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Generalized Models and Non-classical Approaches in Complex Materials 2 pp 237–260Cite as

Generalized Continua Concepts in Coarse-Graining Atomistic Simulations

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Part of the Advanced Structured Materials book series (STRUCTMAT,volume 90)

Abstract

Generalized continuum mechanics (GCM) has attracted increased attention in the context of multiscale materials modeling, an example of which is a bottom-up GCM model, called the atomistic field theory (AFT). Unlike most other GCM models, AFT views a crystalline material as a continuous collection of lattice points; embedded within each point is a unit cell with a group of discrete atoms. As such, AFT concurrently bridges the discrete and continuous descriptions of materials, two fundamentally different viewpoints. In this chapter, we first review the basics of AFT and illustrate how it is realized through coarse-graining atomistic simulations via a concurrent atomistic-continuum (CAC) method. Important aspects of CAC, including its advantages relative to other multiscale methods, code development, and numerical implementations, are discussed. Then, we present recent applications of CAC to a number of metal plasticity problems, including static dislocation properties, fast moving dislocations and phonons, as well as dislocation/grain boundary interactions. We show that, adequately replicating essential aspects of dislocation fields at a fraction of the computational cost of full atomistics, CAC is established as an effective tool for coarse-grained modeling of various nano/micro-scale thermal and mechanical problems in a wide range of monatomic and polyatomic crystalline materials.

Keywords

  • Fast-moving Dislocations
  • Coarse-grained Domain
  • Symmetric Tilt Grain Boundaries (STGB)
  • Full Atomic Resolution
  • Slip Transfer

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.

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References

  1. Maugin, G.A.: Non-Classical Continuum Mechanics: A Dictionary. Springer, Singapore (2016)

    MATH  Google Scholar 

  2. Maugin, G.A.: Some remarks on generalized continuum mechanics. Math. Mech. Solids 20(3), 280–291 (2015)

    MathSciNet  MATH  Google Scholar 

  3. Maugin, G.A.: Generalized continuum mechanics: various paths. In: Continuum Mechanics Through the Twentieth Century, pp. 223–241. Springer (2013)

    Google Scholar 

  4. Maugin, G.A.: Continuum Mechanics Through the Twentieth Century, Solid Mechanics and Its Applications, vol. 196, pp. 978–994. Springer, Berlin (2013)

    Google Scholar 

  5. Maugin, G.A.: Generalized continuum mechanics: what do we mean by that? In: Maugin, G., Metrikine, A. (eds.) Mechanics of Generalized Continua. Advances in Mechanics and Mathematics, pp. 3–13. Springer, New York, NY (2010)

    Google Scholar 

  6. Maugin, G.A.: A historical perspective of generalized continuum mechanics. In: Altenbach, H., Maugin, G., Erofeev, V. (eds.) Mechanics of Generalized Continua. Advanced Structured Materials, vol. 7. pp. 3–19 (2011)

    Google Scholar 

  7. Maugin, G.A., Metrikine, A.V.: Mechanics of Generalized Continua: One Hundred Years After the Cosserats. Springer, New York (2010)

    MATH  Google Scholar 

  8. Chen, Y., Lee, J.: Atomistic formulation of a multiscale field theory for nano/micro solids. Philos. Mag. 85(33–35), 4095–4126 (2005)

    Google Scholar 

  9. Chen, Y.: Reformulation of microscopic balance equations for multiscale materials modeling. J. Chem. Phys. 130(13), 134706 (2009)

    Google Scholar 

  10. Chen, Y., Lee, J., Xiong, L.: A generalized continuum theory and its relation to micromorphic theory. J. Eng. Mech. 135(3), 149–155 (2009)

    Google Scholar 

  11. Chen, Y., Zimmerman, J., Krivtsov, A., McDowell, D.L: Assessment of atomistic coarse-graining methods. Int. J. Eng. Sci. 49(12), 1337–1349 (2011)

    MATH  Google Scholar 

  12. Cosserat, E., Cosserat, F.: Théorie des corps déformables, vol. 3, pp. 17–29, Paris (1909)

    Google Scholar 

  13. Chen, Y., Lee, J.D., Eskandarian, A.: Micropolar theory and its applications to mesoscopic and microscopic problems. Comput. Model. Eng. Sci. 5(1), 35–43 (2004)

