Skip to main content
SpringerLink
Log in

A numerical study into element type and mesh resolution for crystal plasticity finite element modeling of explicit grain structures

  • Original Paper
  • Published:
Computational Mechanics Aims and scope Submit manuscript

Abstract

A large number of massive crystal-plasticity-finite-element (CPFE) simulations are performed and post-processed to reveal the effects of element type and mesh resolution on accuracy of predicted mechanical fields over explicit grain structures. A CPFE model coupled with Abaqus/Standard is used to simulate simple-tension and simple-shear deformations to facilitate such quantitative mesh sensitivity studies. A grid-based polycrystalline grain structure is created synthetically by a phase-field simulation and converted to interface-conformal hexahedral and tetrahedral meshes of variable resolution. Procedures for such interface-conformal mesh generation over complex shapes are developed. FE meshes consisting of either hexahedral or tetrahedral, fully integrated as linear or quadratic elements are used for the CPFE simulations. It is shown that quadratic tetrahedral and linear hexahedral elements are more accurate for CPFE modeling than linear tetrahedral and quadratic hexahedral elements. Furthermore, tetrahedral elements are more desirable due to fast mesh generation and flexibility to describe geometries of grain structures.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Eghtesad A, Zecevic M, Lebensohn RA, McCabe RJ, Knezevic M (2018) Spectral database constitutive representation within a spectral micromechanical solver for computationally efficient polycrystal plasticity modelling. Comput Mech 61:89–104

    MathSciNet  MATH  Google Scholar 

  2. Bathe K-J (1996) Finite element procedures. Englewood Cliffs, Prentice Hall

    MATH  Google Scholar 

  3. Eghtesad A, Barrett TJ, Germaschewski K, Lebensohn RA, McCabe RJ, Knezevic M (2018) OpenMP and MPI implementations of an elasto-viscoplastic fast Fourier transform-based micromechanical solver for fast crystal plasticity modeling. Adv Eng Softw 126:46–60

    Google Scholar 

  4. Eghtesad A, Germaschewski K, Lebensohn RA, Knezevic M (2020) A multi-GPU implementation of a full-field crystal plasticity solver for efficient modeling of high-resolution microstructures. Comput Phys Commun 1:107231

    MathSciNet  Google Scholar 

  5. Peirce D, Asaro RJ, Needleman A (1982) An analysis of nonuniform and localized deformation in ductile single crystals. Acta Metall 30:1087–1119

    Google Scholar 

  6. Diard O, Leclercq S, Rousselier G, Cailletaud G (2002) Distribution of normal stress at grain boundaries in multicrystals: application to an intergranular damage modeling. Comput Mater Sci 25:73–84

    Google Scholar 

  7. Jahedi M, Ardeljan M, Beyerlein IJ, Paydar MH, Knezevic M (2015) Enhancement of orientation gradients during simple shear deformation by application of simple compression. J Appl Phys 117:214309

    Google Scholar 

  8. Ardeljan M, McCabe RJ, Beyerlein IJ, Knezevic M (2015) Explicit incorporation of deformation twins into crystal plasticity finite element models. Comput Methods Appl Mech Eng 295:396–413

    MathSciNet  MATH  Google Scholar 

  9. Zhao Z, Ramesh M, Raabe D, Cuitiño AM, Radovitzky R (2008) Investigation of three-dimensional aspects of grain-scale plastic surface deformation of an aluminum oligocrystal. Int J Plast 24:2278–2297

    MATH  Google Scholar 

  10. Lim H, Carroll JD, Battaile CC, Buchheit TE, Boyce BL, Weinberger CR (2014) Grain-scale experimental validation of crystal plasticity finite element simulations of tantalum oligocrystals. Int J Plast 60:1–18

    Google Scholar 

  11. Savage DJ, Beyerlein IJ, Knezevic M (2017) Coupled texture and non-Schmid effects on yield surfaces of body-centered cubic polycrystals predicted by a crystal plasticity finite element approach. Int J Solids Struct 109:22–32

    Google Scholar 

  12. Knezevic M, Levinson A, Harris R, Mishra RK, Doherty RD, Kalidindi SR (2010) Deformation twinning in AZ31: influence on strain hardening and texture evolution. Acta Mater 58:6230–6242

    Google Scholar 

  13. Kalidindi SR, Bronkhorst CA, Anand L (1992) Crystallographic texture evolution in bulk deformation processing of FCC metals. J Mech Phys Solids 40:537–569

