 869.
(134) 小島陽, 井藤忠男, マグネシウム合金の製造と応用, (2001), シーエムシー出版.
(135) Yoshimoto, S., Yamasaki, M. and Kawamura, Y., “Microstructure and mechanical properties of extruded Mg-Zn-Y alloys with 14H long period ordered structure”, Materials Transactions, Vol. 47, No. 4 (2006), pp. 959–965.
(136) 河村能人, “長周期積層構造層を強化層にした高強度・高耐熱マグネシウム合金”, 金属, Vol. 80, No. 7 (2010), pp. 581–588.
(137) 阿部英司, “シンクロ型 LPSO-Mg 合金の原子構造と結晶学”, まてりあ, Vol. 54, No. 2 (2015), pp. 50–54.
(138) Partridge, P.G., “The crystallography and deformation modes of hexagonal close-packed metals”, Metallurgical Reviews, Vol. 12, No. 1 (1967), pp. 169–194.
(139) Hess, J.B. and Barrett, C.S., “Structure and nature of kink bands in zinc”, JOM, Vol. 1, No. 9 (1949), pp. 599–606.
(140) Barsoum, M.W. and El-Raghy, T., “Room-temperature ductile carbides”, Metallurgical and Mate- rials Transactions A, Vol. 30, No. 2 (1999), pp. 363–369.
(141) Mukai, T., Yamanoi, M., Watanabe, H. and Higashi, K., “Ductility enhancement in AZ31 magne- sium alloy by controlling its grain structure”, Scripta Materialia, Vol. 45, No. 1 (2001), pp. 89–94.
(142) Agnew, S.R., Horton, J.A., Lillo, T.M. and Brown, D.W., “Enhanced ductility in strongly textured magnesium produced by equal channel angular processing”, Scripta Materialia, Vol. 50, No. 3 (2004), pp. 377 – 381.
(143) 松島与三, 多様体入門, (1965), 裳華房.
(144) 松本幸夫, 多様体の基礎 (基礎数学 5), (1988), 東京大学出版会.
(145) 杉田勝実, 岡本良夫, 関根松夫, 理論物理のための微分幾何学 – 可換幾何学から非可換幾何学へ, (2007), 森北出版.
(146) 野水克己, 佐々木武, アファイン微分幾何学 - アファインはめ込みの幾何, (1994), 裳華房.
(147) 久田俊明, 野口裕久, 非線形有限要素法の基礎と応用, (1995), 丸善.
(148) (社) 土木学会, いまさら聞けない計算力学の常識, (2008), 丸善.
(149) (社) 日本塑性加工学会, 非線形有限要素法—線形弾性解析から塑性加工解析まで—, (1994), コロナ社.
(150) 越塚誠一, 粒子法, (2005), 丸善.
(151) 越塚誠一, 柴田和也, 室谷浩平, 粒子法入門流体シミュレーションの基礎から並列計算と可視化まで, (2014), 丸善.
(152) 後藤仁志, 粒子法連続体・混相流・粒状体のための計算科学, (2018), 森北出版.
(153) Gingold, R.A. and Monaghan, J.J., “Smoothed particle hydrodynamics: theory and application to non-spherical stars”, Monthly Notices of the Royal Astronomical Society, Vol. 181, No. 3 (1977), pp. 375 – 389.
(154) Lucy, L.B., “A numerical approach to the testing of the fission hypothesis”, The Astronomical Jour-nal, Vol. 82, No. 12 (1977), pp. 1013 – 1024.
(155) Koshizuka, S., “A particle method for incompressible viscous flow with fluid fragmentation”, Com- putational fluid dynamics journal, Vol. 4, (1995), pp. 29 – 46.
(156) Koshizuka, S. and Oka, Y., “Moving-particle semi-implicit method for fragmentation of incom- pressible fluid”, Nuclear Science and Engineering, Vol. 123, No. 3 (1996), pp. 421 – 434.
(157) Koshizuka, S., Nobe, A. and Oka, Y., “Numerical analysis of breaking waves using the moving particle semi-implicit method”, International Journal for Numerical Methods in Fluids, Vol. 26, No. 7 (1998), pp. 751 – 769.