    MATH  Google Scholar 

  14. Eringen, A.C.: Theory of micropolar elasticity. In: Microcontinuum Field Theories, pp. 101–248. Springer (1999)

    Google Scholar 

  15. Eringen, A.C.: Microcontinuum Field Theories: I. Foundations and Solids. Springer, New York (1999)

    MATH  Google Scholar 

  16. Eringen, A.C.: Mechanics of Micromorphic Continua. Springer (1968)

    Google Scholar 

  17. Chen, Y., Lee, J.D.: Connecting molecular dynamics to micromorphic theory. (I). Instantaneous and averaged mechanical variables. Phys. A 322, 359–376 (2003)

    MATH  Google Scholar 

  18. Chen, Y., Lee, J.D.: Connecting molecular dynamics to micromorphic theory. (II). Balance laws. Phys. A 322, 377–392 (2003)

    MATH  Google Scholar 

  19. Chen, Y., Lee, J., Eskandarian, A.: Atomistic counterpart of micromorphic theory. Acta Mech. 161(1–2), 81–102 (2003)

    MATH  Google Scholar 

  20. Chen, Y., Lee, J.D.: Determining material constants in micromorphic theory through phonon dispersion relations. Int. J. Eng. Sci. 41(8), 871–886 (2003)

    Google Scholar 

  21. Chen, Y., Lee, J.D., Eskandarian, A.: Atomistic viewpoint of the applicability of microcontinuum theories. Int. J. Solids Struct. 41(8), 2085–2097 (2004)

    MATH  Google Scholar 

  22. Chen, Y., Lee, J.D., Eskandarian, A.: Examining the physical foundation of continuum theories from the viewpoint of phonon dispersion relation. Int. J. Eng. Sci. 41, 61–83 (2003)

    MathSciNet  MATH  Google Scholar 

  23. Hoover, W.G.: Computational Statistical Mechanics. Elsevier (1991)

    Google Scholar 

  24. Chen, Y.: Local stress and heat flux in atomistic systems involving three-body forces. J. Chem. Phys. 124(5), 054113 (2006)

    Google Scholar 

  25. Chen, Y., Diaz, A.: Local momentum and heat fluxes in transient transport processes and inhomogeneous systems. Phys. Rev. E 94(5), 053309 (2016)

    Google Scholar 

  26. Chen, Y.: The origin of the distinction between microscopic formulas for stress and Cauchy stress. EPL 116(3), 34003 (2016)

    Google Scholar 

  27. Espanol, P.: Statistical mechanics of coarse-graining. In: Novel Methods in Soft Matter Simulations, pp. 69–115. Springer (2004)

    Google Scholar 

  28. Izvekov, S., Voth, G.A.: Multiscale coarse-graining of liquid-state systems. J. Chem. Phys. 123(13), 134105 (2005)

    Google Scholar 

  29. Izvekov, S., Voth, G.A.: A multiscale coarse-graining method for biomolecular systems. J. Phys. Chem. B 109(7), 2469–2473 (2005)

    Google Scholar 

  30. Noid, W., Chu, J.W., Ayton, G.S., Krishna, V., Izvekov, S., Voth, G.A., Das, A., Andersen, H.C.: The multiscale coarse-graining method. I. A rigorous bridge between atomistic and coarse-grained models. J. Chem. Phys. 128(24), 244114 (2008)

    Google Scholar 

  31. Noid, W., Liu, P., Wang, Y., Chu, J.W., Ayton, G.S., Izvekov, S., Andersen, H.C., Voth, G.A.: The multiscale coarse-graining method. II. Numerical implementation for coarse-grained molecular models. J. Chem. Phys. 128(24), 244115 (2008)

    Google Scholar 

  32. Tadmor, E.B., Ortiz, M., Phillips, R.: Quasicontinuum analysis of defects in solids. Philos. Mag. A 73, 1529–1563 (1996)

    Google Scholar 

  33. Dupuy, L.M., Tadmor, E.B., Miller, R.E., Phillips, R.: Finite-temperature quasicontinuum: molecular dynamics without all the atoms. Phys. Rev. Lett. 95, 060202 (2005)

