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Multilevel crystal plasticity models of single- and polycrystals. Direct models

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The paper continues the review of works on the development and application of multiscale physical models to analyzing the behavior of single- and polycrystals under severe plastic deformation. Unlike mathematical models of plasticity, this class of models operates with meso- and microstructures of deformed material and allows analysis of their evolution. The recently much used so-called direct models that are based on crystal plasticity theories and numerical methods are discussed.

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References

  1. Trusov, P.V. and Shveykin, A.I., Multilevel Crystal Plasticity Models of Single- and Polycrystals. Statistical Models, Phys. Mesomech., 2013, vol. 16, no. 1, pp. 23–33.

    Article  Google Scholar 

  2. Hill, R. and Rice, J.R., Constitutive Analysis of Elastic-Plastic Crystals at Arbitrary Strain, J. Mech. Phys. Solids, 1972, vol. 20, pp. 401–413.

    Article  ADS  MATH  Google Scholar 

  3. Miyamoto, H., Sumikawa, M., and Miyoshi, T., Interpretation of Mechanical Behavior of Pure Aluminum in Terms of Microstructures, Proc. of the 1971 Conf. on Mechanical Behavior of Materials, Kyoto, Japan: Soc. Mater. Sci., 1972, pp. 140–151.

    Google Scholar 

  4. Kalidindi, S.R., Bronkhorst, CA., and Anand, L., Crystallographic Texture Evolution in Bulk Deformation Processing of FCC Metals, J. Mech. Phys. Solids, 1992, vol. 40, no. 3, pp. 537–569.

    Article  ADS  Google Scholar 

  5. Kalidindi, S.R. and Anand, L., Macroscopic Shape Change and Evolution of Crystallographic Texture in Pretextured FCC Metals, J. Mech. Phys. Solids, 1994, vol. 42, no. 3, pp. 459–490.

    Article  ADS  Google Scholar 

  6. Staroselsky, A. and Anand, L., Inelastic Deformation of Polycrystalline Face Centered Cubic Materials by Slip and Twinning, J. Mech. Phys. Solids, 1998, vol. 46, no. 4, pp. 671–696.

    Article  ADS  MATH  Google Scholar 

  7. Van Houtte, P., Simulation of the Rolling and Shear Texture of Brass by the Taylor Theory Adapted for Mechanical Twinning, Acta Metall, 1978, vol. 26, pp. 591–604.

    Article  Google Scholar 

  8. Kothari, M. and Anand, L., Elasto-Viscoplastic Constitutive Equations for Polycrystalline Metals: Application to Tantalum, J. Mech. Phys. Solids, 1998, vol. 46, no. 1, pp. 51–83.

    Article  ADS  MATH  Google Scholar 

  9. Kocks, U.F., Argon, A.S., and Ashby, M.F., Thermodynamics and Kinetics of Slip, Prog. Mater. Sci., 1975, vol. 19, pp. 141–145.

    Google Scholar 

  10. Asaro, R J. and Needleman, A., Texture Development and Strain Hardening in Rate Dependent Polycrystals, Acta Metall, 1985, vol. 33. no. 6, pp. 923–953.

    Google Scholar 

  11. Bate, P., Modeling Deformation Microstructure with the Crystal Plasticity Finite-Element Method, Phil. Trans. R. Soc. Lond. A, 1999, vol. 357, pp. 1589–1601.

    Article  ADS  Google Scholar 

  12. Steck, E.A. and Harder, J., Finite Element Simulation of Local Plastic Flow in Polycrystals, IUTAM Symposium on Micro- and Macrostructural Aspects of Thermoplasticity, Bruhns, O.T. and Stein, E., Eds., Dordrecht: Kluwer Academic Publishers, 1999, pp. 79–88.

    Google Scholar 

  13. Raabe, D., Zhao, Z., and Mao, W., On the Dependence of In-grain Subdivision and Deformation Texture of Aluminum on Grain Interaction, Acta Mater., 2002, vol. 50, pp. 4379–4394.

