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Coarse-Grained Atomistic Modeling and Simulation of Inelastic Material Behavior

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Abstract

This paper presents a new methodology for coarse-grained atomistic simulation of inelastic material behavior including phase transformations in ceramics and dislocation mediated plasticity in metals. The methodology combines an atomistic formulation of balance equations and a modified finite element method. With significantly fewer degrees of freedom than those of a fully atomistic model and without additional constitutive rules but the interatomic force field, the new coarse-grained (CG) method is shown to be feasible in predicting the nonlinear constitutive responses of materials and also reproducing atomic-scale phenomena such as phase transformations (diamond → β-Sn) in silicon and dislocation nucleation and migration, formation of dislocation loops and stacking faults ribbons in single crystal nickel. Direct comparisons between CG and the corresponding full molecular dynamics (MD) simulations show that the present methodology is efficient and promising in modeling and simulation of inelastic material behavior without losing the essential atomistic features. The potential applications and the limitations of the CG method are also discussed.

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References

  1. McDowell, D.L., A perspective on trends in multiscale plasticity. Khan International Medal Lecture. Plasticity 2008, St. Thomas, Virgin Islands, 2008a.

    Google Scholar 

  2. McDowell, D.L., Viscoplasticity of heterogeneous metallic materials. Materials Science and Engineering R: Reports, 2008b, 62: 67–123.

    Article  Google Scholar 

  3. Espanol, P., Statistical mechanics of dissipative particle dynamics. Europhysics Letters, 2004, 30(4): 191–196.

    Article  Google Scholar 

  4. Chen, Y., Zimmerman, J., Krivtsov, A. and McDowell, D.L., Assessment of atomistic coarse-graining methods. International Journal of Engineering Science, 2011, 49: 1337–1349.

    Article  Google Scholar 

  5. Levitt, M., A simplified representation of protein conformations for rapid simulation of protein folding. Journal of Molecular Biology, 1976, 104: 59–107.

    Article  Google Scholar 

  6. Levitt, M. and Warshel, A., Computer simulation of protein folding. Nature, 1975: 694–698.

    Article  Google Scholar 

  7. Reith, D., Meyer, H. and Muller-Plathe, F., Mapping atomistic to coarse-grained polymer models using automatic simplex optimization to fit structural properties. Macromolecules, 2001, 34: 2335–2345.

    Article  Google Scholar 

  8. Born, M. and Huang, K., Dynamical Theory of Crystal Lattices. Oxford University Press, 1954.

  9. Tadmor, E.B., Ortiz, M. and Phillips, R., Quasicontinuum analysis of defects in solids. Philosophical Magazine A, 1996, 73: 1529–1563.

    Article  Google Scholar 

  10. Knap, J. and Ortiz, M., An analysis of the quasicontinuum method. Journal of the Mechanics and Physics of Solids, 2001, 49: 1899–1923.

    Article  Google Scholar 

  11. Rudd, R.E. and Broughton, J.Q., Coarse-grained molecular dynamics and the atomic limit of finite elements. Physical Review B, 1998, 58: R5893–R5896.

    Article  Google Scholar 

  12. Kirkwood, J.G., The statistical mechanical theory of transport processes, I: General theory. Journal of Chemical Physics, 1946, 14: 180–201.

    Article  Google Scholar 

  13. Eringen, A.C. and Suhubi, E.S., Nonlinear theory of simple micro-elastic solids-I. International Journal of Engineering Sciences, 1964, 2: 189–203.

    Article  MathSciNet  Google Scholar 

  14. Chen, Y. and Lee, J.D., Atomistic formulation of a multiscale theory for nano/micro physics. Philosophical Magazine, 2005, 85: 4095–4126.

    Article  Google Scholar 

  15. Chen, Y., Local stress and heat flux in atomistic systems involving three-body forces. Journal of Chemical Physics, 2006, 124: 054113.