    Google Scholar 

  34. Kulkarni, Y., Knap, J., Ortiz, M.: A variational approach to coarse-graining of equilibrium and non-equilibrium atomistic description at finite temperature. J. Mech. Phys. Solids 56, 1417–1449 (2008)

    MathSciNet  MATH  Google Scholar 

  35. Shenoy, V.B., Miller, R., Tadmor, E.B., Phillips, R., Ortiz, M.: Quasicontinuum models of interfacial structure and deformation. Phys. Rev. Lett. 80, 742–745 (1998)

    Google Scholar 

  36. Rudd, R.E., Broughton, J.Q.: Coarse-grained molecular dynamics and the atomic limit of finite elements. Phys. Rev. B 58(10), R5893 (1998)

    Google Scholar 

  37. Irving, J., Kirkwood, J.G.: The statistical mechanical theory of transport processes. IV. The equations of hydrodynamics. J. Chem. Phys. 18(6), 817–829 (1950)

    MathSciNet  Google Scholar 

  38. Kittel, C.: Introduction to Solid State Physics. Wiley, Inc (1956)

    Google Scholar 

  39. Deng, Q, Xiong, L., Chen, Y.: Coarse-graining atomistic dynamics of fracture by finite element method. Int. J. Plast. 26(9), 1402–1414

    Google Scholar 

  40. Xiong, L., Chen, Y.: Coarse-grained simulations of single-crystal silicon. Modell. Simul. Mater. Sci. Eng. 17, 035002 (2009)

    Google Scholar 

  41. Xiong, L., Chen, Y., Lee, J.D.: Atomistic simulation of mechanical properties of diamond and silicon carbide by a field theory. Model. Simul. Mater. Sci. Eng. 15(5), 535 (2007)

    Google Scholar 

  42. Xiong, L., Tucker, G., McDowell, D.L., Chen, Y.: Coarse-grained atomistic simulation of dislocations. J. Mech. Phys. Solids 59(2), 160–177 (2011)

    MATH  Google Scholar 

  43. Xu, S., Che, R., Xiong, L., Chen, Y., McDowell, D.L.: A quasistatic implementation of the concurrent atomistic-continuum method for FCC crystals. Int. J. Plast. 72, 91–126 (2015)

    Google Scholar 

  44. Xu, S., Payne, T.G., Chen, H., Liu, Y., Xiong, L., Chen, Y., McDowell, D.L.: PyCAC: The concurrent atomistic-continuum simulation environment. J. Mater. Res. (2018) in press, https://doi.org/10.1557/jmr.2018.8

    Google Scholar 

  45. Shilkrot, L.E., Curtin, W.A., Miller, R.E.: A coupled atomistic/continuum model of defects in solids. J. Mech. Phys. Solids 50, 2085–2106 (2002)

    MATH  Google Scholar 

  46. Shilkrot, L.E., Miller, R.E., Curtin, W.A.: Coupled atomistic and discrete dislocation plasticity. Phys. Rev. Lett. 89, 025501 (2002)

    Google Scholar 

  47. Xu, S., Xiong, L., Deng, Q., McDowell, D.L.: Mesh refinement schemes for the concurrent atomistic-continuum method. Int. J. Solids Struct. 90, 144–152 (2016)

    Google Scholar 

  48. Zbib, H.M., de la Rubia, T.D., Bulatov, V.: A multiscale model of plasticity based on discrete dislocation dynamics. ASME J. Eng. Mater. Technol. 124(1), 78–87 (2002)

    Google Scholar 

  49. Hochrainer, T., Zaiser, M., Gumbsch, P.: A three-dimensional continuum theory of dislocation systems: kinematics and mean-field formulation. Philos. Mag. 87, 1261–1282 (2007)

    Google Scholar 

  50. Arsenlis, A., Cai, W., Tang, M., Rhee, M., Oppelstrup, T., Hommes, G., Pierce, T.G., Bulatov, V.V.: Enabling strain hardening simulations with dislocation dynamics. Model. Simul. Mater. Sci. Eng. 15, 553–595 (2007)

    Google Scholar 

  51. El-Azab, A., Deng, J., Tang, M.: Statistical characterization of dislocation ensembles. Philos. Mag. 87(8–9), 1201–1223 (2007)