    Article  Google Scholar 

  14. Turner, T.J., Miller, M.P., and Barton, N.R., The Influence of Crystallographic Texture and Slip System Strength on Deformation Induced Shape Changes in AA 7050 Thick Plate, Mech. Mater., 2002, vol. 34, pp. 605–625.

    Article  Google Scholar 

  15. Cailletaud, G., Diard, O., Feyel, F., and Forest, S., Computational Crystal Plasticity: From Single Crystal to Homogenized Polycrystal, Technische Mechanik, 2003, vol. 23, no. 2–4, pp. 130–145.

    Google Scholar 

  16. Diard, O., Leclercq, S., Rousselier, G., and Cailletaud, G., Evaluation of Finite Element Based Analysis of 3D Multi-crystalline Aggregates Plasticity. Application to Crystal Plasticity Model Identification and the Study of Stress and Strain Fields near Grain Boundaries, Int. J. Plasticity, 2005, vol. 21, pp. 691–722.

    Article  MATH  Google Scholar 

  17. Clayton, J.D. and McDowell, D.L., A Multiscale Multiplicative Decomposition for Elastoplasticity of Polycrystals, Int. J. Plasticity, 2003, vol. 19, pp. 1401–1444.

    Article  MATH  Google Scholar 

  18. Bower, A.F. and Wininger, E., A Two-Dimensional Finite Element Method for Simulating the Constitutive Response and Microstructure of Polycrystals during High Temperature Plastic Deformation, J. Mech. Phys. Solids, 2004, vol. 52, pp. 1289–1317.

    Article  ADS  MATH  Google Scholar 

  19. Erieau, P. and Rey, C, Modeling of Deformation and Rotation Bands and of Deformation Induced Grain Boundaries in IF Steel Aggregate during Large Plane Strain Compression, Int. J. Plasticity, 2004, vol. 20, pp. 1763–1788.

    Article  MATH  Google Scholar 

  20. Raabe, D., Zhao, Z., and Roters, F., Study on the Orientational Stability of Cube-oriented FCC Crystals under Plane Strain by Use of a Texture Component Crystal Plasticity Finite Element Method, Scripta Mater., 2004, vol. 50, pp. 1085–1090.

    Article  Google Scholar 

  21. Roters, F., Application of Crystal Plasticity FEM from Single Crystal to Bulk Polycrystal, Comput. Mater. Sci., 2005, vol. 32, pp. 509–517.

    Article  Google Scholar 

  22. Anand, L., Single-crystal Elasto-Viscoplasticity: Application to Texture Evolution in Polycrystalline Metals at Large Strains, Comput. Meth. Appl. Mech., 2004, vol. 193, pp. 5359–5383.

    Article  MathSciNet  MATH  Google Scholar 

  23. Prasannavenkatesan, R., Li, B.Q., Field, D.P., and Weiland, H., A Parallel Macro/Micro Elastoplasticity Model for Aluminum Deformation and Comparison with Experiments, Metal. Mater. Trans. A, 2005, vol. 36, pp. 241–256.

    Article  Google Scholar 

  24. Tikhovskiy, I., Raabe, D., and Roters, F., Simulation of the Deformation Texture of a 17% Cr Ferritic Stainless Steel Using the Texture Component Crystal Plasticity Finite Element Method Considering Texture Gradients, Scripta Mater., 2006, vol. 54, pp. 1537–1542.

    Article  Google Scholar 

  25. Hartig, Ch., and Mecking, H., Finite Element Modelling of Two Phase Fe-Cu Polycrystals, Comput. Mater. Sci., 2005, vol. 32, pp. 370–377.

    Article  Google Scholar 

  26. Hartig, Ch. and Mecking, H., Crystal Plastic Finite Element Simulation of Fe-Cu Polycrystals, Proc. ICOTOM 14. Mater. Sci. Forum, 2005, vol. 495–497, pp. 1621–1626.

    Article  Google Scholar 

  27. Buchheit, T.E., Wellman, G.W., and Battaile, C.C., Investigating the Limits of Polycrystal Plasticity Modeling, Int. J. Plasticity, 2005, vol. 21, pp. 221–249.

