A perspective on trends in multiscale plasticity

International Journal of Plasticity - Tập 26 - Trang 1280-1309 - 2010
David L. McDowell1
1GWW School of Mechanical Engineering, School of Materials Science & Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405, USA

Tài liệu tham khảo

Abu Al-Rub, 2007, A thermodynamic based higher-order gradient theory for size dependent plasticity, International Journal of Solids and Structures, 44, 2888, 10.1016/j.ijsolstr.2006.08.034 Acharya, 2003, Driving forces and boundary conditions in continuum dislocation mechanics, Proceedings of the Royal Society of London A, 459, 1343, 10.1098/rspa.2002.1095 Acharya, 2000, Lattice incompatibility and a gradient theory of crystal plasticity, Journal of the Mechanics and Physics of Solids, 48, 1565, 10.1016/S0022-5096(99)00075-7 Acharya, 2006, Continuum theory and methods for coarse-grained, mesoscopic plasticity, Scripta Materialia, 54, 705, 10.1016/j.scriptamat.2005.10.070 Acharya, 2008, New perspectives in plasticity theory: dislocation nucleation, waves and partial continuity of the plastic strain rate, Mathematics and Mechanics of Solids, 13, 292, 10.1177/1081286507086903 Adams, 2004, Microstructures by design: Linear problems in elastic-plastic design, International Journal of Plasticity, 20, 1577, 10.1016/j.ijplas.2003.11.008 Aifantis, 1987, The physics of plastic deformation, International Journal of Plasticity, 3, 211, 10.1016/0749-6419(87)90021-0 Aifantis, 1995, Pattern formation in plasticity, International Journal of Engineering Science, 33, 2161, 10.1016/0020-7225(95)00086-D Aifantis, 2003, Update on a class of gradient theories, Mechanics of Materials, 35, 259, 10.1016/S0167-6636(02)00278-8 Akasheh, 2007, Dislocation dynamics analysis of dislocation intersections in nanoscale metallic multilayered composites, Journal of Applied Physics, 101, 084314, 10.1063/1.2721093 Amodeo, 1988, A review of experimental-observations and theoretical-models of dislocation cells and subgrains, Res Mechanica, 23, 137 Arsenlis, 1999, Crystallographic aspects of geometrically-necessary and statistically-stored dislocation density, Acta Materialia, 47, 1597, 10.1016/S1359-6454(99)00020-8 Arsenlis, 2002, Modeling the evolution of crystallographic dislocation density in crystal plasticity, Journal of the Mechanics and Physics of Solids, 50, 1979, 10.1016/S0022-5096(01)00134-X Asaro, 2005, Mechanistic models for the activation volume and rate sensitivity in metals with nanocrystalline grains and nano-scale twins, Acta Materialia, 53, 3369, 10.1016/j.actamat.2005.03.047 Ashby, 1970, The deformation of plastically non-homogeneous materials, Philosophical Magazine, 21, 399, 10.1080/14786437008238426 Bammann, 1982, On a proposal for a continuum with microstructure, Acta Mechanica, 45, 91, 10.1007/BF01295573 Bassani, 2001, Complex macroscopic plastic flow arising from non-planar dislocation core structures, Materials Science and Engineering A, 319–321, 97, 10.1016/S0921-5093(00)02008-6 Bayley, 2006, A comparison of dislocation-induced back stress formulations in strain gradient crystal plasticity, International Journal of Solids and Structures, 43, 7268, 10.1016/j.ijsolstr.2006.05.011 Belak, J., Turchi, P.E.A., Dorr, M.R., Richards, D.F., Fattebert, J.-L., Wickett, M.E., Streitz, F.H., 2009. Coupling of atomistic and meso-scale phase-field modeling of rapid solidification. In: 2009 APS March Meeting, Pittsburgh, PA, March 16–20. Bergugnat, J.-B., 2002. Strain and lattice rotation fields of deformed polycrystals. MS Thesis, GWW School of Mechanical Engineering, Georgia Institute of Technology, 2002. Bilby, 1956, Continuous distributions of dislocations III, Proceedings of the Royal Society of London A, 236, 481, 10.1098/rspa.1956.0150 Bilby, 1955, Continuous distributions of dislocations: a new application of the methods of non-Riemannian geometry, Proceedings of the Royal Society of London A, 231, 263, 10.1098/rspa.1955.0171 Bilby, B.A., Gardner, L.R.T., Stroh, A.N., 1957. Continuous distributions of dislocations and the theory of plasticity. In: Proc. 9th Int. Congr. Appl. Mech. Bruxelles, vol. 8, Université de Bruxelles, pp. 35–44. Butler, 1998, Polycrystal constraint and grain subdivision, International Journal of Plasticity, 14, 703, 10.1016/S0749-6419(98)00018-7 Butler, 2002, X-ray microbeam Laue pattern studies of the spreading of orientation in OFHC copper at large strains, ASME Journal of Engineering Materials and Technology, 124, 48, 10.1115/1.1421050 Capolungo, L., Spearot, D.E., Cherkaoui, M., McDowell, D.L., Qu, J., Jacob, K., 2007. Dislocation nucleation from bicrystal interfaces and grain boundary ledges: relationship to nanocrystalline deformation. Journal of the Mechanics and Physics of Solids doi:10.1016/j.jmps.2007.04.001. Carstensen, 2002, Non-convex potentials and microstructures in finite-strain plasticity, Proceedings of the Royal Society of London, A458, 299, 10.1098/rspa.2001.0864 Chaboche, 1989, Constitutive equations for cyclic plasticity and cyclic viscoplasticity, International Journal of Plasticity, 5, 247, 10.1016/0749-6419(89)90015-6 Chambon, 2004, A strain space gradient plasticity theory for finite strain, Computer Methods in Applied Mechanics and Engineering, 193, 2797, 10.1016/j.cma.2003.10.016 Chen, 2002, Phase-field models for microstructure evolution, Annual Review of Materials Research, 32, 113, 10.1146/annurev.matsci.32.112001.132041 Chen, 2009, A generalized continuum theory and its relation to micromorphic theory, ASCE Journal of Engineering Mechanics, 135, 149, 10.1061/(ASCE)0733-9399(2009)135:3(149) Cheng, 2003, Strength and tension/compression asymmetry in