    Google Scholar 

  52. Devincre, B., Hoc, T., Kubin, L.: Dislocation mean free paths and strain hardening of crystals. Science 320(5884), 1745–1748 (2008)

    Google Scholar 

  53. Motz, C., Weygan, D., Senger, J., Gumbsch, P.: Initial dislocation structures in 3-D discrete dislocation dynamics and their influence on microscale plasticity. Acta Mater. 57(6), 1744–1754 (2009)

    Google Scholar 

  54. Zaiser, M., Sandfeld, S.: Scaling properties of dislocation simulations in the similitude regime. Model. Simul. Mater. Sci. Eng. 22:065012, (2014)

    Google Scholar 

  55. Groma, I., Zaiser, M., Ispanovity, P.D.: Dislocation patterning in a two-dimensional continuum theory of dislocations. Phys. Rev. B 93, 214110 (2016)

    Google Scholar 

  56. Xia, S., El-Azab, A.: Computational modelling of mesoscale dislocation patterning and plastic deformation of single crystals. Model. Simul. Mater. Sci. Eng. 23(5), 55009 (2015)

    Google Scholar 

  57. Xiong, L., Chen, Y.: Effects of dopants on the mechanical properties of nanocrystalline silicon carbide thin film. Comput. Model. Eng. Sci. 24, 203–214 (2008)

    Google Scholar 

  58. Xiong, L., Chen, Y.: Coarse-grained simulations of single-crystal silicon. Model. Simul. Mater. Sci. Eng. 17, 035002 (2009)

    Google Scholar 

  59. Deng, Q., Chen, Y.: A coarse-grained atomistic method for 3D dynamic fracture simulation. Int. J. Multiscale Comput. Eng. 11, 227–237 (2013)

    Google Scholar 

  60. Xiong, L., Deng, Q., Tucker, G., McDowell, D.L., Chen, Y.: A concurrent scheme for passing dislocations from atomistic to continuum domains. Acta Mater. 60, 899–913 (2012)

    Google Scholar 

  61. Xiong, L., Deng, Q., Tucker, G., McDowell, D.L., Chen, Y.: Coarse-grained atomistic simulations of dislocations in Al, Ni and Cu crystals. Int. J. Plast. 38, 86–101 (2012)

    Google Scholar 

  62. Xiong, L., McDowell, D.L., Chen, Y.: Nucleation and growth of dislocation loops in Cu, Al and Si by a concurrent atomistic-continuum method. Scr. Mater. 67, 633–636 (2012)

    Google Scholar 

  63. Xiong, L., Chen, Y.: Coarse-grained atomistic modeling and simulation of inelastic material behavior. Acta Mech. Solida Sin. 25, 244–261 (2012)

    Google Scholar 

  64. Xiong, L., McDowell, D.L., Chen, Y.: Sub-THz Phonon drag on dislocations by coarse-grained atomistic simulations. Int. J. Plast. 55, 268–278 (2014)

    Google Scholar 

  65. Xiong, L., Xu, S., McDowell, D.L., Chen, Y.: Concurrent atomistic-continuum simulations of dislocation-void interactions in fcc crystals. Int. J. Plast. 65, 33–42 (2015)

    Google Scholar 

  66. Xiong, L., Rigelesaiyin, J., Chen, X., Xu, S., McDowell, D.L., Chen, Y.: Coarse-grained elastodynamics of fast moving dislocations. Acta Mater. 104, 143–155 (2016)

    Google Scholar 

  67. Yang, S., Xiong, L., Deng, Q., Chen, Y.: Concurrent atomistic and continuum simulation of strontium titanate. Acta Mater. 61, 89–102 (2013)

    Google Scholar 

  68. Yang, S., Chen, Y.: Concurrent atomistic and continuum simulation of bi-crystal strontium titanate with tilt grain boundary. Proc. Roy. Soc. A 471, 20140758 (2015)

    Google Scholar 

  69. Yang, S., Zhang, N., Chen, Y.: Concurrent atomistic-continuum simulation of polycrystalline strontium titanate. Philos. Mag. 95, 2697–2716 (2015)

    Google Scholar 

  70. Yang, S., Chen, Y.: Concurrent atomistic-continuum simulation of defects in polyatomic ionic materials. In: Weinberger, C., Tucker, G. (eds.) Multiscale Materials Modeling for Nanomechanics. Springer International Publishing, Switzerland (2016)