    Article  MATH  Google Scholar 

  28. Kovač, M. and Cizelj, L., Modeling Elasto-Plastic Behavior of Polycrystalline Grain Structure of Steels at Mesoscopic Level, Nucl. Eng. Design., 2005, vol. 235, pp. 1939–1950.

    Article  Google Scholar 

  29. Peeters, B., Kalidindi, S.R., Teodosiu, C, van Houtte, P., and Aernoudt, E., A Theoretical Investigation of the Influence of Dislocation Sheets on Evolution of Yield Surfaces in Single-Phase b.c.c. Polycrystalls, J. Mech. Phys. Solids, 2002, vol. 50(4), pp. 783–807.

    Article  Google Scholar 

  30. Walde, T. and Riedel, H., Interactive Texture- and Finite-Element Simulation Including the Bauschinger Effect, Proc. ICOTOM 14. Mater. Sci. Forum, 2005, vol. 495–497, pp. 1523–1528.

    Article  Google Scholar 

  31. Delannay, L., Jacques, P.J., and Kalidindi, S.R., Finite Element Modeling of Crystal Plasticity with Grains Shaped as Truncated Octahedrons, Int. J. Plasticity, 2006, vol. 22, pp. 1879–1898.

    Article  MATH  Google Scholar 

  32. Zaafarani, N., Raabe, D., Singh, R.N., Roters, F., and Zaefferer, S., Three-Dimensional Investigation of the Texture and Microstructure Below a Nanoindent in a Cu Single Crystal Using 3D EBSD and Crystal Plasticity Finite Element Simulations, Acta Mater., 2006, vol. 54, pp. 1863–1876.

    Article  Google Scholar 

  33. Li, W., Yang, H., and Sun, Z.C., Explicit Incremental-Up-date Algorithm for Modeling Crystal Elasto-Viscoplastic Response in Finite Element Simulation, Trans. Nonferrous Met. Soc. China, 2006, vol. 16, pp. S624–S630.

    Article  Google Scholar 

  34. Kuchnicki, S.N., Cuitino, A.M., and Radovitzky, R.A., Efficient and Robust Constitutive Integrators for Single-Crystal Plasticity Modeling, Int. J. Plasticity, 2006, vol. 22, pp. 1988–2011.

    Article  MATH  Google Scholar 

  35. Terada, K. and Watanabe, I., Computational Aspects of Tangent Moduli Tensors in Rate-Independent Crystal Elastoplasticity, Comput. Mech., 2007, vol. 40, pp. 497–511.

    Article  MATH  Google Scholar 

  36. Ocenarsek, J., Ripoll, M.R., Weygand, S.M., and Riedel, H., Multi-Grain Finite Element Model for Studying the Wire Drawing Process, Comput. Mater. Sci., 2007, vol. 39, pp. 23–28.

    Article  Google Scholar 

  37. Asaro, R J., Micromechanics of Crystals and Polycrystals, Adv. Appl. Mech., 1983, vol. 23, pp. 1–115.

    Article  Google Scholar 

  38. Si, L.-Y., Lu, C, Tieu, K., and Liu, X.-H., Simulation of Polycrystalline Aluminum Tensile Test with Crystal Plasticity Finite Element Method, Trans. Nonferrous Met. Soc. China, 2007, vol. 17, pp. 1412–1416.

    Article  Google Scholar 

  39. Si, L.-Y, Lu, C, Huynh, N.N., Tieu, K., and Liu, X.-H., Simulation of Rolling Behaviour of Cubic Oriented Al Single Crystal with Crystal Plasticity FEM, J. Mater. Process. Tech., 2008, vol. 201, no. 1–3, pp. 79–84.

    Article  Google Scholar 

  40. Watanabe, I., Terada, K., de Souza Neto, E.A., and Peric, D., Characterization of Macroscopic Tensile Strength of Polycrystalline Metals with Two-Scale Finite Element Analysis, J. Mech. Phys. Solids, 2008, vol. 56, pp. 1105–1125.