nanostructured and ultrafine-grain metals, Acta Materialia, 51, 4505, 10.1016/S1359-6454(03)00286-6 Chung, 2003, On a formulation for a multiscale atomistic-continuum homogenization method, International Journal of Solids and Structures, 40, 2563, 10.1016/S0020-7683(03)00058-1 Clark, 1992, On the criteria for slip transmission across interfaces in polycrystals, Scripta Metallurgica et Materialia, 26, 203, 10.1016/0956-716X(92)90173-C Clayton, 2003, A multiscale multiplicative decomposition for elastoplasticity of polycrystals, International Journal of Plasticity, 19, 1401, 10.1016/S0749-6419(02)00109-2 Clayton, 2002, Distributions of stretch and rotation in polycrystalline OFHC Cu, ASME Journal of Engineering Materials and Technology, 124, 302, 10.1115/1.1479354 Clayton, 2005, A geometric framework for the kinematics of crystals with defects, Philosophical Magazine, 85, 3983, 10.1080/14786430500363312 Clayton, 2006, Modeling dislocations and disclinations with finite micropolar elastoplasticity, International Journal of Plasticity, 22, 210, 10.1016/j.ijplas.2004.12.001 Cleri, 2002, Microstructure evolution from the atomic scale up, Computational Materials Science, 24, 21, 10.1016/S0927-0256(02)00160-X Cleveringa, 1997, Comparison of discrete dislocation and continuum plasticity predictions for a composite material, Acta Materialia, 45, 3163, 10.1016/S1359-6454(97)00011-6 Cocks, 1996, Variational principles, numerical schemes and bounding theorems for deformation by Nabarro–Herring creep, Journal of the Mechanics and Physics of Solids, 44, 1429, 10.1016/0022-5096(96)00040-3 Curtarolo, 2002, Dynamics of an inhomogeneously coarse grained multiscale system, Physical Review Letters, 88, 255504, 10.1103/PhysRevLett.88.255504 Dao, 1993, Non-Schmid effects and localized plastic flow in intermetallic alloys, Materials Science and Engineering A, 170, 143, 10.1016/0921-5093(93)90376-P Dao, 1996, Non-Schmid effects on the behavior of polycrystals – with applications to Ni3Al, Metallurgical Transactions A, 27A, 81, 10.1007/BF02647749 Deo, 2002, First passage time Markov chain analysis of rare events for kinetic Monte Carlo: double kink nucleation during dislocation glide, Modeling and Simulation in Materials Science and Engineering, 10, 581, 10.1088/0965-0393/10/5/308 Derlet, 2002, Length scale effects in the simulation of deformation properties of nanocrystalline metals, Scripta Materialia, 47, 719, 10.1016/S1359-6462(02)00182-3 Derlet, 2009, Atomistic simulations of dislocations in confined volumes, MRS Bulletin, 34, 184, 10.1557/mrs2009.50 Dillon, 1977, Strain gradients in plasticity, Acta Mechanica, 26, 189, 10.1007/BF01177146 Dillon, 1970, A strain gradient theory of plasticity, International Journal of Solids and Structures, 6, 1513, 10.1016/0020-7683(70)90061-2 Dimiduk, 2006, Preface to the viewpoint set on: statistical mechanics and coarse graining of dislocation behavior for continuum plasticity, Scripta Materialia, 54, 701, 10.1016/j.scriptamat.2005.11.027 Dimiduk, 2007, Overview of experiments on microcrystal plasticity in fcc-derivative materials: selected challenges for modeling and simulation of plasticity, Modelling and Simulation in Materials Science and Engineering, 15, 135, 10.1088/0965-0393/15/2/009 Drucker, 1984, Material response and continuum relations: or from microscales to macroscales, ASME Journal of Engineering Materials and Technology, 106, 286, 10.1115/1.3225717 Dupuy, 2005, Finite-temperature quasicontinuum: molecular dynamics without all the atoms, Physical Review Letters, 95, 060202, 10.1103/PhysRevLett.95.060202 Dvorak, 1993, Micromechanics of inelastic composite materials: theory and experiment. Nadai Lecture, ASME Journal of Engineering Materials and Technology, 115, 327, 10.1115/1.2904226 Eringen, 1972, Nonlocal polar elastic continua, International Journal of Engineering Science, 10, 1, 10.1016/0020-7225(72)90070-5 Eringen, 1999 Eringen, A.C., Claus, Jr., W.D., 1970. A micromorphic approach to dislocation theory and its relation to several existing theories. In: Simmons, J.A., de Wit, R., Bullough, R. (Eds.), Fundamental Aspects of Dislocation Theory 2, pp. 1023–1040. Evers, 2004, Non-local crystal plasticity model with intrinsic SSC and GND effects, Journal of the Mechanics and Physics of Solids, 52, 2379, 10.1016/j.jmps.2004.03.007 Fleck, 1993, A phenomenological theory for strain gradient effects in plasticity, Journal of the Mechanics and Physics of Solids, 41, 1825, 10.1016/0022-5096(93)90072-N Fleck, 1994, Strain gradient plasticity: theory and experiments, Acta Metallurgica Materialia, 42, 475, 10.1016/0956-7151(94)90502-9 Forest, 2003, Elastoviscoplastic constitutive frameworks for generalized continua, Acta Mechanica, 160, 71, 10.1007/s00707-002-0975-0 Forest, 2000, Cosserat modelling of size effects in the mechanical behaviour of polycrystals and multi-phase materials, International Journal of Solids and Structures, 37, 7105, 10.1016/S0020-7683(99)00330-3 Fox, 1968, On the continuum theory of dislocations and plasticity, The Quarterly Journal of Mechanics and Applied Mathematics, 21, 67, 10.1093/qjmam/21.1.67 Friedman, 1998, Scaling theory of the Hall–Petch relation for multilayers, Physical Review Letters, 81, 2715, 10.1103/PhysRevLett.81.2715 Ganapathysubramanian, 2004, Design across length scales: a reduced-order model of polycrystal plasticity for the control of microstructure-sensitive material properties, Computer Methods in Applied Mechanics and Engineering, 193, 5017, 10.1016/j.cma.2004.04.004 Gao, 1999, Mechanism-based strain gradient plasticity—I. Theory, Journal of the Mechanics and Physics of Solids, 47, 1239, 10.1016/S0022-5096(98)00103-3 