    Article  Google Scholar 

  16. Chen, Y., Reformulation of microscopic balance equations for multiscale materials modeling. Journal of Chemical Physics, 2009, 130: 134706.

    Article  Google Scholar 

  17. Xiong, L. and Chen, Y., Multiscale modeling and simulation of single-crystal MgO through an atomistic field theory. International Journal of Solids and Structures, 2009a, 46: 1448–1455.

    Article  Google Scholar 

  18. Xiong, L. and Chen, Y., Coarse-grained simulations of single-crystal silicon. Modelling and Simulation in Materials Science and Engineering, 2009b, 17: 035002.

    Article  Google Scholar 

  19. Xiong, L., Deng, Q., Tucker, G., McDowell, D.L. and Chen, Y., A concurrent scheme for passing dislocations from atomistic to continuum regions. Acta Materialia, 2012, 60(3): 899–913.

    Article  Google Scholar 

  20. Xiong, L, Tucker, G., McDowell, D.L. and Chen, Y., Coarse-grained atomistic simulation of dislocations. Journal of the Mechanics and Physics of Solids, 2011, 59: 160–177.

    Article  Google Scholar 

  21. Deng, Q., Xiong, L. and Chen, Y., Coarse-graining atomistic dynamics of brittle fracture by finite element method. International Journal of Plasticity, 2010, 26(9): 1402–1414.

    Article  Google Scholar 

  22. Irving, J. and Kirkwood, J., The statistical mechanical theory of transport processes. IV. The Equations of Hydrodynami. Journal of Chemical Physics, 1950, 8: 817–829.

    Article  Google Scholar 

  23. Evans, D.J. and Morriss, G.P., Statistical Mechanics of Nonequilibrium Liquids. Academic Press, 1990.

  24. Tersoff, J., Modeling solid-state chemistry: interatomic potentials for multicomponent systems. Physical Review B, 1989, 39: 5566–5568.

    Article  Google Scholar 

  25. Mishin, Y., Farkas, D., Mehl, M.J. and Papaconstantopoulos, D.A., Interatomic potentials for monoatomic metals from experimental data and ab initio calculations. Physical Review B, 1999, 59: 3393–3407.

    Article  Google Scholar 

  26. Mishin, Y., Mehl, M.J., Papaconstantopoulos, D.A., Voter, A.F. and Kress, J.D., Structural stability and lattice defects in copper: Ab initio, tight-binding and embedded-atom calculation. Physical Review B, 2001, 63: 224106.

    Article  Google Scholar 

  27. Zope, R.R. and Mishin, Y., Interatomic potentials for atomistic simulations of the Ti-Al system. Physical Review B, 2003, 68: 024102.

    Article  Google Scholar 

  28. Smith and Forester, The DL-POLY User Manual. CCLRC Daresbury Laboratory, UK: Warrington, 2001.

    Google Scholar 

  29. Hoover, W.G., Canonical dynamics: Equilibrium phase-space distributions. Physical Review A, 1985, 31: 1695.

    Article  Google Scholar 

  30. Gupta, M.C. and Ruoff, A.L., Static compression of silicon in the [100] and in the [111] directions. Journal of Applied Physics, 1980, 51: 1072–1075.

    Article  Google Scholar 

  31. Hu, J.Z., Merkle, L.D., Menoni, C.S. and Spain, I.L., Crystal data for high-pressure phases of silicon. Physical Review B, 1986, 34: 4679–4684.

    Article  Google Scholar 

  32. Olijnyk, H., Sikka, S.K. and Holzapfel, W.B. Structural phase transitions in Si and Ge under pressures up to 50 GPa. Physics Letters A, 1984, 103: 137–140.

    Article  Google Scholar 

  33. McMahon, M.I. and Nelmes, R.J., New high-pressure phase of Si. Physical Review B, 1993, 47: 8337–8340.

    Article  Google Scholar 

  34. Hanfland, M., Schwarz, U., Syassen, K. and Takemura, K., Crystal structure of the high-pressure phase silicon VI. Physical Review Letter, 1999, 82: 1197–1200.