    Article  MathSciNet  MATH  Google Scholar 

  41. Bieler, T.R., Eisenlohr, P., Roters, F., Kumar, D., Mason, D.E., Crimp, M.A., and Raabe, D., The Role of Heterogeneous Deformation on Damage Nucleation at Grain Boundaries in Single Phase Metals, Int. J. Plasticity, 2009, vol. 25, no. 9, pp. 1655–1683.

    Article  MATH  Google Scholar 

  42. Hekansson, P., Wallin, M., and Ristinmaa, M., Prediction of Stored Energy in Polycrystalline Materials during Cyclic Loading, Int. J. Solids Struct., 2008, vol. 45, pp. 1570–1586.

    Article  Google Scholar 

  43. Rezvanian, O., Zikry, M.A., and Rajendran, A.M., Micro-structural Modeling in f.c.c. Crystalline Materials in a Unified Dislocation-Density Framework, Mater. Sci. Eng. A, 2008, vol. 494, p. 80–85.

    Article  Google Scholar 

  44. De Souza Neto, E.A. and Feijòo, R.A., On the Equivalence between Spatial and Naterial Volume Averaging of Stress in Large Strain Multi-scale Solid Constitutive Models, Mech. Mater., 2008, vol. 40, pp. 803–811.

    Article  Google Scholar 

  45. Haldrup, K., McGinty, R.D., and McDowell, D.L., Effects of Constraints on Lattice Re-orientation and Strain in Poly-crystal Plasticity Simulations, Comput. Mater. Sci., 2009, vol. 44, pp. 1198–1207.

    Article  Google Scholar 

  46. Prakash, A., Weygand, S.M., and Riedel, H., Modeling the Evolution of Texture and Grain Shape in Mg Alloy AZ31 Using the Crystal Plasticity Finite Element Method, Comp. Mater. Sci., 2009, vol. 45, pp. 744–750.

    Article  Google Scholar 

  47. Saai, A., Louche, H., Tabourot, L., and Chang, HJ., Experimental and Numerical Study of the Thermo-Mechanical Behavior of Al Bi-crystal in Tension Using Full Field Measurements and Micromechanical Modeling, Mech. Mater., 2010, vol. 42, pp. 275–292.

    Article  Google Scholar 

  48. Dingreville, R., Battaile, C.C., Brewer, L.N., Holm, E.A., and Boyce, B.L., The Effect of Microstructural Representation on Simulations of Microplastic Ratcheting, Int. J. Plasticity, 2010, vol. 26, pp. 617–633.

    Article  MATH  Google Scholar 

  49. Quey, R., Dawson, P.R., and Barbe, F., Large-scale 3D Random Polycrystals for the Finite Element Method: Generation, Meshing and Remeshing, Comput. Meth. Appl. Mech. Engng, 2011.

    Google Scholar 

  50. Mach, J.C., Beaudoin, A J., and Acharya, A., Continuity in the Plastic Strain Rate and its Influence on Texture Evolution, J. Mech. Phys. Solids, 2010, vol. 58, pp. 105–128.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  51. Choi, S.-H., Kim, D.H., Lee, H.W., and Shin, E J., Simulation of Texture Evolution and Macroscopic Properties in Mg Alloys Using the Crystal Plasticity Finite Element Method, Mater. Sci. Eng. A, 2010, vol. 527, pp. 1151–1159.

    Article  Google Scholar 

  52. Deshpande, V.S., Needleman, A., and van der Giessen, E., Finite Strain Discrete Dislocation Plasticity, J. Mech. Phys. Solids, 2003, vol. 51, pp. 2057–2083.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  53. Hassing, P.M., Fang, H., and Wang, Q., Identification of Material Parameters for McGinty’s Model Using Adaptive RBFs and Optimization, Struct. Multidisc. Optim., 2010, vol. 42, pp. 233–242.

    Article  Google Scholar 

  54. Groh, S., Marin, E.B., Horstemeyer, M.F., and Zbib, H.M., Multiscale Modeling of the Plasticity in an Aluminum Single Crystal, Int. J. Plasticity, 2009, vol. 25, no. 8, pp. 1456–1473.