    Google Scholar 

  14. Kalidindi SR, Duvvuru HK, Knezevic M (2006) Spectral calibration of crystal plasticity models. Acta Mater 54:1795–1804

    Google Scholar 

  15. Miehe C, Schröder J, Schotte J (1999) Computational homogenization analysis in finite plasticity Simulation of texture development in polycrystalline materials. Comput Methods Appl Mech Eng 171:387–418

    MathSciNet  MATH  Google Scholar 

  16. Beaudoin AJ, Dawson PR, Mathur KK, Kocks UF, Korzekwa DA (1994) Application of polycrystal plasticity to sheet forming. Comput Methods Appl Mech Eng 117:49–70

    MATH  Google Scholar 

  17. Sarma GB, Dawson PR (1996) Texture predictions using a polycrystal plasticity model incorporating neighbor interactions. Int J Plast 12:1023–1054

    MATH  Google Scholar 

  18. Ardeljan M, Beyerlein IJ, Knezevic M (2014) A dislocation density based crystal plasticity finite element model: application to a two-phase polycrystalline HCP/BCC composites. J Mech Phys Solids 66:16–31

    Google Scholar 

  19. Sarma GB, Dawson PR (1996) Effects of interactions among crystals on the inhomogeneous deformations of polycrystals. Acta Mater 44:1937–1953

    Google Scholar 

  20. Mika DP, Dawson PR (1998) Effects of grain interaction on deformation in polycrystals. Mater Sci Eng A 257:62–76

    Google Scholar 

  21. Delannay L, Jacques PJ, Kalidindi SR (2006) Finite element modeling of crystal plasticity with grains shaped as truncated octahedrons. Int J Plast 22:1879–1898

    MATH  Google Scholar 

  22. Ritz H, Dawson P (2008) Sensitivity to grain discretization of the simulated crystal stress distributions in FCC polycrystals. Modell Simul Mater Sci Eng 17:015001

    Google Scholar 

  23. Kalidindi SR, Bhattacharya A, Doherty R (2004) Detailed Analysis of Plastic Deformation in Columnar Polycrystalline Aluminum Using Orientation Image Mapping and Crystal Plasticity Models. Proc R Soc Lond Math Phys Eng Sci 460:1935–1956

    Google Scholar 

  24. Diard O, Leclercq S, Rousselier G, Cailletaud G (2005) Evaluation of finite element based analysis of 3D multicrystalline aggregates plasticity: application to crystal plasticity model identification and the study of stress and strain fields near grain boundaries. Int J Plast 21:691–722

    MATH  Google Scholar 

  25. Shenoy M, Tjiptowidjojo Y, McDowell D (2008) Microstructure-sensitive modeling of polycrystalline IN 100. Int J Plast 24:1694–1730

    MATH  Google Scholar 

  26. Ardeljan M, Savage DJ, Kumar A, Beyerlein IJ, Knezevic M (2016) The plasticity of highly oriented nano-layered Zr/Nb composites. Acta Mater 115:189–203

    Google Scholar 

  27. Lim H, Battaile CC, Bishop JE, Foulk JW (2019) Investigating mesh sensitivity and polycrystalline RVEs in crystal plasticity finite element simulations. Int J Plast 121:101–115

    Google Scholar 

  28. Lim H, Abdeljawad F, Owen SJ, Hanks BW, Foulk JW, Battaile CC (2016) Incorporating physically-based microstructures in materials modeling: bridging phase field and crystal plasticity frameworks. Modell Simul Mater Sci Eng 24:045016

    Google Scholar 

  29. Lim H, Carroll JD, Battaile CC, Boyce BL, Weinberger CR (2015) Quantitative comparison between experimental measurements and CP-FEM predictions of plastic deformation in a tantalum oligocrystal. Int J Mech Sci 92:98–108

    Google Scholar 

  30. Knezevic M, Kalidindi SR (2007) Fast computation of first-order elastic-plastic closures for polycrystalline cubic-orthorhombic microstructures. Comput Mater Sci 39:643–648

    Google Scholar 

  31. Taylor GI (1938) Plastic strain in metals. J Inst Met 62:307–324

    Google Scholar 

  32. Lebensohn RA, Tomé CN (1993) A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals: application to zirconium alloys. Acta Metall Mater 41:2611–2624