Gerken, 2008, A crystal plasticity model that incorporates stresses and strains due to slip gradients, Journal of the Mechanics and Physics of Solids, 56, 1651, 10.1016/j.jmps.2007.07.012 Ghosh, 2001, A multi-level computational model for multi-scale damage analysis in composite and porous materials, International Journal of Solids and Structures, 38, 2335, 10.1016/S0020-7683(00)00167-0 Ghosh, 2007, Concurrent multi-level model for damage evolution in micro structurally debonding composites, Mechanics of Materials, 39, 241, 10.1016/j.mechmat.2006.05.004 Groh, 2009, Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25, 1456, 10.1016/j.ijplas.2008.11.003 Groma, 1997, Link between the microscopic and mesocopic length-scale description of the collective behavior of dislocations, Physical Review B, 56, 5807, 10.1103/PhysRevB.56.5807 Gumbsch, 1995, An atomistic study of brittle fracture: toward explicit failure criteria from atomistic modeling, Journal of Materials Research, 10, 2897, 10.1557/JMR.1995.2897 Gurtin, 2002, A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations, Journal of the Mechanics and Physics of Solids, 50, 5, 10.1016/S0022-5096(01)00104-1 Gurtin, M.E., 2007. A theory of grain boundaries that accounts automatically for grain misorientation and grain-boundary orientation. Journal of the Mechanics and Physics of Solids, doi:10.1016/j.jmps.2007.05.002. Gurtin, 2007, A gradient theory for single-crystal plasticity, Modelling and Simulation in Materials Science and Engineering, 15, S263, 10.1088/0965-0393/15/1/S20 Hao, 2003, A hierarchical multi-physics model for design of high toughness steels, Journal of Computer-Aided Materials Design, 10, 99, 10.1023/B:JCAD.0000036813.66891.41 Hao, 2004, Multi-scale constitutive model and computational framework for the design of ultra-high strength, high toughness steels, Computer Methods in Applied Mechanics and Engineering, 193, 1865, 10.1016/j.cma.2003.12.026 Hartley, 2003, A method for linking thermally activated dislocation mechanisms of yielding with continuum plasticity theory, Philosophical Magazine, 83, 3783, 10.1080/14786430310001599522 Hirth, 2007, Spacing defects and disconnections in grain boundaries, Acta Materialia, 55, 5428, 10.1016/j.actamat.2007.06.004 Horstemeyer, 1998, Modeling effects of dislocation substructure in polycrystal elastoviscoplasticity, Mechanics of Materials, 27, 145, 10.1016/S0167-6636(97)00037-9 Huang, 2004, A conventional theory of mechanism-based strain gradient plasticity, International Journal of Plasticity, 20, 753, 10.1016/j.ijplas.2003.08.002 Hughes, 1997, Scaling of microstructural parameters: misorientations of deformation induced boundaries, Acta Materialia, 45, 105, 10.1016/S1359-6454(96)00153-X Hutchinson, 2000, Plasticity at the micron scale, International Journal of Solids and Structures, 37, 225, 10.1016/S0020-7683(99)00090-6 Kalidindi, 2001, Modeling anisotropic strain hardening and deformation textures in low stacking fault energy fcc metals, International Journal of Plasticity, 17, 837, 10.1016/S0749-6419(00)00071-1 Kalidindi, 2004, Microstructure sensitive design of an orthotropic plate subjected to tensile load, International Journal of Plasticity, 20, 1561, 10.1016/j.ijplas.2003.11.007 Kalidindi, S.R., Houskamp, J., Proust, G., Duvvuru, H., 2005. Microstructure sensitive design with first order homogenization theories and finite element codes. In: Materials Science Forum, v 495–497, n PART 1, Textures of Materials, ICOTOM 14 – Proceedings of the 14th International Conference on Textures of Materials, pp. 23–30. Khachaturyan, 2001, Nanoscale phase field microelasticity theory of dislocations: model and 3D simulations, Acta Materialia, 49, 1847, 10.1016/S1359-6454(01)00075-1 Knezevic, 2008, Delineation of first-order closures for plastic properties requiring explicit consideration of strain hardening and crystallographic texture evolution, International Journal of Plasticity, 24, 327, 10.1016/j.ijplas.2007.05.002 Kocks, 1970, The relation between polycrystal deformation and single-crystal deformation, Metallurgical Transactions, 1, 1121, 10.1007/BF02900224 Kondo, K., 1953. On the geometrical and physical foundations of the theory of yielding. In: Proc. 2nd Japan Congr. Appl. Mech., Japan National Committee for Theoretical and Applied Mechanics, Science Council of Japan, Tokyo, pp. 41–47. Koslowski, 2004, Dislocation structures and the deformation of materials, Physical Review Letters, 93, 265503, 10.1103/PhysRevLett.93.265503 Kossecka, 1974, Mathematical theory of defects. Part I. Statics, Archives of Mechanics, 26, 995 Kossecka, 1977, Disclination kinematics, Archives of Mechanics, 29, 633 Kouznetsova, 2002, Multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme, International Journal for Numerical Methods in Engineering, 54, 1235, 10.1002/nme.541 Kouznetsova, 2004, Multi-scale second-order computational homogenization of multi-phase materials: a nested finite element solution strategy, Computer Methods in Applied Mechanics and Engineering, 193, 5525, 10.1016/j.cma.2003.12.073 Kratochvil, 1990, Instability origin of dislocation cell misorientation, Scripta Metallurgica et Materialia, 24, 1225, 10.1016/0956-716X(90)90332-B Kratochvil, 2003, Pattern formation in the framework of the continuum theory of dislocations, Physical Review B, 67, 094105, 10.1103/PhysRevB.67.094105 Kratochvil, 2007, Statistically based continuum model of misoriented dislocation cell structure formation, Physical Review B, 75, 064104, 10.1103/PhysRevB.75.064104 Kreuzer, 2005, Discrete dislocation simulation of nanoindentation: the influence of obstacles and a limited number of