Crystal Plasticity

  • M. F. Horstemeyer
  • G. P. Potirniche
  • E. B. Marin


Besides Dislocation Dynamics, crystal plasticity can be considered a mesoscale formulation, since the details of the equations start at the scale of the crystal or grain. In this section, the topics of classical crystal plasticity formulations, kinematics, kinetics, and the polycrystalline average methods will be discussed.


Slip System Deformation Gradient Crystal Plasticity Resolve Shear Stress Kinematic Hardening 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    P.R. Dawson, “On Modeling of Mechanical Property Changes During Flat Rolling of Aluminum,” Int. J. Solids Structures, 23(7), 947–968, 1987.CrossRefGoogle Scholar
  2. [2]
    D. Peirce, R.J. Asaro, and A. Needleman, “An analysis of nonuniform and localized deformation in Ductile single crystals,” Acta. Metall., 30, pp. 1087–1119, 1982.CrossRefGoogle Scholar
  3. [3]
    M.M. Rashid and S. Nemat-Nasser, “A constitutive algorithm for rate dependent crystal plasticity,” Computuer Methods in Applied Mechanics and Engineering, 94, 201–228, 1990.CrossRefGoogle Scholar
  4. [4]
    U.F. Kocks, C.N. Tomé, and H.R. Wenk, “Texture and anisotropy: preferred orientations in polycrystals and their effect on materials properties,” Cambridge University Press, 1998.Google Scholar
  5. [5]
    L. Anand and M. Kothari, “Computational procedure for rate-independent crystal plasticity,” Journal of the Mechanics and Physics of Solids, 44(4), 525–558, 1996.MATHCrossRefMathSciNetADSGoogle Scholar
  6. [6]
    A.M. Cuitino and M. Ortiz, “Computational modelling of single crystals,” Modelling Simul. Mater. Sci. Eng., 1, 225–263, 1992.CrossRefADSGoogle Scholar
  7. [7]
    P.R. Dawson and E.B. Marin, “Computational mechanics for metal deformation processes using polycrystal plasticity,” Advances in Applied Mechanics, 34, 78–171, 1998.Google Scholar
  8. [8]
    G.I. Taylor and C.R Elam, “The distortion of an aluminum crystal during a tensile test,” Proc. Royal Soc. London, A102, 643–667, 1923.ADSGoogle Scholar
  9. [9]
    E. Schmid, “Ueber die Schubverfestigung von Einkristallen bei Plasticher Deformation,” Z. Physics, 40, 54–74, 1926.CrossRefADSGoogle Scholar
  10. [10]
    G.I. Taylor, “Plastic strain in metals,” J. Inst. Metals, 62, 307, 1938.Google Scholar
  11. [11]
    J.F.W. Bishop and R. Hill, “A theoretical derivation of the plastic properties of a polycrystalline face-centered metal,” Phil. Mat. Ser., 7(42), 1298–1307, 1951.MathSciNetGoogle Scholar
  12. [12]
    K.S. Havner, Finite Plastic Deformation of Crystalline Solids, Cambridg University Press, 1992.Google Scholar
  13. [13]
    E.H. Lee and D.T. Liu, “Finite strain elastic-plastic theory with application to planewave analysis,” J. Appl. Phys., 38, 391–408, 1967.Google Scholar
  14. [14]
    J.W. Hutchinson, “Bounds and self-consistent estimates for creep of polycrystalline materials,” Proc. R. Soc. Lond. A, 348, 101–127, 1976.MATHCrossRefADSGoogle Scholar
  15. [15]
    M.F. Horstemeyer and D.L. McDowell, “Modeling effects of dislocation substructure in polycrystal elastoviscoplasticity,” Mech. Math., 27, 145–163, 1998.CrossRefGoogle Scholar
  16. [16]
    G.Z. Sachs, Verein Deut. Ing., 72, 734, 1928.Google Scholar
  17. [17]
    R.I. Borja and J.R. Wren, “Discrete micromechanics of elastoplastic crystals,” Internationaljournal for Numerical Methods in Engineering, 36, 3815–3840, 1993.MATHCrossRefGoogle Scholar
  18. [18]
    J. Schroder and C. Miehe, “Aspects of computational rate independent crystal plasticity,” Compututational Materials Science, 9, 168–176, 1997.CrossRefGoogle Scholar
  19. [19]
    S.R. Kalidindi, “Polycrystal plasticity: constitutive modeling and deformation processing,” PhD. Thesis. MIT, Cambridge, MA, 1992.Google Scholar
  20. [20]
    C. Miehe and J. Schroder, “A Comparative study of stress update algorithms for rate-independent and rate-dependent crystal plasticity,” Int. J. Num. Met. in Eng., 50, 273–298, 2001.MATHCrossRefMathSciNetGoogle Scholar
  21. [21]
    R.D. McGinty, “Multiscale representation of polycrystalline inelasticity,” PhD. Thesis, Georgia Institute of Technology, Atlanta, GA, 2001.Google Scholar
  22. [22]
    W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling, Numerical Recipes, The Art of Scientific Computing, Cambridge University Press, 1986.Google Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  • M. F. Horstemeyer
    • 1
  • G. P. Potirniche
    • 1
  • E. B. Marin
    • 2
  1. 1.Mississippi State UniversityMississippi StateUSA
  2. 2.Sandia National LaboratoriesLivermoreUSA

Personalised recommendations