    Google Scholar 

  71. Chen, X., Xiong, L., McDowell, D.L., Chen, Y.: Effects of phonons on mobility of dislocations and dislocation arrays. Scr. Mater. 137, 22–26 (2017)

    Google Scholar 

  72. Chen, X., Li, W., Xiong, L., Li, Y., Yang, S., Zheng, Z., McDowell, D.L., Chen, Y.: Ballistic-diffusive phonon heat transport across grain boundaries. Acta Mater. 136, 355–365 (2017)

    Google Scholar 

  73. Chen, X., Diaz, A., Xiong, L., Chen, Y.: Passing waves from atomistic to continuum. J. Comput. Phys. 354, 393–402 (2018)

    MathSciNet  Google Scholar 

  74. Chen, X., Li, W., Diaz, A., Li, Y., McDowell, D.L., Chen, Y.: Recent progress in the concurrent atomistic-continuum method and its application in phonon transport. MRS Commun. 7(4), 785–797 (2017)

    Google Scholar 

  75. Li, J: AtomEye: an efficient atomistic configuration viewer. Model. Simul. Mater. Sci. Eng. 11(2), 173 (2003)

    Google Scholar 

  76. Stukowski, A: Visualization and analysis of atomistic simulation data with OVITO—the Open Visualization Tool. Model. Simul. Mater. Sci. Eng. 18(1), 015012 (2010)

    Google Scholar 

  77. Jones, J.E.: On the determination of molecular fields. II. From the equation of state of a gas. Proc. R. Soc. Lond. A 106(738), 463–477 (1924)

    Google Scholar 

  78. Daw, M.S., Baskes, M.I.: Embedded-atom method: derivation and application to impurities, surfaces, and other defects in metals. Phys. Rev. B 29(12), 6443–6453 (1984)

    Google Scholar 

  79. Xu, S.: The concurrent atomistic-continuum method: Advancements and applications in plasticity of face-centered cubic metals. Ph.D. Dissertation, Georgia Institute of Technology (2016)

    Google Scholar 

  80. Allen, M.P., Tildesley, D.J.: Computer Simulation of Liquids. Oxford University Press, USA (1989)

    MATH  Google Scholar 

  81. Verlet, L.: Computer “experiments” on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules. Phys. Rev. 159, 98–103 (1967)

    Google Scholar 

  82. Swope, W.C., Andersen, H.C., Berens, P.H., Wilson, K.R.: A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters. J. Chem. Phys. 76(1), 637–649 (1982)

    Google Scholar 

  83. Xu, S., Xiong, L., Chen, Y., McDowell, D.L.: Sequential slip transfer of mixed-character dislocations across Σ3 coherent twin boundary in FCC metals: A concurrent atomistic-continuum study. npj Comput. Mater. 2, 15016 (2016)

    Google Scholar 

  84. Xu, S., Xiong, L., Chen, Y., McDowell, D.L.: A concurrent atomistic-continuum study of slip transfer of sequential mixed character dislocations across symmetric tilt grain boundaries in Ni. JOM 69, 814–821 (2017)

    Google Scholar 

  85. McDowell, D.L.: A perspective on trends in multiscale plasticity. Int. J. Plast. 26, 1280–1309 (2010)

    MATH  Google Scholar 

  86. Xu, S., Xiong, L., Chen, Y., McDowell, D.L.: An analysis of key characteristics of the Frank-Read source process in FCC metals. J. Mech. Phys. Solids 96, 460–476 (2016)

    Google Scholar 

  87. Xu, S., Xiong, L., Chen, Y., McDowell, D.L.: Shear stress- and line length-dependent screw dislocation cross-slip in FCC Ni. Acta Mater. 122, 412–419 (2017)

    Google Scholar 

  88. Xu, S., Xiong, L., Chen, Y., McDowell, D.L.: Edge dislocations bowing out from a row of collinear obstacles in Al. Scr. Mater. 123, 135–139 (2016)

    Google Scholar 

  89. Xu, S., Xiong, L., Chen, Y., McDowell, D.L.: Validation of the concurrent atomistic-continuum method on screw dislocation/stacking fault interactions. Crystals 7, 120 (2017)