dislocation sources, Philosophical Magazine, 85, 3301, 10.1080/14786430500156120 Kröner, 1963, On the physical reality of torque stresses in continuum mechanics, International Journal of Engineering Science, 1, 261, 10.1016/0020-7225(63)90037-5 Kröner, 1966 Kröner, 1983, Field theory of defects in Bravais crystals, 357 Kubin, 1992, The modeling of dislocation patterns, Scripta Metallurgica, 27, 957, 10.1016/0956-716X(92)90456-O Kuhlmann-Wilsdorf, 1989, Theory of plastic deformation: properties of low energy dislocation structures, Materials Science and Engineering A, 113, 1, 10.1016/0921-5093(89)90290-6 Kulkarni, 2008, A variational approach to coarse-graining of equilibrium and non-equilibrium atomistic description at finite temperature, Journal of the Mechanics and Physics of Solids, 56, 1417, 10.1016/j.jmps.2007.09.005 Lacy, T., McDowell, D.L., Talreja, R., 1997. Effects of damage distribution on evolution. In: McDowell, D.L. (Ed.), Applications of Continuum Damage Mechanics to Fatigue and Fracture, ASTM STP 1315, pp. 131–149. Lacy, 1999, Gradient concepts for evolution of damage, Mechanics of Materials, 31, 831, 10.1016/S0167-6636(99)00029-0 Larsson, 2007, A second-order homogenization procedure for multi-scale analysis based on micropolar kinematics, International Journal of Numerical Methods in Engineering, 69, 2485, 10.1002/nme.1854 Le, 1996, On the determination of the crystal reference in nonlinear continuum theory of dislocations, Proceedings of the Royal Society of London A, 452, 359, 10.1098/rspa.1996.0019 Lebensohn, 2004, Macroscopic properties and field fluctuations in model power-law polycrystals: full-field solutions versus self-consistent estimates, Proceedings of the Royal Society of London A, 460, 1381, 10.1098/rspa.2003.1212 Lee, 1989, Prediction of slip transfer mechanisms across grain boundaries, Scripta Metallurgica, 23, 799, 10.1016/0036-9748(89)90534-6 Lee, 1990, An in situ transmission electron microscope deformation study of the slip transfer mechanisms in metals, Metallurgical Transactions A, 21A, 2437, 10.1007/BF02646988 Lee, 1990, TEM in situ deformation study of the interaction of lattice dislocations with grain boundaries in metals, Philosophical Magazine A, 62, 131, 10.1080/01418619008244340 Leffers, 1994, Lattice rotations during plastic deformation with grain subdivision, Materials Science Forum, 157–162, 1815, 10.4028/www.scientific.net/MSF.157-162.1815 LeSar, 2004, Incorporation of local structure in continuous theory of dislocations, Physical Review B, 69, 172105, 10.1103/PhysRevB.69.172105 Li, 2007, The mechanics and physics of defect nucleation, MRS Bulletin, 32, 151, 10.1557/mrs2007.48 Li, 2002, Atomistic mechanisms governing elastic limit and incipient plasticity in crystals, Nature, 418, 307, 10.1038/nature00865 Li, D.S., Bouhattate, J., Garmestani, H., 2005. Processing path model to describe texture evolution during mechanical processing. In: Materials Science Forum, v 495–497, n PART 2, Textures of Materials, ICOTOM 14 – Proceedings of the 14th International Conference on Textures of Materials, pp. 977–982. Li, 2007, Deciding the nature of the coarse equation through microscopic simulations: the baby-bathwater scheme, SIAM Review, 49, 469, 10.1137/070692303 Liu, 2003, The size effect on void growth in ductile materials, Journal of the Mechanics and Physics of Solids, 51, 1171, 10.1016/S0022-5096(03)00037-1 Liu, 2004, An introduction to computational nanomechanics and materials, Computer Methods in Applied Mechanics and Engineering, 193, 1529, 10.1016/j.cma.2003.12.008 Liu, 2006, Bridging scale methods for nanomechanics and materials, Computer Methods in Applied Mechanics and Engineering, 195, 1407, 10.1016/j.cma.2005.05.042 Liu, 2009, Theoretical strength of face-centred-cubic single crystal copper based on a continuum model, Chinese Physics Letters, 26, 026103, 10.1088/0256-307X/26/2/026103 Luscher, D.J., McDowell, D.L., 2009. An extended multiscale principle of virtual velocities approach for evolving microstructure. Mesomechanics 2009, Elsevier, Procedia Engineering, University of Oxford, June 24–26. Luscher, D.J., McDowell, D.L., Bronkhorst, C.A., 2009. A second gradient theoretical framework for hierarchical multiscale modeling of materials. International Journal of Plasticity, submitted for publication. Lyon, 2004, Gradient-based non-linear microstructure design, Journal of the Mechanics and Physics of Solids, 52, 2569, 10.1016/j.jmps.2004.04.009 Ma, 2006, A dislocation density based constitutive model for crystal plasticity FEM including geometrically necessary dislocations, Acta Materialia, 54, 2169, 10.1016/j.actamat.2006.01.005 Ma, 2006, On the consideration of interactions between dislocations and grain boundaries in crystal plasticity finite element modeling – theory, experiments and simulations, Acta Materialia, 54, 2181, 10.1016/j.actamat.2006.01.004 Marin, 1996, Associative versus non-associative porous viscoplasticity based on internal state variable concepts, International Journal of Plasticity, 12, 629, 10.1016/S0749-6419(96)00023-X Marin, 1998, Models for compressible elasto-plasticity based on internal state variables, International Journal of Damage Mechanics, 7, 47, 10.1177/105678959800700103 McDowell, 1985, An experimental study of the structure of constitutive equations for nonproportional cyclic plasticity, ASME Journal of Engineering Materials and Technology, 107, 307, 10.1115/1.3225824 McDowell, D.L., 1994. Multiaxial effects in metallic materials. In: Symposium on Durability and Damage Tolerance, ASME AD – vol. 43, ASME Winter Annual Meeting, Chicago, IL, November 6–11, pp. 213–267. McDowell, D.L., 