Abo Bibliothek: Guest
Digitales Portal Digitale Bibliothek eBooks Zeitschriften Referenzen und Berichte Forschungssammlungen
Nanoscience and Technology: An International Journal
ESCI SJR: 0.228 SNIP: 0.484 CiteScore™: 0.37

ISSN Druckformat: 2572-4258
ISSN Online: 2572-4266

Nanoscience and Technology: An International Journal

Formerly Known as Nanomechanics Science and Technology: An International Journal

DOI: 10.1615/NanoSciTechnolIntJ.2018028673
pages 1-20


Alexey I. Shveykin
Perm National Research Polytechnic University, 29 Komsomolsky Ave., Perm, 614990, Russian Federation
Peter V. Trusov
Perm National Research Polytechnic University, 29 Komsomolsky Ave., Perm, 614990, Russian Federation


Multilevel models of materials give an explicit description of the physical mechanisms, evolution of material structure, and physical and mechanical properties in inelastic deformation. This allows one to apply such models to improve the existing technologies of mechanical treatment (including the ones for submicrocrystalline and nanocrystalline materials) and develop some new ones. A key point in multilevel modeling of polycrystalline metals and alloys is the formulation of kinematic and constitutive relations at the mesolevel (the level of individual crystallites), which would apply to large displacement gradients peculiar to most processes of thermomechanical treatment of metals and alloys. Various formulations of the constitutive mesolevel models used in multilevel models of polycrystalline metals and alloys are considered. These are the relations in the unloaded configuration in the finite form, which are based on the motion decomposition with an explicit separation of the motion of the moving coordinate system, and the relations written in the rate form in the current configuration. The relationships used in these formulations to describe the rotations of the crystallite lattices are analyzed and compared. The analysis reveals the equivalence or closeness (in the sense of the response to be estimated) of the spins under consideration (with the exception of the logarithmic spin). The results of numerical calculations carried out for a polycrystal under arbitrarily chosen kinematic impacts lend support to the analytical conclusions.


  1. Amodeo, J., Dancette, S., and Delannay, L., Atomistically-Informed Crystal Plasticity in MgO Poly-crystals under Pressure, Int. J. Plasticity, vol. 82, pp. 177-191, 2016.

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

  3. Ardeljan, M., Beyerlein, I.J., and Knezevic, M., A Dislocation Density based Crystal Plasticity Finite Element Model: Application to a Two-Phase Polycrystalline HCP/BCC Composites, J. Mech. Phys. Solids, vol. 66, pp. 16-31, 2014.

  4. Ardeljan, M., Beyerlein, I.J., McWilliams, B.A., and Knezevic, M., Strain Rate and Temperature Sensitive Multi-Level Crystal Plasticity Model for Large Plastic Deformation Behavior: Application to AZ31 Magnesium Alloy, Int. J. Plasticity, vol. 83, pp. 90-109, 2016.

  5. Bronkhorst, C.A., Kalidindi, S.R., and Anand, L., Polycrystalline Plasticity and the Evolution of Crystallographic Texture in FCC Metals, Phil. Trans. Roy. Soc. London A: Math. Phys. Eng. Sci., vol. 341, no. 1662, pp. 443-477, 1992.

  6. Bruhns, O.T., Xiao, H., and Meyers, A., Some Basic Issues in Traditional Eulerian Formulations of Finite Elastoplasticity, Int. J. Plasticity, vol. 19, pp. 2007-2026, 2003.

  7. 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, vol. 26, pp. 617-633, 2010.

  8. Evrard, P., Alvarez-Armas, I., Aubin, V., and Degallaix, S., Poly-Crystalline Modeling of the Cyclic Hardening/Softening Behavior of an Austenitic-Ferritic Stainless Steel, Mech. Mater., vol. 42, pp. 395-404, 2010.

  9. Gerard, C., Cailletaud, G., and Bacroix, B., Modeling of Latent Hardening Produced by Complex Loading Paths in FCC Alloys, Int. J. Plasticity, vol. 42, pp. 194-212, 2013.