(158) Liu, M.B. and Liu, G.R., “Smoothed Particle Hydrodynamics (SPH): an Overview and Recent De- velopments”, Archives of Computational Methods in Engineering, Vol. 17, (2010), pp. 25 – 76.
(159) Monaghan, J.J. and Lattanzio, J.C., “A refined particle method for astrophysical problems”, Astron- omy and astrophysics, Vol. 149, No. 1 (1985), pp. 135 – 143.
(160) Wendland, H., “Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree”, Advances in Computational Mathematics, Vol. 4, (1995), pp. 389 – 396.
(161) Guan, P.C., Chi, S.W., Chen, J.S., Slawson, T.R. and Roth, M.J., “Semi-Lagrangian reproducing kernel particle method for fragment-impact problems”, International Journal of Impact Engineer- ing, Vol. 38, No. 12 (2011), pp. 1033 – 1047.
(162) Belytschko, T. and Xiao, S., “Stability analysis of particle methods with corrected derivatives”, Computers & Mathematics with Applications, Vol. 43, No. 3 (2002), pp. 329 – 350.
(163) Chen, J.S. and Wu, Y., “Stability in lagrangian and semi-lagrangian reproducing kernel discretiza- tions using nodal integration in nonlinear solid mechanics”, Advances in Meshfree Techniques, (2007), pp. 55 – 76.
(164) Guan, P.C., Chen, J.S., Wu, Y., Teng, H., Gaidos, J., Hofstetter, K. and Alsaleh, M., “Semi- Lagrangian reproducing kernel formulation and application to modeling earth moving operations”, Mechanics of Materials, Vol. 41, No. 6 (2009), pp. 670 – 683.
(165) Wei, H., Chen, J.S., Beckwith, F. and Baek, J., “A naturally stabilized semi-Lagrangian meshfree formulation for multiphase porous media with application to landslide modeling”, Journal of Engi- neering Mechanics, Vol. 146, No. 4 (2020), p. 04020012.
(166) Chen, J.S., Chunhui, P., Wu, C.T. and Liu, W.K., “Reproducing Kernel Particle Methods for large deformation analysis of non-linear structures”, Computer Methods in Applied Mechanics and En- gineering, Vol. 139, No. 1 (1996), pp. 195 – 227.
(167) Rabczuk, T., Belytschko, T. and Xiao, S.P., “Stable particle methods based on Lagrangian kernels”, Computer Methods in Applied Mechanics and Engineering, Vol. 193, No. 12 (2004), pp. 1035 – 1063.
(168) Rabczuk, T. and Belytschko, T., “A three-dimensional large deformation meshfree method for arbi- trary evolving cracks”, Computer Methods in Applied Mechanics and Engineering, Vol. 196, No. 29 (2007), pp. 2777 – 2799.
(169) 鈴木克幸, 長嶋利夫, 萩原世也, メッシュフリー解析法, (2006), 丸善.
(170) Chen, J.S., Hillman, M. and Chi, S.W., “Meshfree methods: progress made after 20 years”, Journal of Engineering Mechanics, Vol. 143, No. 4 (2017), p. 04017001.
(171) Belytschko, T., Lu, Y.Y. and Gu, L., “Element-free Galerkin methods”, International Journal for Numerical Methods in Engineering, Vol. 37, No. 2 (1994), pp. 229 – 256.
(172) Belytschko, T., Gu, L. and Lu, Y.Y., “Fracture and crack growth by element free Galerkin methods”, Modelling and Simulation in Materials Science and Engineering, Vol. 2, No. 3A (1994), pp. 519 – 534.
(173) Liu, W.K., Jun, S. and Zhang, Y.F., “Reproducing kernel particle methods”, International Journal for Numerical Methods in Fluids, Vol. 20, 8 ‐ 9 (1995), pp. 1081–1106.
(174) Chen, J.S., Wu, C.T., Yoon, S. and You, Y., “A stabilized conforming nodal integration for Galerkin mesh-free methods”, International Journal for Numerical Methods in Engineering, Vol. 50, No. 2 (2001), pp. 435 – 466.
(175) Lancaster, P. and Salkauskas, K., “Surfaces generated by moving least squares methods”, Mathe- matics of computation, Vol. 37, No. 155 (1981), pp. 141–158.
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