1997. Evolving structure and internal state variables. Nadai Award Lecture, ASME Materials Division, ASME IMECE, Dallas, TX, November 20. McDowell, D.L., 1999a. Non-associative aspects of multiscale evolutionary phenomena. In: Picu, R.C., Krempl, E. (Eds.), Proceedings 4th International Conference on Constitutive Laws for Engineering Materials, pp. 54–57. McDowell, 1999, Damage mechanics in metal fatigue: a discriminating perspective, International Journal of Damage Mechanics, 8, 377, 10.1177/105678959900800406 McDowell, D.L., 2001. Materials design: a useful research focus for inelastic behavior of structural metals. In: Sih, G.C., Panin, V.E. (Eds.), Special Issue of the Theoretical and Applied Fracture Mechanics, Prospects of Mesomechanics in the 21st Century: Current Thinking on Multiscale Mechanics Problems, vol. 37, pp. 245–259. McDowell, D.L., 2005. Internal state variable theory. In: Sidney Yip, Horstemeyer, M.F. (Eds.), Handbook of Materials Modeling, Part A: Methods, Springer, The Netherlands, pp. 1151–1170. McDowell, 2007, Simulation-assisted materials design for the concurrent design of materials and products, JOM, 59, 21, 10.1007/s11837-007-0111-7 McDowell, D.L., 2008a. A perspective on trends in multiscale plasticity. Khan International Medal Lecture, Plasticity 2008, St. Thomas, Virgin Islands, January 8. McDowell, 2008, Viscoplasticity of heterogeneous metallic materials, Materials Science and Engineering R: Reports, 62, 67, 10.1016/j.mser.2008.04.003 McDowell, 2008, Concurrent design of hierarchical materials and structures, Scientific Modeling and Simulation (CMNS), 15, 207, 10.1007/s10820-008-9100-6 McDowell, 1988, Biaxial path dependence of deformation substructure of type 304 stainless steel, Metallurgical Transactions, 19A, 1277, 10.1007/BF02662589 McDowell, 1993, A combined kinematic-isotropic hardening theory for porous inelasticity of ductile metals, International Journal of Damage Mechanics, 2, 137, 10.1177/105678959300200203 McDowell, 2007, Plasticity-related microstructure–property relations for materials design, Key Engineering Materials, 340–341, 21, 10.4028/www.scientific.net/KEM.340-341.21 McDowell, D.L., Panchal, J.H., Choi, H.-J., Seepersad, C.C., Allen, J.K., Mistree, F., 2009. Integrated design of multiscale, multifunctional materials and products. Elsevier, p. 392, ISBN-13:978-1-85617-662-0. McGinty, 1999, Multi-scale polycrystal plasticity, ASME Journal of Engineering Materials and Technology, 121, 203, 10.1115/1.2812367 McGinty, 2004, Application of multiscale crystal plasticity models to forming limit diagrams, ASME Journal of Engineering Materials and Technology, 126, 285, 10.1115/1.1753264 Menzel, 2000, On the formulation of higher gradient plasticity for single and polycrystals, Journal of the Mechanics and Physics of Solids, 48, 1777, 10.1016/S0022-5096(99)00024-1 Mesarovic, 2005, Energy, configurational forces and characteristic lengths associated with the continuum description of geometrically necessary dislocations, International Journal of Plasticity, 21, 1855, 10.1016/j.ijplas.2004.09.002 Meyers, 1982, A model for the effect of grain size on the yield stress of metals, Philosophical Magazine A, 46, 737, 10.1080/01418618208236928 Miller, 1998, Quasicontinuum simulation of fracture at the atomic scale, Modelling and Simulation in Materials Science and Engineering, 6, 607, 10.1088/0965-0393/6/5/008 Miller, 1998, Quasicontinuum models of fracture and plasticity, Engineering Fracture Mechanics, 61, 427, 10.1016/S0013-7944(98)00047-2 Mishin, 1999, Interatomic potentials for monoatomic metals from experimental data and ab initio calculations, Physical Review B, 59, 3393, 10.1103/PhysRevB.59.3393 Mishin, 2001, Structural stability and lattice defects in copper. Ab initio, tight-binding and embedded atom calculations, Physical Review B, 63, 224106, 10.1103/PhysRevB.63.224106 Moldovan, 2002, Role of grain rotation during grain growth in a columnar microstructure by mesoscale simulation, Acta Materialia, 50, 3397, 10.1016/S1359-6454(02)00153-2 Moosbrugger, 1989, On a class of kinematic hardening rules for nonproportional cyclic plasticity, ASME Journal of Engineering Materials and Technology, 111, 87, 10.1115/1.3226439 Moosbrugger, 1990, A rate dependent bounding surface model with a generalized image point for cyclic nonproportional viscoplasticity, Journal of the Mechanics and Physics of Solids, 38, 627, 10.1016/0022-5096(90)90026-Z Mroz, 1967, On the description of anisotropic work hardening, Journal of the Mechanics and Physics of Solids, 15, 163, 10.1016/0022-5096(67)90030-0 Mura, 1987 Muralidharan, 2003, A concurrent multiscale finite difference time domain/molecular dynamics method for bridging an elastic continuum to an atomic system, Modelling and Simulation in Materials Science and Engineering, 11, 487, 10.1088/0965-0393/11/4/306 Naghdi, 1993, A dynamical theory of structured solids. I. Basic developments, Philosophical Transactions of the Royal Society of London A, 345, 425, 10.1098/rsta.1993.0140 Nazarov, 1996, Random disclination ensembles in ultrafine-grained materials produced by severe plastic deformation, Scripta Materialia, 34, 729, 10.1016/1359-6462(95)00573-0 Needleman, 1980, Plastic creep flow effects in the diffusive cavitation of grain boundaries, Acta Metallurgica, 28, 1315, 10.1016/0001-6160(80)90001-2 Nicola, 2006, Plastic deformation of freestanding thin films: experiments and modeling, Journal of the Mechanics and Physics of Solids, 54, 2089, 10.1016/j.jmps.2006.04.005 Nicola, 2007, Surface versus bulk nucleation of dislocations during contact, Journal of the Mechanics and Physics of Solids, 55, 1120, 