    Google Scholar 

  90. Xiong, L., Chen, X., Zhang, N., McDowell, D.L., Chen, Y.: Prediction of phonon properties of 1D polyatomic systems using concurrent atomistic-continuum simulation. Arch. Appl. Mech. 84, 1665–1675 (2014)

    Google Scholar 

  91. Rice, J.R.: Inelastic constitutive relations for solids: An internal variable theory and its application to metal plasticity. J. Mech. Phys. Solids 19, 433–455 (1971)

    MATH  Google Scholar 

  92. Muschik, W.: Non-Equilibrium Thermodynamics with Application to Solids. Springer, New York (1993)

    MATH  Google Scholar 

  93. Hull, D., Bacon, D.J.: Introduction to Dislocations, 5th edn. Butterworth-Heinemann, Oxford, UK (2011)

    Google Scholar 

  94. Anderson, P.M., Hirth, J.P., Lothe, J.: Theory of Dislocations, 3rd edn. Cambridge University Press (2017)

    Google Scholar 

  95. Nye, J.F.: Some geometrical relations in dislocated crystals. Acta Mater. 1(2), 153–162 (1953)

    Google Scholar 

  96. Hill, R., Sneddon, I.N. (eds.): Progress in Solid Mechanics, vol. 1, p. 330. North-Holland Publishing Company (1960)

    Google Scholar 

  97. Mishin, Y., Mehl, M.J., Papaconstantopoulos, D.A., Voter, A.F., Kress, J.D.: Structural stability and lattice defects in copper: Ab initio, tight-binding, and embedded-atom calculations. Phys. Rev. B 63(22), 224106 (2001)

    Google Scholar 

  98. Plimpton, S.: Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117, 1–19 (1995)

    MATH  Google Scholar 

  99. Hirel, P.: Atomsk: A tool for manipulating and converting atomic data files. Comput. Phys. Commun. 197, 212–219 (2015)

    Google Scholar 

  100. Hartley, C.S., Mishin, Y.: Representation of dislocation cores using Nye tensor distributions. Mater. Sci. Eng. A 400, 18–21 (2005)

    Google Scholar 

  101. Gurrutxaga-Lerma, B., Balint, D.S., Dini, D., Eakins, D.E., Sutton, A.P.: A dynamic discrete dislocation plasticity method for the simulation of plastic relaxation under shock loading. Proc. R. Soc. A 469, 20130141 (2013)

    MathSciNet  MATH  Google Scholar 

  102. Chen, X., Chernatynskiy, A., Xiong, L., Chen, Y.: A coherent phonon pulse model for transient phonon thermal transport. Comput. Phys. Commun. 195, 112–116 (2015)

    Google Scholar 

  103. Ramesh, K.T.: Nanomaterials: Mechanics and Mechanisms. Springer (2009)

    Google Scholar 

  104. Kacher, J., Eftink, B.P., Cui, B., Robertson, I.M.: Dislocation interactions with grain boundaries. Curr. Opin. Solid State Mater. Sci. 18, 227–243 (2014)

    Google Scholar 

  105. Counts, W.A., Braginsky, M.V., Battaile, C.C., Holm, E.A.: Predicting the Hall-Petch effect in fcc metals using non-local crystal plasticity. Int. J. Plast. 24, 1243–1263 (2008)

    MATH  Google Scholar 

  106. Spearot, D.E., Sangid, M.D.: Insights on slip transmission at grain boundaries from atomistic simulations. Curr. Opin. Solid State Mater. Sci. 18, 188–195 (2014)

    Google Scholar 

  107. Stukowski, A.: Structure identification methods for atomistic simulations of crystalline materials. Model. Simul. Mater. Sci. Eng. 20, 045021 (2012)

    Google Scholar 

  108. Mishin, Y., Farkas, D., Mehl, M.J., Papaconstantopoulos, D.A.: Interatomic potentials for monoatomic metals from experimental data and ab initio calculations. Phys. Rev. B 59, 3393 (1999)

    Google Scholar 

  109. Voter, A.F., Chen, S.P.: Accurate interatomic potentials for Ni, Al, and Ni3Al. Mater. Res. Soc. Symp. Proc. 82, 175 (1987)