    Article  Google Scholar 

  35. Zhao, Y.X., Buehler, F., Sites, J.R. and Spain, I.L., New metastable phases of silicon. Solid State Commun, 1986, 59: 679–682.

    Article  Google Scholar 

  36. Bradby, J.E., Williams, J.S., Wong-Leung, J., Swain, M.V. and Munroe, P., Mechanical deformation in silicon by micro-indentation. Journal of Materials Research, 2001, 16(5): 1500–1507.

    Article  Google Scholar 

  37. Domnich, V. and Gogotsi, Y., Phase transformations in silicon under contact loading. Reviews on Advanced Materials Science, 2002, 3: 1–36.

    Article  Google Scholar 

  38. Zarudi, I., Zhang, L.C. and Swain, M.V., Microstructure evolution in monocrystalline silicon during cyclic microindentations. Journal of Materials Research, 2003, 18(4): 758–761.

    Article  Google Scholar 

  39. Yin, T. and Cohen, M.L., Theory of static structural properties, crystal stability, and phase transformations: application to Si and Ge. Physical Review B, 1982, 26: 5668–5687.

    Article  Google Scholar 

  40. Mujica, A., Radescu, S., Munoz, A. and Needs, R.J., Comparative study of novel structures in silicon and germanium. Physica Status Solidi B, 2001, 223: 379–384.

    Article  Google Scholar 

  41. Cheng, C., Huang, W.H., and Li, H.J., Thermodynamics of uniaxial phase transition: ab initio study of the diamond-to-beta-tin transition in Si and Ge. Physical Review B, 2001, 63: 153202.

    Article  Google Scholar 

  42. Lee, I.H., Jeong, J.W. and Chang, K.J., Invariant-molecular dynamics study of the diamond-to-B-Sn transitions in Si under hydrostatic and uniaxial compressions. Physical Review B, 1997, 55: 5689–5693.

    Article  Google Scholar 

  43. Cheong, W.C.D. and Zhang, L.C., Molecular dynamics simulation of phase transformations in silicon monocrystals due to nano-indentation. Nanotechnology, 2000: 173–180.

    Article  Google Scholar 

  44. Cheong, W.C.D. and Zhang, L.C., A stress criterion for the beta-Sn transformation in silicon under indentation and uniaxial compression. Key Engineering Materials, 2003: 233–236.

  45. Zarudi, I., Zhang, L.C., Cheong, W.C.D. and Yu, T.X., The difference of phase distributions in silicon after indentation with Berkovich and spherical indenters. Acta Materialia, 2005, 53(18): 4795–4800.

    Article  Google Scholar 

  46. Durandurdu, M., Diamond to β → Sn phase transition of silicon under hydrostatic and nonhydrostatic compressions. Journal of Physics: Condensed Matter, 2008, 20: 325232.

    Google Scholar 

  47. Ivashchenko, V.I., Turchi, P.E.A. and Shevchenko, V.I., Simulations of indentation-induced phase transformations in crystalline and amorphous silicon. Physical Review B, 2008, 78: 035205.

    Article  Google Scholar 

  48. Suri, M. and Dumitrica, T., Efficient sticking of surface-passivated Si nanospheres via phase-transition plasticity. Physical Review B Rapid Communication, 2008, 78: R081405.

    Article  Google Scholar 

  49. Donohue, J., The Structure of Tthe Elements. New York: Wiley, 1974.

    Google Scholar 

  50. McDowell, D.L., A Perspective on trends in multiscale plasticity. International Journal of Plasticity, 2010, 26: 1280–1309.

    Article  Google Scholar 

  51. Chen, C.Q., Cui, J.Z., Duan, H.L., Feng, X.Q., He, L.H., Hu, G.K., Huang, M.J., Huo, Y.Z., Ji, B.H., Liu, B., Peng, X.H., Shi, H.J., Sun, Q.P., Wang, J.X., Wang, Y.S., Zhao, H.P., Zhao, Y.P., Zheng, Q.S. and Zou, W.N., Perspectives in mechanics of heterogeneous solids. Acta Mechanica Solida Sinica, 2011, 24: 1–26.