    Article  ADS  MATH  Google Scholar 

  55. Fajoui, J., Gloaguen, D., Courant, B., and Guillen, R., Micromechanical Modelling of the Elastoplastic Behavior of Metallic Material under Strain-Path Changes, Comput. Mech., 2009, vol. 44, pp. 285–296.

    Article  MATH  Google Scholar 

  56. Madej, L., Hodgson, P.D., and Pietrzyk, M., Development of the Multi-scale Analysis Model to Simulate Strain Localization Occurring during Material Processing, Arch. Comput. Methods Eng., 2009, vol. 16, pp. 287–318.

    Article  MathSciNet  Google Scholar 

  57. Tinga, T., Brekelmans, W.A.M., and Geers, M.G.D., A Strain-Gradient Crystal Plasticity Framework for Single Crystal Nickel-Based Superalloys, Report National Aerospace Laboratory NLR-TP-2005-628, Amsterdam, 2005.

    Google Scholar 

  58. Balokhonov, R.R., Hierarchical Modelling of Deformation and Fracture of Materials with Composite Structure, Doctoral (Phys.-Math.) Dissertation, Tomsk: ISPMS SB RAS, 2008.

    Google Scholar 

  59. Romanova, V.A., 3D Modelling of Deformation and Fracture in Heterogeneous Materials, Doctoral (Phys.-Math.) Dissertation, Tomsk: ISPMS, SB RAS, 2008.

    Google Scholar 

  60. Bertram, A., Böhlke, T., and Kraska, M., Texture Development of Aluminum Polycrystals under Finite Plastic Deformations, IUTAM Symposium on Micro- and Macrostructural Aspects of Thermoplasticity, Bruhns, O.T. and Stein, E., Eds., Dordrecht: Kluwer Academic Publishers, 1999, pp. 127–136.

    Google Scholar 

  61. Bate, P.S. and da Quinta, F.J., Texture Development in the Cold Rolling of IF Steel, Mater. Sci. Engng. A, 2004, vol. 380, pp. 365–377.

    Article  Google Scholar 

  62. Li, S., Kalidindi, S.R., and Beyerlein, I J., A Crystal Plasticity Finite Element Analysis of Texture Evolution in Equal Channel Angular Extrusion, Mater. Sci. Engng. A, 2005, vol. 410–411, pp. 207–212.

    Article  Google Scholar 

  63. Kalidindi, S.R., Donohue, B.R., and Li, S., Modeling Texture Evolution in Equal Channel Angular Extrusion Using Crystal Plasticity Finite Element Models, Int. J. Plasticity, 2009, vol. 25, pp. 768–779.

    Article  MATH  Google Scholar 

  64. Inal, K. and Neale, K.W., High Performance Computational Modeling of Microstructural Phenomena in Polycrystalline Metals, Advances in Engineering Structures, Mechanics & Construction, Pandey, M., et al., Eds., Dordrecht: Springer, 2006, pp. 583–593.

    Chapter  Google Scholar 

  65. Lee, M.-G., Wang, J., and Anderson, P.M., Texture Evolution Maps for Upset Deformation of Body-Centered Cubic Metals, Mater. Sci. Engng. A, 2007, vol. 463, pp. 263–270.

    Article  Google Scholar 

  66. Zhao, Z., Kuchnicki, S., Radovitzky, R., and Cuitino, A., Influence of In-grain Mesh Resolution on the Prediction of Deformation Textures in FCC Polycrystals by Crystal Plasticity FEM, Acta Mater., 2007, vol. 55, pp. 2361–2373.

    Article  Google Scholar 

  67. Van Houtte, P., Kanjarla, A.K., van Bael, A., Seefeldt, M., and Delannay, L., Multiscale Modelling of the Plastic Anisotropy and Deformation Texture of Polycrystalline Materials, Eur. J. Mech A. Solids, 2006, vol. 25, pp. 634–648.

    Article  MathSciNet  MATH  Google Scholar 

  68. Van Houtte1, P., van Bael, A., Seefeldt, M., and Delannay, L., The Application of Multiscale Modelling for the Prediction of Plastic Anisotropy and Deformation Textures, Proc. ICOTOM 14. Mater. Sci. Forum, 2005, vol. 495–497, pp. 31–44.