  10. Ghoniem, N.M., Busso, E.P., Kioussis, N., and Huang, H., Multiscale Modelling of Nanomechanics and Micromechanics: An Overview, Phil. Mag., vol. 83, nos. 31-34, pp. 3475-3528, 2003.

  11. Ha, S., Jang, J.-H., and Kim, K.T., Finite Element Implementation of Dislocation-Density-Based Crystal Plasticity Model and Its Application to Pure Aluminum Crystalline Materials, Int. J. Mech. Sci, vol. 120, pp. 249-262, 2017.

  12. Harder, J., FEM-Simulation of the Hardening Behavior of FCC Single Crystals, Acta Mechanica, vol. 150, pp. 197-217, 2001.

  13. Holmedal, B., Van Houtte, P., and An, Y., A Crystal Plasticity Model for Strain-Path Changes in Metals, Int. J. Plasticity, vol. 24, pp. 1360-1379, 2008.

  14. Horstemeyer, M.F., Potirniche, G.P., and Marin, E.B., Crystal Plasticity, in: S. Yip (Ed.), Handbook of Materials Modeling, The Netherlands: Springer, pp. 1133-1149, 2005.

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

  16. Khadyko, M., Dumoulin, S., Cailletaud, G., and Hopperstad, O.S., Latent Hardening and Plastic Anisotropy Evolution in AA6060 Aluminium Alloy, Int. J. Plasticity, vol. 76, pp. 51-74, 2016.

  17. Kuhlmann-Wilsdorf, D., Kulkarni, S.S., Moore, J.T., and Starke, E.A. Jr., Deformation Bands, the LEDS Theory, and Their Importance in Texture Development: Part I. Previous Evidence and New Observations, Metallurg. Mater. Trans. A, vol. 30A, pp. 2491-2501, 1999.

  18. Mandel, J., Equations Constitutives et Directeurs dans les Milieux Plastiques et Viscoplastiquest, Int. J. Solids Struct, vol. 9, pp. 725-740, 1973.

  19. McDowell, D.L., A Perspective on Trends in Multiscale Plasticity, Int. J. Plasticity, vol. 26, pp. 1280-1309, 2010.

  20. McDowell, D.L., Viscoplasticity of Heterogeneous Metallic Materials, Mater. Sci. Eng. Res., vol. 62, pp. 67-123, 2008.

  21. McGinty, R.D. and McDowell, D.L., A Semi-Implicit Integration Scheme for Rate Independent Finite Crystal Plasticity, Int. J. Plasticity, vol. 22, pp. 996-1025, 2006.

  22. Proust, G., Tome, C.N., Jain, A., and Agnew, S.R., Modeling the Effect of Twinning and Detwinning during Strain-Path Changes of Magnesium Alloy AZ31, Int. J. Plasticity, vol. 25, pp. 861-880, 2009.

  23. 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 Materialia, vol. 58, pp. 1152-1211, 2010.

  24. Shveikin, A.I. and Trusov, P.V., Correlation between Geometrically Nonlinear Elastoviscoplastic Constitutive Relations Formulated in Terms of the Actual and Unloaded Configurations for Crystallites, Phys. Mesomech, vol. 21, no. 3, pp. 193-202, 2018.

  25. Shveykin, A.I. and Sharifullina, E.R., Development of Multilevel Models based on Crystal Plasticity: Description of Grain Boundary Sliding and Evolution of Grain Structure, Nanosci. Technol.: An Int. J, vol. 6, no. 4, pp. 281-298, 2015.

  26. Shveykin, A.I., Multilevel Models of Polycrystalline Metals: Comparison of Constitutive Relations for Crystallites, Probl. Strength Plasticity, vol. 79, no. 4, pp. 385-397, 2017 (in Russian).

  27. Truesdell, C., A First Course in Rational Continuum Mechanics, New York: Academic Press, 1977.

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

  29. Trusov, P.V. and Shveykin, A.I., Multilevel Crystal Plasticity Models of Single- and Polycrystals. Direct Models, Phys. Mesomech, vol. 16, no. 2, pp. 99-124, 2013b.