    Article  Google Scholar 

  52. McDowell, D.L., Materials design: a useful research focus for inelastic behavior of structural metals. In: Sih, G.C., Panin, V.E. (Eds.), Special Issue of the Theoretical and Applied Fracture Mechanics, Prospects of Mesomechanics in the 21st Century: Current Thinking on Multiscale Mechanics Problems, 2001, 37: 245–259.

    Article  Google Scholar 

  53. McDowell, D.L. and Olson, G.B., Concurrent design of hierarchical materials and structures. Scientific Modeling and Simulation, 2008, 15(1): 207.

    Google Scholar 

  54. Gumbsch, P., An atomistic study of brittle fracture: toward explicit failure criteria from atomistic modeling. Journal of Materials Research, 1995, 10: 2897–2907.

    Article  Google Scholar 

  55. Weinan, E. and Huang, Z., Matching conditions in atomistic-continuum modeling of materials. Physical Review Letters, 2001, 8713(13): 135501.

    Google Scholar 

  56. Shilkrot, L.E., Curtin, W.A. and Miller, R.E., A coupled atomistic/continuum model of defects in solids. Journal of the Mechanics and Physics of Solids, 2002a, 50: 2085–106.

    Article  Google Scholar 

  57. Shilkrot, L.E., Miller, R.E. and Curtin, W.A., Coupled atomistic and discrete dislocation plasticity. Physical Review Letter, 2002b, 89: 025501–4.

    Article  Google Scholar 

  58. Shilkrot, L.E., Miller, R.E. and Curtin, W.A., Multiscale plasticity modeling: coupled atomistics and discrete dislocation mechanics. Journal of the Mechanics and Physics of Solids, 2004, 52: 755–87.

    Article  MathSciNet  Google Scholar 

  59. Shenoy, V.B., Miller, R., Tadmor, E.B., Phillips, R. and Ortiz, M., Quasicontinuum models of interfacial structure and deformation. Physical Review Letters, 1998, 80(4): 742–745.

    Article  Google Scholar 

  60. Shenoy, V.B., Miller, R., Tadmor, E.B., Rodney, D., Phillips, R. and Ortiz, M., An adaptive finite element approach to atomic-scale mechanics-the quasicontinuum method. Journal of the Mechanics and Physics of Solids, 1999, 47(3): 611–642.

    Article  MathSciNet  Google Scholar 

  61. Khachaturyan, A.G., Wang, Y.U., Jin and Cuitino, A.M., Nanoscale phase field microelasticity theory of dislocations: model and 3D simulations. Acta Materialia, 2001, 49: 1847–1857.

    Article  Google Scholar 

  62. Chen, L.Q., Phase-field models for microstructure evolution. Annual Review of Materials Research, 2002, 32: 113–140.

    Article  Google Scholar 

  63. Shen, C. and Wang, Y., Modeling dislocation network and dislocation-precipitate interaction at mesoscopic scale using phase field method. International Journal of Multiscale Computational Engineering, 2003, 1(1): 91–104.

    Article  Google Scholar 

  64. Amodeo, R.J. and Ghoniem, N.M., A review of experimental-observations and theoretical-models of dislocation cells and subgrains. Res Mechanica, 1998, 23(2–3): 137–160.

    Google Scholar 

  65. Amodeo, R.J. and Ghoniem, N.M., Dislocation dynamics. I. A proposed methodology for deformation micromechanics. Physical Review B, 1990a, 41: 6958–6967.

    Article  Google Scholar 

  66. Amodeo, R.J. and Ghoniem, N.M., Dislocation dynamics. II. Applications to the formation of persistent slip bands, planar arrays, and dislocation cells. Physical Review B, 1990b, 41: 6968–6976.