10.1016/j.jmps.2006.12.005 Nix, 1998, Indentation size effects in crystalline materials: a law for strain gradient plasticity, Journal of the Mechanics and Physics of Solids, 46, 411, 10.1016/S0022-5096(97)00086-0 Nuggehally, 2007, Adaptive model selection procedure for concurrent multiscale problems, Journal of Multiscale Computational Engineering, 5, 369, 10.1615/IntJMultCompEng.v5.i5.20 Nye, 1953, Some geometrical relations in dislocated crystals, Acta Metallurgica, 1, 153, 10.1016/0001-6160(53)90054-6 Ohashi, 2007, A multiscale approach for modeling scale-dependent yield stress in polycrystalline metals, International Journal of Plasticity, 23, 897, 10.1016/j.ijplas.2006.10.002 Ohno, 1990, Recent topics in constitutive modeling of cyclic plasticity and viscoplasticity, Applied Mechanics Reviews, 43, 283, 10.1115/1.3119155 Ohno, 2007, Higher-order stress and grain size effects due to self-energy of geometrically necessary dislocations, Journal of the Mechanics and Physics of Solids, 55, 1879, 10.1016/j.jmps.2007.02.007 Ohno, 1991, Transformation of a nonlinear kinematic hardening rule to a multisurface form under isothermal and nonisothermal conditions, International Journal of Plasticity, 7, 879, 10.1016/0749-6419(91)90023-R Olson, 1997, Computational design of hierarchically structured materials, Science, 277, 1237, 10.1126/science.277.5330.1237 Olson, 2000, Designing a new material world, Science, 288, 993, 10.1126/science.288.5468.993 Ortiz, 1999, Nonconvex energy minimization and dislocation structures in ductile single crystals, Journal of the Mechanics and Physics of Solids, 47, 397, 10.1016/S0022-5096(97)00096-3 Ortiz, 2000, A theory of subgrain dislocation structures, Journal of the Mechanics and Physics of Solids, 48, 2077, 10.1016/S0022-5096(99)00104-0 Ostoja-Starzewski, 1998, Random field models of heterogeneous materials, International Journal of Solids and Structures, 35, 2429, 10.1016/S0020-7683(97)00144-3 Ostoja-Starzewski, 2005, Scale effects in plasticity of random media: status and challenges, International Journal of Plasticity, 21, 1119, 10.1016/j.ijplas.2004.06.008 Ostoja-Starzewski, 2006, Material spatial randomness: from statistical to representative volume element, Probabilistic Engineering Mechanics, 21, 112, 10.1016/j.probengmech.2005.07.007 Paidar, 1984, A theory of the anomalous yield behaviour in L12 ordered alloys, Acta Metallurgica, 32, 435, 10.1016/0001-6160(84)90117-2 Pantleon, 2002, Formation of disorientations in dislocation structures during plastic deformation, Solid State Phenomena, 87, 73, 10.4028/www.scientific.net/SSP.87.73 Park, 2005, The bridging scale for two-dimensional atomistic/continuum coupling, Philosophical Magazine, 85, 79, 10.1080/14786430412331300163 Pollock, T.M., Allison, J., 2007. Committee on Integrated Computational Materials Engineering: developing a roadmap for a grand challenge in materials. National Materials Advisory Board, National Academy of Engineering <http://www7.nationalacademies.org/nmab/CICME_home_page.html>. Przybyla, C.P., McDowell, D.L., 2009. Microstructure-sensitive extreme value probabilities for high cycle fatigue of Ni-Base superalloy IN100. International Journal of Plasticity, doi:10.1016/j.ijplas.2009.08.001. Przybyla, 2010, Microstructure-sensitive modeling of high cycle fatigue, International Journal of Fatigue, 32, 512, 10.1016/j.ijfatigue.2009.03.021 Qin, 1992, Non-Schmid yield behavior in single crystals, Journal of the Mechanics and Physics of Solids, 40, 813, 10.1016/0022-5096(92)90005-M Qu, 2005, A finite-temperature dynamic coupled atomistic/discrete dislocation method, Modelling and Simulation in Materials Science and Engineering, 13, 1101, 10.1088/0965-0393/13/7/007 Racherla, 2007, Strain burst phenomena in the necking of a sheet that deforms by non-associated plastic flow, Modelling and Simulation in Materials Science and Engineering, 15, S297, 10.1088/0965-0393/15/1/S23 Rafii-Tabar, 1998, A multi-scale atomistic-continuum modeling of crack propagation in a two-dimensional macroscopic plate, Journal of Physics – Condensed Matter, 10, 2375, 10.1088/0953-8984/10/11/003 Ramasubramaniam, 2007, Coupled quantum-atomistic and quantum-continuum mechanics methods in materials research, MRS Bulletin, 32, 913, 10.1557/mrs2007.188 Rice, 1971, Inelastic constitutive relations for solids: an internal variable theory and its application to metal plasticity, Journal of the Mechanics and Physics of Solids, 19, 433, 10.1016/0022-5096(71)90010-X Rickman, 2006, Issues in the coarse-graining of dislocation energetics and dynamics, Scripta Materialia, 54, 735, 10.1016/j.scriptamat.2005.11.030 Roy, 2006, Size effects and idealized dislocation microstructure at small scales: predictions of a phenomenological model of mesoscopic field dislocation mechanics, Journal of the Mechanics and Physics of Solids, 54, 1711, 10.1016/j.jmps.2006.01.012 Roy, 2007, Phenomenological mesoscopic dislocation mechanics, lower-order gradient plasticity and transport of mean excess dislocation density, Modelling and Simulation in Materials Science and Engineering, 15, S167, 10.1088/0965-0393/15/1/S14 Rudd, 1998, Coarse-grained molecular dynamics and the atomic limit of finite elements, Physical Review B, 58, R5893, 10.1103/PhysRevB.58.R5893 Rudd, 2000, Concurrent coupling of length scales in solid state systems, Physica Status Solidi B – Basic Research, 217, 251, 10.1002/(SICI)1521-3951(200001)217:1<251::AID-PSSB251>3.0.CO;2-A Rudd, 2005, Coarse-grained molecular dynamics: nonlinear finite elements and finite temperature, Physical Review B, 72, 144104, 10.1103/PhysRevB.72.144104 Sakai, 1998, A novel deformation process in an