    Article  Google Scholar 

  69. Peeters, B., Seefeldt, M., Teodosiu, C, van Houtte, P., and Aernoudt, E., Work Hardening-Softening Behaviour of BCC Polycrystalls during Changing Strain Paths: I. An Integrated Model Based on Substructure and Texture Evolution, and its Prediction of the Stress-Strain of an IF Steel during Two-Stage Strain Paths, Acta Mater., 2001, vol. 49, pp.1607–1619.

    Article  Google Scholar 

  70. Peeters, B., Bacroix, B., Teodosiu, C, van Houtte, P., and Aernoudt, E., Work Hardening-Softening Behaviour of BCC Polycrystalls during Changing Strain Paths: II. TEM Observations of Dislocation Sheets in an IF Steel during Two-Stage Strain Paths and Their Representation in Terms of Dislocation Densities, Acta Mater., 2001, vol. 49, pp. 1621–1632.

    Article  Google Scholar 

  71. Gérard, C., Bacroix, B., Bornert, M., Cailletaud, G., Crépin, J., and Leclercq, S., Hardening Description for FCC Materials under Complex Loading Paths, Comput. Mater. Sci., 2009, vol. 45, pp. 751–755.

    Article  Google Scholar 

  72. Semiatin, S.L., Salem, A.A., and Saran, M J., Models for Severe Plastic Deformation by Equal-Channel Angular Extrusion, JOM, 2004, October, pp. 69–77.

    Google Scholar 

  73. Guan, Y., Pourboghrat, F., and Barlat, F., Finite Element Modeling of Tube Hydroforming of Polycrystalline Aluminum Alloy Extrusions, Int. J. Plasticity, 2006, vol. 22, pp. 2366–2393.

    Article  MATH  Google Scholar 

  74. Gambin, W., Plasticity of Crystals with Interacting Slip Systems, Eng. Trans., 1991, vol. 39, pp. 303–324.

    MathSciNet  Google Scholar 

  75. Gambin, W., Refined Analysis of Elastic-Plastic Crystals, Int. J. Solids Struct, 1992, vol. 29, pp. 2013–2021.

    Article  MATH  Google Scholar 

  76. Yang, D.Y and Kim, K.J., Design of Processes and Products through Simulation of Three-Dimensional Extrusion, J. Mater. Process. Tech., 2007, vol. 191, pp. 2–6.

    Article  Google Scholar 

  77. Li, S., Orientation Stability in Equal Channel Angular Extrusion. Part I: Face-Centered Cubic and Body-Centered Cubic Materials, Acta Mater., 2008, vol. 56, pp. 1018–1030.

    Article  Google Scholar 

  78. Li, S., Orientation Stability in Equal Channel Angular Extrusion. Part II: Hexagonal Close-Packed Materials, Acta Mater., 2008, vol. 56, pp. 1031–1043.

    Article  Google Scholar 

  79. Physical Mesomechanics of Heterogeneous Media and Computer-Aided Design of Materials, Panin, V.E., Ed., Cambridge: Cambridge Interscience Publishing, 1998.

    Google Scholar 

  80. Adams, B.L., Henrie, A., Henrie, B., Lyon, M., Kalidindi, S.R., and Garmestani, H., Microstructure-Sensitive Design of a Compliant Beam, J. Mech. Phys. Solids, 2001, vol. 49, no. 8, pp. 1639–1663.

    Article  ADS  MATH  Google Scholar 

  81. Kalidindi, S.R., Houskamp, J., Proust, G., and Duvvuru, H., Microstructure Sensitive Design with First Order Homogenization Theories and Finite Element Codes, Proc. ICOTOM 14. Mater. Sci. Forum, 2005, vol. 495–497, pp. 23–30.

    Article  Google Scholar 

  82. Sundararaghavan, V and Zabaras, N., Design of Microstructure-Sensitive Properties in Elasto-Viscoplastic Polycrystals Using Multi-scale Homogenization, Int. J. Plasti-city, 2006, vol. 22, no. 10, pp. 1799–1824.