    Article  Google Scholar 

  67. Kubin, L.P., Canova, G., The modeling of dislocation patterns. Scripta Metallurgica, 1992, 27: 957–962.

    Article  Google Scholar 

  68. Van der Giessen, E. and Needleman, A., Discrete dislocation plasticity: a simple planar model. Modelling and Simulation in Materials Science and Engineering, 1995, 3: 689–735.

    Article  Google Scholar 

  69. Groma, I., Link between the microscopic and mesocopic length-scale description of the collective behavior of dislocations. Physical Review B, 1997, 56(10): 5807–5813.

    Article  Google Scholar 

  70. Arsenlis, A. and Parks, D.M., Crystallographic aspects of geometrically-necessary and statistically-stored dislocation density. Acta Materialia, 1999, 47(5): 1597–1611.

    Article  Google Scholar 

  71. Arsenlis, A. and Parks, D.M., Modeling the evolution of crystallographic dislocation density in crystal plasticity. Journal of the Mechanics and Physics of Solids, 2002, 50: 1979–2009.

    Article  Google Scholar 

  72. Rhee, M., Zbib, H.M., Herth, J.P., Huang, H. and de la Rubia, T., Models for long-short-range interactions and cross slip in 3D dislocation simulation of BCC single crystals. Modelling and Simulation in Materials Science and Engineering, 1998, 6(4): 467–492.

    Article  Google Scholar 

  73. Zbib, H.M., Rhee, M. and Hirth, J.P., On plastic deformation and the dynamics of 3D dislocations. International Journal of Mechanical Sciences, 1998, 40: 113–127.

    Article  Google Scholar 

  74. Zbib, H.M. and de la Rubia, T.D., A multiscale model of plasticity. International Journal of Plasticity, 2002, 18(9): 1133–1163.

    Article  Google Scholar 

  75. Rickman, J.M. and LeSar, R., Issues in the coarse-graining of dislocation energetics and dynamics. Scripta Materialia, 2006, 54: 735–739.

    Article  Google Scholar 

  76. Huang, M.S., Li, Z.H. and Wang, C., Discrete dislocation dynamics modeling of microvoid growth and its intrinsic mechanism in single crystals. Acta Materialia, 2007, 55(4): 1387–1396.

    Article  Google Scholar 

  77. Li, Z.H., Hou, C.T., Huang, M.S. and Ouyang, C.J., Strengthening mechanism in micro-polycrystals with penetrable grain boundaries by discrete dislocation dynamics simulation and Hall-Patch effect. Computational Materials Science, 2009, 46(4): 1124–1134.

    Article  Google Scholar 

  78. Hou, C.T., Li, Z.H., Huang, M.S. and Ouyang, C.J., Cyclic hardening behavior of polycrstals with penetrable grain boundaries: two-dimensional discrete dislocation dynamics simulations. Acta Mechanica Solida Sinica, 2009, 22(4): 295–306.

    Article  Google Scholar 

  79. Li, J., AtomEye: an efficient atomistic configuration viewer. Modelling and Simulation in Materials Science and Engineering, 2003, 11: 173–177.

    Article  Google Scholar 

  80. Steinbach, I., Phase-field models in materials science. Modelling and Simulation in Materials Science and Engineering, 2009, 17: 073001.

    Article  Google Scholar 

  81. Arsenlis, A., Cai, W., Tang, M., Rhee, M., Oppelstrup, T., Hommes, G., Pierce, T.G. and Bulatov, V.V., Enabling strain hardening simulations with dislocation dynamics. Modelling and Simulation in Materials Science and Engineering, 2007, 15: 553–595.

    Article  Google Scholar 

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Xiong, L., Chen, Y. Coarse-Grained Atomistic Modeling and Simulation of Inelastic Material Behavior. Acta Mech. Solida Sin. 25, 244–261 (2012). https://doi.org/10.1016/S0894-9166(12)60023-8

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  • DOI: https://doi.org/10.1016/S0894-9166(12)60023-8

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