    Google Scholar 

  33. Lebensohn RA, Zecevic M, Knezevic M, McCabe RJ (2016) Average intragranular misorientation trends in polycrystalline materials predicted by a viscoplastic self-consistent approach. Acta Mater 104:228–236

    Google Scholar 

  34. Zecevic M, Pantleon W, Lebensohn RA, McCabe RJ, Knezevic M (2017) Predicting intragranular misorientation distributions in polycrystalline metals using the viscoplastic self-consistent formulation. Acta Mater 140:398–410

    Google Scholar 

  35. Knezevic M, Kalidindi SR, Fullwood D (2008) Computationally efficient database and spectral interpolation for fully plastic Taylor-type crystal plasticity calculations of face-centered cubic polycrystals. Int J Plast 24:1264–1276

    MATH  Google Scholar 

  36. Knezevic M, Al-Harbi HF, Kalidindi SR (2009) Crystal plasticity simulations using discrete Fourier transforms. Acta Mater 57:1777–1784

    Google Scholar 

  37. Zecevic M, Knezevic M, Beyerlein IJ, McCabe RJ (2016) Origin of texture development in orthorhombic uranium. Mater Sci Eng A 665:108–124

    Google Scholar 

  38. Knezevic M, Beyerlein IJ, Lovato ML, Tomé CN, Richards AW, McCabe RJ (2014) A strain-rate and temperature dependent constitutive model for BCC metals incorporating non-Schmid effects: application to tantalum–tungsten alloys. Int J Plast 62:93–104

    Google Scholar 

  39. Knezevic M, Capolungo L, Tomé CN, Lebensohn RA, Alexander DJ, Mihaila B, McCabe RJ (2012) Anisotropic stress-strain response and microstructure evolution of textured α-uranium. Acta Mater 60:702–715

    Google Scholar 

  40. Knezevic M, Nizolek T, Ardeljan M, Beyerlein IJ, Mara NA, Pollock TM (2014) Texture evolution in two-phase Zr/Nb lamellar composites during accumulative roll bonding. Int J Plast 57:16–28

    Google Scholar 

  41. Knezevic M, Savage DJ (2014) A high-performance computational framework for fast crystal plasticity simulations. Comput Mater Sci 83:101–106

    Google Scholar 

  42. Knezevic M, Zecevic M, Beyerlein IJ, Lebensohn RA (2016) A numerical procedure enabling accurate descriptions of strain rate-sensitive flow of polycrystals within crystal visco-plasticity theory. Comput Methods Appl Mech Eng 308:468–482

    MathSciNet  MATH  Google Scholar 

  43. Savage DJ, Knezevic M (2015) Computer implementations of iterative and non-iterative crystal plasticity solvers on high performance graphics hardware. Comput Mech 56:677–690

    MathSciNet  MATH  Google Scholar 

  44. Barrett TJ, Knezevic M (2019) Deep drawing simulations using the finite element method embedding a multi-level crystal plasticity constitutive law: experimental verification and sensitivity analysis. Comput Methods Appl Mech Eng 354:245–270

    MathSciNet  MATH  Google Scholar 

  45. De Berg M, Van Kreveld M, Overmars M, Schwarzkopf OC (2000) Computational geometry. Springer, Berlin

    MATH  Google Scholar 

  46. Zhang P, Karimpour M, Balint D, Lin J (2012) Three-dimensional virtual grain structure generation with grain size control. Mech Mater 55:89–101

    Google Scholar 

  47. Boots B (1982) The arrangement of cells in “random” networks. Metallography 15:53–62

    Google Scholar 

  48. Aboav D (1970) The arrangement of grains in a polycrystal. Metallography 3:383–390

    Google Scholar 

  49. Groeber MA, Jackson MA (2014) DREAM: 3D: A digital representation environment for the analysis of microstructure in 3D. Integrating Materials and Manufacturing Innovation 3:5

    Google Scholar 

  50. Chen L-Q (2002) Phase-field models for microstructure evolution. Annu Rev Mater Res 32:113–140

    Google Scholar 

  51. Rollett A, Raabe D (2001) A hybrid model for mesoscopic simulation of recrystallization. Comput Mater Sci 21:69–78

    Google Scholar 

  52. Rollett AD (1997) Overview of modeling and simulation of recrystallization. Prog Mater Sci 42:79–99

    Google Scholar 

  53. Raabe D (1999) Introduction of a scalable three-dimensional cellular automaton with a probabilistic switching rule for the discrete mesoscale simulation of recrystallization phenomena. Philos Mag A 79:2339–2358