    Article  MATH  Google Scholar 

  83. Proust, G. and Kalidindi, S.R., Procedures for Construction of Anisotropic Elastic-Plastic Property Closures for Face-Centered Cubic Polycrystals Using First-Order Bounding Relations, J. Mech. Phys. Solids, 2006, vol. 54, pp. 1744–1762.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  84. Nakamachi, E., Kuramae, H., Sakamoto, H., and Mori-moto, H., Process Metallurgy Design of Aluminum Alloy Sheet Rolling by Using Two-scale Finite Element Analysis and Optimization Algorithm, Int. J. Mech. Sci., 2010, vol. 52, pp. 146–157.

    Article  Google Scholar 

  85. Habraken, A.M., Modelling the Plastic Anisotropy of Metals, Arch. Comput. Meth. Engng., 2004, vol. 11, no. 1, pp. 3–96.

    Article  MATH  Google Scholar 

  86. McDowell, D.L., Viscoplasticity of Heterogeneous Metallic Materials, Mater. Sci. Eng. R, 2008, vol. 62, pp. 67–123.

    Article  Google Scholar 

  87. Horstemeyer, M.F., Multiscale Modeling: A Review, Practical Aspects of Computational Chemistry, Leszczynski, J. and Shukla, M.K., Eds., Dordrecht: Springer Science Business Media B.V., 2009, pp. 87–135.

    Chapter  Google Scholar 

  88. Roters, F., Eisenlohr, P., Hantcherli, L., Tjahjanto, D.D., Bieler, T.R., and Raabe, D., Overview of Constitutive Laws, Kinematics, Homogenization and Multiscale Methods in Crystal Plasticity Finite-Element Modeling: Theory, Experiments, Applications, Acta Mater., 2010, vol. 58, pp. 1152–1211.

    Article  Google Scholar 

  89. McDowell, D.L., A Perspective on Trends in Multiscale Plasticity, Int. J. Plasticity, 2010, vol. 26, no. 9, pp. 1280–1309.

    Article  MATH  Google Scholar 

  90. Rybin, V.V., High Plastic Strains and Fracture of Metals, Moscow: Metallurgiya, 1986.

    Google Scholar 

  91. Rybin, V.V., Mechanisms of Mesostructure Formation under Developed Plastic Deformation, Voprosy Materialoved., 2002, vol. 29, no. 1, pp. 11–33.

    MathSciNet  Google Scholar 

  92. Rybin, V.V., Mechanisms of Mesostructure Formation at Developed Plastic Deformation, Voprosy Materialoved., 2003, vol. 33, no. 1, pp. 9–28.

    MathSciNet  Google Scholar 

  93. Trusov, P.V. and Volegov, P.S., Crystal Plasticity Theories and Their Applications to the Description of Inelastic Deformations of Materials. Part 1: Rigid-Plastic and Elastoplastic Theories, PNRPU Mechanics Bulletin, 2011, no. 1, pp. 5–45.

    Google Scholar 

  94. Trusov, P.V. and Volegov, P.S., Crystal Plasticity Theories and Their Applications to the Description of Inelastic Deformations of Materials. Part 2: Viscoplastic and Elastoviscoplastic Theories, PNRPU Mechanics Bulletin, 2011, no. 2, p. 101–131.

    Google Scholar 

  95. Trusov, P.V. and Volegov, P.S., Crystal Plasticity Theories and Their Applications to the Description of Inelastic Deformations of Materials. Part 3: Hardening and Gradient Theories, PNRPU Mechanics Bulletin, 2011, no. 3, pp. 146–197.

    Google Scholar 

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Original Russian Text © P.V. Trusov, A.I. Shveykin, 2011, published in Fizicheskaya Mezomekhanika, 2011, Vol. 14, No. 5, pp. 5–30.

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Trusov, P.V., Shveykin, A.I. Multilevel crystal plasticity models of single- and polycrystals. Direct models. Phys Mesomech 16, 99–124 (2013). https://doi.org/10.1134/S1029959913020021

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