aggregate: a candidate for superplastic deformation, Scripta Materialia, 38, 909, 10.1016/S1359-6462(97)00568-X Sankaran, 2007, Computing property variability of polycrystals induced by grain size and orientation uncertainties, Acta Materialia, 55, 2279, 10.1016/j.actamat.2006.11.025 Schroeter, B.M., 2001. Techniques for micro- and meso-scale measurements of rotation and stretch processes in metallic polycrystals. MS Thesis, GWW School of Mechanical Engineering, Georgia Institute of Technology. Schroeter, 2003, Measurement of deformation fields in polycrystalline OFHC copper, International Journal of Plasticity, 19, 1355, 10.1016/S0749-6419(02)00040-2 Schuh, 2005, Quantitative insight into dislocation nucleation from high-temperature nanoindentation experiments, Nature Materials, 4, 617, 10.1038/nmat1429 Sedlacek, 2005, Variational approach to subgrain formation, Zeitschrift Fur Metallkunde, 96, 602, 10.3139/146.101077 Sedlacek, 2003, The importance of being curved: bowing dislocations in a continuum description, Philosophical Magazine, 83, 3735, 10.1080/14786430310001600213 Seefeldt, 2001, Disclinations in large-strain plastic deformation and work-hardening, Review on Advanced Materials Science, 2, 44 Seefeldt, 2002, Modeling of plastic deformation by means of dislocation-disclination dynamics, Solid State Phenomena, 87, 93, 10.4028/www.scientific.net/SSP.87.93 Seefeldt, 2001, Modeling the initial stage of grain subdivision with the help of a coupled substructure and texture evolution algorithm, Acta Materialia, 49, 2129, 10.1016/S1359-6454(01)00126-4 Seefeldt, 2001, A disclination-based model for grain subdivision, Materials Science and Engineering A, 319–321, 192, 10.1016/S0921-5093(01)00994-7 Seepersad, C.C., Fernandez, M.G., Panchal, J.H., Choi, H.-J., Allen, J.K., McDowell, D.L., Mistree, F., 2004. Foundations for a systems-based approach for materials design. In: 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference. AIAA MAO, Albany, NY, pp. AIAA-2004–4300. Shen, 2003, Modeling dislocation network and dislocation–precipitate interaction at mesoscopic scale using phase field method, International Journal of Multiscale Computational Engineering, 1, 91, 10.1615/IntJMultCompEng.v1.i1.80 Shenoy, 1998, Quasicontinuum models of interfacial structure and deformation, Physical Review Letters, 80, 742, 10.1103/PhysRevLett.80.742 Shenoy, 1999, An adaptive finite element approach to atomic-scale mechanics – the quasicontinuum method, Journal of the Mechanics and Physics of Solids, 47, 611, 10.1016/S0022-5096(98)00051-9 Shenoy, 2008, Microstructure-sensitive modeling of polycrystalline IN 100, International Journal of Plasticity, 24, 1694, 10.1016/j.ijplas.2008.01.001 Shiari, 2005, Coupled atomistic/discrete dislocation simulations of nanoindentation at finite temperature, ASME Journal of Engineering Materials and Technology, 127, 358, 10.1115/1.1924561 Shilkrot, 2002, A coupled atomistic/continuum model of defects in solids, Journal of the Mechanics and Physics of Solids, 50, 2085, 10.1016/S0022-5096(02)00017-0 Shilkrot, 2004, Multiscale plasticity modeling: coupled atomistics and discrete dislocation mechanics, Journal of the Mechanics and Physics of Solids, 52, 755, 10.1016/j.jmps.2003.09.023 Shizawa, 1999, A thermodynamical theory of gradient elastoplasticity with dislocation density tensor, I: fundamentals. International Journal of Plasticity, 15, 899, 10.1016/S0749-6419(99)00018-2 Shizawa, 1999, ASME Journal of Engineering Materials and Technology, 121, 247, 10.1115/1.2812372 Spearot, 2005, Nucleation of dislocations from [001] bicrystal interfaces in aluminum, Acta Materialia, 53, 3579, 10.1016/j.actamat.2005.04.012 Spearot, 2007, Dislocation nucleation from bicrystal interfaces with dissociated structure, International Journal of Plasticity, 23, 143, 10.1016/j.ijplas.2006.03.008 Spearot, 2007, Tensile strength of 〈100〉 and 〈110〉 tilt bicrystal copper interfaces, Acta Materialia, 55, 705, 10.1016/j.actamat.2006.08.060 Suquet, 1987, vol. 272 Sutton, 1983, On the structure of tilt grain boundaries in cubic metals I. Symmetrical tilt boundaries, Philosophical Transactions of the Royal Society of London A, 309, 1, 10.1098/rsta.1983.0020 Sutton, 1983, On the structure of tilt grain boundaries in cubic metals II. Asymmetrical tilt boundaries, Philosophical Transactions of the Royal Society of London A, 309, 37, 10.1098/rsta.1983.0021 Sutton, 1983, On the structure of tilt grain boundaries in cubic metals. III. Generalizations of the structural study and implications for the properties of grain boundaries, Philosophical Transactions of the Royal Society of London A, 309, 55, 10.1098/rsta.1983.0022 Tadmor, 1996, Quasicontinuum analysis of defects in solids, Philosophical Magazine A, 73, 1529, 10.1080/01418619608243000 Tadmor, 1996, Mixed atomistic and continuum models of deformation in solids, Langmuir, 12, 4529, 10.1021/la9508912 Taguchi, 1993 Tschopp, 2007, Structures and energies of Σ3 asymmetric tilt grain boundaries, Philosophical Magazine, 87, 3147, 10.1080/14786430701255895 Tschopp, 2007, Tension-compression asymmetry in homogeneous dislocation nucleation in single crystal copper, Applied Physics Letters, 90, 121911 Tschopp, 2007, Asymmetric tilt grain boundary structure and energy in copper and aluminium, Philosophical Magazine, 87, 3871, 10.1080/14786430701455321 Tschopp, 2007, Structural unit and faceting description of summation Σ3 asymmetric tilt grain boundaries, Journal of Materials Science, 42, 7806, 10.1007/s10853-007-1626-6 Tschopp, 2008, Dislocation nucleation in Σ3 asymmetric tilt grain boundaries, International Journal of Plasticity, 24, 191, 