    Google Scholar 

  54. Marx V, Reher FR, Gottstein G (1999) Simulation of primary recrystallization using a modified three-dimensional cellular automaton. Acta Mater 47:1219–1230

    Google Scholar 

  55. Spowart JE, Mullens HE, Puchala BT (2003) Collecting and analyzing microstructures in three dimensions: a fully automated approach. JOM 55:35–37

    Google Scholar 

  56. Spowart JE (2006) Automated serial sectioning for 3-D analysis of microstructures. Scr Mater 55:5–10

    Google Scholar 

  57. Zaafarani N, Raabe D, Singh R, Roters F, Zaefferer S (2006) 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 54:1863–1876

    Google Scholar 

  58. Calcagnotto M, Ponge D, Demir E, Raabe D (2010) Orientation gradients and geometrically necessary dislocations in ultrafine grained dual-phase steels studied by 2D and 3D EBSD. Mater Sci Eng, A 527:2738–2746

    Google Scholar 

  59. Khorashadizadeh A, Raabe D, Zaefferer S, Rohrer G, Rollett A, Winning M (2011) Five-parameter grain boundary analysis by 3D EBSD of an ultra fine grained CuZr alloy processed by equal channel angular pressing. Adv Eng Mater 13:237–244

    Google Scholar 

  60. Zaefferer S, Wright S, Raabe D (2008) Three-dimensional orientation microscopy in a focused ion beam–scanning electron microscope: a new dimension of microstructure characterization. Metall Mater Trans A 39:374–389

    Google Scholar 

  61. Yi S, Schestakow I, Zaefferer S (2009) Twinning-related microstructural evolution during hot rolling and subsequent annealing of pure magnesium. Mater Sci Eng A 516:58–64

    Google Scholar 

  62. Uchic MD, Groeber MA, Dimiduk DM, Simmons JP (2006) 3D microstructural characterization of nickel superalloys via serial-sectioning using a dual beam FIB-SEM. Scr Mater 55:23–28

    Google Scholar 

  63. Li SF, Lind J, Hefferan CM, Pokharel R, Lienert U, Rollett AD, Suter RM (2012) Three-dimensional plastic response in polycrystalline copper via near-field high-energy X-ray diffraction microscopy. J Appl Crystallogr 45:1098–1108

    Google Scholar 

  64. Lind J, Li SF, Pokharel R, Lienert U, Rollett AD, Suter RM (2014) Tensile twin nucleation events coupled to neighboring slip observed in three dimensions. Acta Mater 76:213–220

    Google Scholar 

  65. Stein CA, Cerrone A, Ozturk T, Lee S, Kenesei P, Tucker H, Pokharel R, Lind J, Hefferan C, Suter RM, Ingraffea AR, Rollett AD (2014) Fatigue crack initiation, slip localization and twin boundaries in a nickel-based superalloy. Curr Opin Solid State Mater Sci 18:244–252

    Google Scholar 

  66. Ludwig W, Schmidt S, Lauridsen EM, Poulsen HF (2008) X-ray diffraction contrast tomography: a novel technique for three-dimensional grain mapping of polycrystals. I. Direct beam case. J Appl Crystallogr 41:302–309

    Google Scholar 

  67. Johnson G, King A, Honnicke MG, Marrow J, Ludwig W (2008) X-ray diffraction contrast tomography: a novel technique for three-dimensional grain mapping of polycrystals. II. The combined case. J Appl Crystallogr 41:310–318

    Google Scholar 

  68. Qidwai SM, Turner DM, Niezgoda SR, Lewis AC, Geltmacher AB, Rowenhorst DJ, Kalidindi SR (2012) Estimating the response of polycrystalline materials using sets of weighted statistical volume elements. Acta Mater 60:5284–5299

    Google Scholar 

  69. Choi YS, Groeber MA, Turner TJ, Dimiduk DM, Woodward C, Uchic MD, Parthasarathy TA (2012) A crystal-plasticity FEM study on effects of simplified grain representation and mesh types on mesoscopic plasticity heterogeneities. Mater Sci Eng, A 553:37–44