    Google Scholar 

  110. Angelo, J.E., Moody, N.R., Baskes, M.I.: Trapping of hydrogen to lattice-defects in nickel. Model. Simul. Mater. Sci. Eng. 3, 289 (1995)

    Google Scholar 

  111. Foiles, S.M., Hoyt, J.J.: Computation of grain boundary stiffness and mobility from boundary fluctuations. Acta Mater. 54, 3351 (2006)

    Google Scholar 

  112. Zhou, X.W., Johnson, R.A., Wadley, H.N.G.: Misfit-energy-increasing dislocations in vapor-deposited CoFe/NiFe multilayers. Phys. Rev. B 69, 144113 (2004)

    Google Scholar 

  113. Lipkin, D.M., Clarke, D.R., Beltz, G.E.: A strain-gradient model of cleavage fracture in plastically deforming materials. Acta Mater. 44, 4051–4058 (1996)

    Google Scholar 

  114. Hussein, A.M., El-Awady, J.A.: Quantifying dislocation microstructure evolution and cyclic hardening in fatigued face-centered cubic single crystals. J. Mech. Phys. Solids 91, 126–144 (2016)

    Google Scholar 

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Acknowledgements

These results are in part based upon work supported by the National Science Foundation as a collaborative effort between Georgia Tech (CMMI-1232878) and University of Florida (CMMI-1233113). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. The authors thank Dr. Jinghong Fan, Dr. Qian Deng, Dr. Shengfeng Yang, Dr. Xiang Chen, Mr. Rui Che, and Mr. Weixuan Li for helpful discussions, Mr. Kevin Chu for building the Python scripting interface in PyCAC, and Dr. Aleksandr Blekh for arranging execution of PyCAC via MATIN. The work of SX was supported in part by Georgia Tech Institute for Materials and in part by the Elings Prize Fellowship in Science offered by the California NanoSystems Institute (CNSI) on the UC Santa Barbara campus. SX also acknowledges support from the Center for Scientific Computing from the CNSI, MRL: an NSF MRSEC (DMR-1121053). LX acknowledges the support from the Department of Energy, Office of Basic Energy Sciences under Award Number DE-SC0006539. The work of LX was also supported in part by the National Science Foundation under Award Number CMMI-1536925. DLM is grateful for the additional support of the Carter N. Paden, Jr. Distinguished Chair in Metals Processing. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1053575.

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Authors and Affiliations

  1. California NanoSystems Institute, University of California, Santa Barbara, Santa Barbara, CA, 93106-6105, USA

    Shuozhi Xu

  2. Department of Aerospace Engineering, Iowa State University, Ames, IA, 50011, USA

    Ji Rigelesaiyin & Liming Xiong

  3. Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, 32611-6250, USA

    Youping Chen

  4. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, 30332-0405, USA

    David L. McDowell

  5. School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, GA, 30332-0245, USA

    David L. McDowell

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  1. Shuozhi Xu
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  4. Youping Chen
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  5. David L. McDowell
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Editors and Affiliations

  1. Institut für Mechanik, Otto-von-Guericke-Universität Magdeburg, Magdeburg, Germany

    Holm Altenbach

  2. Centre National de la Recherche Scientifique, UMR 7190, Institut Jean Le Rond d’Alembert, Sorbonne Université, Paris, France

    Joël Pouget

  3. Centre National de la Recherche Scientifique, UMR 7190, Institut Jean Le Rond d’Alembert, Sorbonne Université, Paris, France

    Martine Rousseau

  4. Centre National de la Recherche Scientifique, UMR 7190, Institut Jean Le Rond d’Alembert, Sorbonne Université, Paris, France

    Bernard Collet

  5. Centre National de la Recherche Scientifique, UMR 7190, Institut Jean Le Rond d’Alembert, Sorbonne Université, Paris, France

    Thomas Michelitsch

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Xu, S., Rigelesaiyin, J., Xiong, L., Chen, Y., McDowell, D.L. (2018). Generalized Continua Concepts in Coarse-Graining Atomistic Simulations. In: Altenbach, H., Pouget, J., Rousseau, M., Collet, B., Michelitsch, T. (eds) Generalized Models and Non-classical Approaches in Complex Materials 2. Advanced Structured Materials, vol 90. Springer, Cham. https://doi.org/10.1007/978-3-319-77504-3_12

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