10.1016/j.ijplas.2007.02.010 Tschopp, 2008, Grain boundary dislocation sources in nanocrystalline copper, Scripta Materialia, 58, 299, 10.1016/j.scriptamat.2007.10.010 Tschopp, 2008, Influence of single crystal orientation on homogeneous dislocation nucleation under uniaxial loading, Journal of the Mechanics and Physics of Solids, 56, 1806, 10.1016/j.jmps.2007.11.012 Tschopp, 2007, Atomistic simulations of homogeneous dislocation nucleation in single crystal copper, Modeling and Simulation in Materials Science and Engineering, 15, 693, 10.1088/0965-0393/15/7/001 Tschopp, M.A., Spearot, D.E., McDowell, D.L., 2008. Influence of grain boundary structure on dislocation nucleation in fcc metals. In: Dislocations in Solids, A Tribute to F.R.N. Nabarro (Ed.), J.P. Hirth, vol. 14, Elsevier Publ., pp. 43–139. Uchic, 2005, A methodology to investigate size scale effects in crystalline plasticity using uniaxial compression testing, Materials Science and Engineering A, 400–401, 268, 10.1016/j.msea.2005.03.082 Uchic, 2004, Sample dimensions influence strength and crystal plasticity, Science, 305, 986, 10.1126/science.1098993 Ungar, 2006, Subgrain size-distributions, dislocation structures, stacking- and twin faults and vacancy concentrations in SPD materials determined by X-ray line profile analysis, Materials Science Forum, 503–504, 133, 10.4028/www.scientific.net/MSF.503-504.133 Ungar, 2005, Vacancy concentrations determined from the diffuse background scattering of X-rays in plastically deformed copper, Zeitschrift fur Metallkunde, 96, 578, 10.3139/146.101073 Ungar, 2007, Vacancy production during plastic deformation in copper determined by in situ X-ray diffraction, Materials Science and Engineering A, 462, 398, 10.1016/j.msea.2006.03.156 Van Swygenhoven, 1999, Microscopic description of plasticity in computer generated metallic nanophase samples: A comparison between Cu and Ni, Acta Materialia, 47, 3117, 10.1016/S1359-6454(99)00109-3 Vernerey, 2007, Multi-scale micromorphic theory for hierarchical materials, Journal of the Mechanics and Physics of Solids, 55, 2603, 10.1016/j.jmps.2007.04.008 Viatkina, 2007, Modelling of the internal stress in dislocation cell structures, European Journal of Mechanics A/Solids, 26, 982, 10.1016/j.euromechsol.2007.05.001 Walgraef, 1985, On the formation and stability of dislocation patterns, I–III, International Journal of Engineering Science, 12, 1351, 10.1016/0020-7225(85)90113-2 Wang, 2006, Microstructure-based multiscale constitutive modeling of γ–γ′ Ni-base superalloys, International Journal of Multiscale Computational Engineering, 4, 663, 10.1615/IntJMultCompEng.v4.i5-6.70 Wang, W., Zhong, Y., Lu, K., Lu, L., McDowell, D.L., Zhu, T., 2009. Strength fluctuations and size Effects in nanoindentation. Physical Review Letters, submitted for publication. Warner, 2006, Atomistic based continuum investigation of plastic deformation in nanocrystalline copper, International Journal of Plasticity, 22, 754, 10.1016/j.ijplas.2005.04.014 Weinan, 2001, Matching conditions in atomistic-continuum modeling of materials, Physical Review Letters, 8713, 135501 Zaichenko, 1999, Disclination mechanism of plastic deformation of nanocrystalline materials, Interface Science, 7, 57, 10.1023/A:1008714612121 Zaiser, 2001, Statistical modeling of dislocation systems, Material Science and Engineering A, 309–310, 304, 10.1016/S0921-5093(00)01676-2 Zbib, 1992, On the gradient-dependent theory of plasticity and shear banding, Acta Mechanica, 92, 209, 10.1007/BF01174177 Zbib, 2002, A multiscale model of plasticity, International Journal of Plasticity, 18, 1133, 10.1016/S0749-6419(01)00044-4 Zbib, 2004, Recent advances in multiscale modeling of plasticity, International Journal of Plasticity, 20 Zbib, 2002, A multiscale model of plasticity based on discrete dislocation dynamics, ASME Journal of Engineering Materials and Technology, 124, 78, 10.1115/1.1421351 Zehetbauer, 2005, Vacancies in plastically deformed copper, Zeitschrift fur Metallkunde/Materials Research and Advanced Techniques, 96, 1044 Zhou, 2005, Thermomechanical continuum representation of atomistic deformation at arbitrary size scales, Proceedings of the Royal Society A, 461, 3437, 10.1098/rspa.2005.1468 Zhou, 2002, Equivalent continuum for dynamically deforming atomistic particle systems, Philosophical Magazine A, 82, 2547, 10.1080/01418610208240052 Zhou, 2005, Coarse-grained free-energy-functional treatment of quasistatic multiscale processes in heterogeneous materials, Journal of Chemical Physics, 123, 164109, 10.1063/1.2064607 Zhu, 2004, Atomistic study of dislocation loop emission from a crack tip, Physical Review Letters, 93, 025503, 10.1103/PhysRevLett.93.025503 Zhu, 2004, Predictive modeling of nanoindentation-induced homogeneous dislocation nucleation in copper, Journal of the Mechanics and Physics of Solids, 52, 691, 10.1016/j.jmps.2003.07.006 Zhu, 2007, Interfacial plasticity governs strain rate sensitivity and ductility in nanostructured metals, Proceedings of the National Academy of Sciences of the United States of America, 104, 3031, 10.1073/pnas.0611097104 Zhu, 2008, Temperature and strain-rate dependence of surface dislocation nucleation, Physical Review Letters, 100, 025502, 10.1103/PhysRevLett.100.025502 Ziegler, H., 1983. An introduction to thermomechanics. In: Becker, E., Budiansky, B., Koiter, W.T., Lauwerier, H.A. (Eds.), North Holland Series in Applied Mathematics and Mechanics, vol. 21, second ed. North Holland, Amsterdam, New York. Zohdi, 2003, Constrained inverse formulations in random material design, Computer Methods in Applied Mechanics and Engineering, 192, 3179, 10.1016/S0045-7825(03)00345-1