    Google Scholar 

  70. Knezevic M, Drach B, Ardeljan M, Beyerlein IJ (2014) Three dimensional predictions of grain scale plasticity and grain boundaries using crystal plasticity finite element models. Comput Methods Appl Mech Eng 277:239–259

    Google Scholar 

  71. Barrett TJ, Savage DJ, Ardeljan M, Knezevic M (2018) An automated procedure for geometry creation and finite element mesh generation: application to explicit grain structure models and machining distortion. Comput Mater Sci 141:269–281

    Google Scholar 

  72. Ardeljan M, Knezevic M, Nizolek T, Beyerlein IJ, Mara NA, Pollock TM (2015) A study of microstructure-driven strain localizations in two-phase polycrystalline HCP/BCC composites using a multi-scale model. Int J Plast 74:35–57

    Google Scholar 

  73. Knezevic M, Daymond MR, Beyerlein IJ (2016) Modeling discrete twin lamellae in a microstructural framework. Scr Mater 121:84–88

    Google Scholar 

  74. Wang S, Zhuang W, Cao J, Lin J (2010) An investigation of springback scatter in forming ultra-thin metal-sheet channel parts using crystal plasticity FE analysis. Int J Adv Manuf Technol 47:845–852

    Google Scholar 

  75. Zhuang W, Wang S, Cao J, Lin J, Hartl C (2010) Modelling of localised thinning features in the hydroforming of micro-tubes using the crystal-plasticity FE method. Int J Adv Manuf Technol 47:859–865

    Google Scholar 

  76. Cubit https://cubit.sandia.gov/

  77. Asaro RJ, Needleman A (1985) Texture development and strain hardening in rate dependent polycrystals. Acta Metall Mater 33:923–953

    Google Scholar 

  78. Hutchinson JW (1976) Bounds and self-consistent estimates for creep of polycrystalline materials. Proc R Soc Lond A 348:101–126

    MATH  Google Scholar 

  79. Zecevic M, Beyerlein IJ, McCabe RJ, McWilliams BA, Knezevic M (2016) Transitioning rate sensitivities across multiple length scales: microstructure-property relationships in the Taylor cylinder impact test on zirconium. Int J Plast 84:138–159

    Google Scholar 

  80. Kocks U, Argon A, Ashby M (1975) Progress in materials science. Thermodyn Kinet Slip 19:110–170

    Google Scholar 

  81. Beyerlein IJ, Tomé CN (2008) A dislocation-based constitutive law for pure Zr including temperature effects. Int J Plast 24:867–895

    MATH  Google Scholar 

  82. Madec R, Devincre B, Kubin L, Hoc T, Rodney D (2003) The role of collinear interaction in dislocation-induced hardening. Science 301:1879–1882

    Google Scholar 

  83. Knezevic M, Carpenter JS, Lovato ML, McCabe RJ (2014) Deformation behavior of the cobalt-based superalloy Haynes 25: experimental characterization and crystal plasticity modeling. Acta Mater 63:162–168

    Google Scholar 

  84. Knezevic M, McCabe RJ, Tomé CN, Lebensohn RA, Chen SR, Cady CM, Gray Iii GT, Mihaila B (2013) Modeling mechanical response and texture evolution of α-uranium as a function of strain rate and temperature using polycrystal plasticity. Int J Plast 43:70–84

    Google Scholar 

  85. Zecevic M, Knezevic M, Beyerlein IJ, McCabe RJ (2016) Texture formation in orthorhombic alpha-uranium under simple compression and rolling to high strains. J Nucl Mater 473:143–156

    Google Scholar 

  86. Knezevic M, Zecevic M, Beyerlein IJ, Bingert JF, McCabe RJ (2015) Strain rate and temperature effects on the selection of primary and secondary slip and twinning systems in HCP Zr. Acta Mater 88:55–73

    Google Scholar 

  87. Mecking H, Kocks UF (1981) Kinetics of flow and strain-hardening. Acta Metall Mater 29:1865–1875

    Google Scholar 

  88. Madec R, Devincre B, Kubin LP (2002) From dislocation junctions to forest hardening. Phys Rev Lett 89:255508

    Google Scholar 

  89. Eghtesad A, Knezevic M (2020) High-performance full-field crystal plasticity with dislocation-based hardening and slip system back-stress laws: application to modeling deformation of dual-phase steels. J Mech Phys Solids 134:103750