  30. Trusov, P.V. and Shveykin, A.I., On Motion Decomposition and Constitutive Relations in Geometrically Nonlinear Elastoviscoplasticity of Crystallites, Phys. Mesomech., vol. 20, no. 4, pp. 377-391, 2017.

  31. Trusov, P.V., Kondratev, N.S., and Shveykin, A.I., About Geometrically Nonlinear Constitutive Relations for Elastic Material, PNRPU Mechanics Bull., vol. 3, pp. 182-200, 2015.

  32. Trusov, P.V., Shveykin, A.I., and Kondratev, N.S., Multilevel Metal Models: Formulation for Large Displacements Gradients, Nanosci. Technol.: An Int. J., vol. 8, no. 2, pp. 133-166, 2017a.

  33. Trusov, P. V., Shveykin, A.I., and Yanz, A.Yu., Motion Decomposition, Frame-Indifferent Derivatives, and Constitutive Relations at Large Displacement Gradients from the Viewpoint of Multilevel Modeling, Phys. Mesomech., vol. 20, no. 4, pp. 357-376, 2017b.

  34. Trusov, P.V., Shveykin, A.I., Nechaeva, E.S., and Volegov, P.S., Multilevel Models of Inelastic Deformation of Materials and Their Application for Description of Internal Structure Evolution, Phys. Mesomech, vol. 15, nos. 3-4, pp. 155-175, 2012.

  35. Van Houtte, P., Crystal Plasticity based Modeling of Deformation Textures, in A. Haldar, S. Suwas, and D. Bhattacharjee (Eds.), Microstructure and Texture in Steels, Berlin: Springer, pp. 209-224, 2009.

  36. Van Houtte, P., Li, S., Seefeldt, M., and Delannay, L., Deformation Texture Prediction: From the Taylor Model to the Advanced Lamel Model, Int. J. Plasticity, vol. 21, pp. 589-624, 2005.

  37. Xiao, H., Bruhns, O.T., and Meyers, A., A Consistent Finite Elastoplasticity Theory Combining Additive and Multiplicative Decomposition of the Stretching and the Deformation Gradient, Int. J. Plasticity, vol. 16, pp. 143-177, 2000.

  38. Xiao, H., Bruhns, O.T., and Meyers, A., A Natural Generalization of Hypoelasticity and Eulerian Rate Type Formulation of Hyperelasticity, J. Elasticity, vol. 56, pp. 59-93, 1999.

  39. Xiao, H., Bruhns, O.T., and Meyers, A., Logarithmic Strain, Logarithmic Spin and Logarithmic Rate, Acta Mechanica, vol. 124, pp. 89-105, 1997.

  40. Zhu, Y., Kang, G., Kan, Q., and Bruhns, O.T., Logarithmic Stress Rate based Constitutive Model for Cyclic Loading in Finite Plasticity, Int. J. Plasticity, vol. 54, pp. 34-55, 2014.

Articles with similar content:

A Numerical Investigation of Structure-Property Relations in Fiber Composite Materials
International Journal for Multiscale Computational Engineering, Vol.5, 2007, issue 2
Patrizia Trovalusci, V. Sansalone
Nanoscience and Technology: An International Journal, Vol.8, 2017, issue 2
Alexey I. Shveykin, Peter V. Trusov, Nikita S. Kondratev
Multiscale Transformation Field Analysis of Progressive Damage in Fibrous Laminates
International Journal for Multiscale Computational Engineering, Vol.8, 2010, issue 1
Ritesh Khire, Prabhat Hajela, Yehia Bahei-El-Din
Nanoscience and Technology: An International Journal, Vol.6, 2015, issue 4
Alexey I. Shveykin, E. R. Sharifullina
Investigation of the Influence of Control Forces on the Stability of a Satellite with a Gravitational Stabilizer by Means of Computer Algebra
Journal of Automation and Information Sciences, Vol.50, 2018, issue 7
Andrey V. Banshchikov