    MathSciNet  Google Scholar 

  90. Lavrentev FF (1980) The type of dislocation interaction as the factor determining work hardening. Mater Sci Eng 46:191–208

    Google Scholar 

  91. Essmann U, Mughrabi H (1979) Annihilation of dislocations during tensile and cyclic deformation and limits of dislocation densities. Philos Mag A 40:731–756

    Google Scholar 

  92. Mughrabi H (1987) A two-parameter description of heterogeneous dislocation distributions in deformed metal crystals. Materials science and engineering 85:15–31

    Google Scholar 

  93. Jackson PJ (1985) Dislocation modelling of shear in f.c.c. crystals. Prog Mater Sci 29:139–175

    Google Scholar 

  94. Wang Z, Beyerlein I, LeSar R (2007) The importance of cross-slip in high-rate deformation. Modell Simul Mater Sci Eng 15:675

    Google Scholar 

  95. Peeters B, Bacroix B, Teodosiu C, Van Houtte P, Aernoudt E (2001) Work-hardening/softening behaviour of b.c.c. polycrystals 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 49:1621–1632

    Google Scholar 

  96. Kocks UF, Mecking H (2003) Physics and phenomenology of strain hardening: the FCC case. Prog Mater Sci 48:171–273

    Google Scholar 

  97. Owen SJ, Brown JA, Ernst CD, Lim H, Long KN (2017) Hexahedral mesh generation for computational materials modeling. Procedia engineering 203:167–179

    Google Scholar 

  98. Owen SJ, Staten ML and Sorensen MC (2011) Parallel hex meshing from volume fractions. In: Proceedings of the 20th international meshing roundtable. Springer, pp 161–178

  99. Allen SM, Cahn JW (1979) A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening. Acta Metall 27:1085–1095

    Google Scholar 

  100. Abdeljawad F, Foiles SM (2015) Stabilization of nanocrystalline alloys via grain boundary segregation: a diffuse interface model. Acta Mater 101:159–171

    Google Scholar 

  101. Abdeljawad F, Völker B, Davis R, McMeeking RM, Haataja M (2014) Connecting microstructural coarsening processes to electrochemical performance in solid oxide fuel cells: an integrated modeling approach. J Power Sources 250:319–331

    Google Scholar 

  102. Ardeljan M, Beyerlein IJ, Knezevic M (2017) Effect of dislocation density-twin interactions on twin growth in AZ31 as revealed by explicit crystal plasticity finite element modeling. Int J Plast 99:81–101

    Google Scholar 

  103. Ardeljan M, Knezevic M (2018) Explicit modeling of double twinning in AZ31 using crystal plasticity finite elements for predicting the mechanical fields for twin variant selection and fracture analyses. Acta Mater 157:339–354

    Google Scholar 

  104. (2013) Patran Version 2013, MSC Software Corporation, Newport Beach, CA, USA

  105. (2017) ABAQUS Version 6, Dassault Systèmes, Providence, RI, USA

Download references

Acknowledgements

This work is based upon a project supported by the U.S. National Science Foundation under grant no. CMMI-1650641. The authors gratefully acknowledge this support. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of New Hampshire, Durham, NH, 03824, USA

    William G. Feather & Marko Knezevic

  2. Department of Computational Materials and Data Science, Sandia National Laboratories, Albuquerque, NM, 87185, USA

    Hojun Lim

Authors
  1. William G. Feather
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hojun Lim
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Marko Knezevic
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Marko Knezevic.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendices

Appendix 1

See Table 8.

Table 8 Bunge-Euler angles (\( \phi_{1} \), \( {\varPhi} \), \( \phi_{2} \)) in degrees and corresponding volume fraction (VF) of crystals used to initialize the model
Full size table

Appendix 2

See Figs. 8 and 9.

Fig. 8
figure 8figure 8

a Equivalent strain and b pressure contours after simple tension to a displacement of U = 0.22

Full size image
Fig. 9
figure 9figure 9

a Equivalent strain and b pressure contours after simple shear to a displacement of 0.22

Full size image

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Feather, W.G., Lim, H. & Knezevic, M. A numerical study into element type and mesh resolution for crystal plasticity finite element modeling of explicit grain structures. Comput Mech 67, 33–55 (2021). https://doi.org/10.1007/s00466-020-01918-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00466-020-01918-x

Keywords

Search

Navigation