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Multiscale Modeling of Nanocomposite Materials

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Virtual Testing and Predictive Modeling

Abstract

Composite and nanocomposite materials have the potential to provide significant increases in specific stiffness and specific strength relative to materials used for many engineering structural applications. To facilitate the design and development of nanocomposite materials, structure–property relationships must be established that predict the bulk mechanical response of these materials as a function of the molecular- and micro-structure. Although many multiscale modeling techniques have been developed to predict the mechanical properties of composite materials based on the molecular structure, all of these techniques are limited in terms of their treatment of amorphous molecular structures, time-dependent deformations, molecular behavior detail, and applicability to large deformations. The proper incorporation of these issues into a multiscale framework may provide efficient and accurate tools for establishing structure–property relationships of composite materials made of combinations of polymers, metals, and ceramics. The objective of this chapter is to describe a general framework for multiscale modeling of composite materials. First, the fundamental aspects of efficient and accurate modeling techniques will be discussed. This will be followed by a review of current state-of-the-art modeling approaches. Finally, a specific example will be presented that describes the application of the approach to a specific nanocomposite material system.

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References

  1. A.R. Leach, Molecular Modelling: Principles and Applications. Prentice Hall, New York, 2001

    Google Scholar 

  2. C. Truesdell and W. Noll, The Non-Linear Field Theories of Mechanics. Springer-Verlag, New York, 2004

    Google Scholar 

  3. C.A. Truesdell and R.A. Toupin, The Classical Field Theories, in Encyclopedia of Physics, Volume III/1: Principals of Classical Mechanics and Field Theory, Flugge S, Editor. 1960, Springer-Verlag, Berlin, Germany.

    Google Scholar 

  4. K.J. Bathe, Finite Element Procedures. Prentice-Hall, Inc., Englewood Cliffs, NJ, 1996

    Google Scholar 

  5. C.T. Herakovich, Mechanics of Fibrous Composites. John Wiley & Sons, Inc., New York, 1998

    Google Scholar 

  6. M. Jiang, K. Alzebdeh, I. Jasiuk, and M. Ostoja-Starzewski, “Scale and Boundary Conditions Effects in Elastic Properties of Random Composites,” Acta Mech., Vol. 148, 2001, pp. 63–78

    Article  MATH  Google Scholar 

  7. M. Jiang, I. Jasiuk, and M. Ostoja-Starzewski, “Apparent Elastic and Elastoplastic Behavior of Periodic Composites,” Int. J. Solids Struct., Vol. 39, 2002, pp. 199–212

    Article  MATH  Google Scholar 

  8. G.M. Odegard, T.S. Gates, L.M. Nicholson, and K.E. Wise, “Equivalent-Continuum Modeling of Nano-Structured Materials,” Compos. Sci. Technol., Vol. 62, 2002, 1869–1880

    Google Scholar 

  9. A.C. Eringen, Microcontinuum Field Theories. Springer-Verlag, New York, 1999

    Book  MATH  Google Scholar 

  10. A.C. Eringen, Nonlocal Continuum Field Theories. Springer-Verlag, New York, 2002

    MATH  Google Scholar 

  11. E.C. Aifantis, “On the Microstructural Origin of Certain Inelastic Models”. J. Eng. Mater. Technol-Trans. Asme, Vol. 106, 1984, pp. 326–330

    Article  Google Scholar 

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

    MATH  Google Scholar 

  13. C. Kittel, Introduction to Solid State Physics. John Wiley & Sons, New York, 1956

    Google Scholar 

  14. F.F. Abraham, J.Q. Broughton, N. Bernstein, and E. Kaxiras, “Spanning the Continuum to Quantum Length Scales in a Dynamic Simulation of Brittle Fracture”. Europhys. Lett., Vol. 44, 1998, pp. 783–787

    Article  Google Scholar 

  15. R.E. Rudd and J.Q. Broughton, “Coarse-Grained Molecular Dynamics and the Atomic Limit of Finite Elements,” Phys. Rev. B, Vol. 58, 1998, pp. 5893–5896

    Article  Google Scholar 

  16. E.B. Tadmor, M. Ortiz, and R. Phillips, “Quasicontinuum Analysis of Defects in Solids,” Philos. Mag. A, Vol. 73, 1996, pp. 1529–1593

    Article  Google Scholar 

  17. W.A. Curtin and R.E. Miller, “Atomistic/Continuum Coupling in Computational Materials Science,” Model. Simul. Mater. Sci. Eng., Vol. 11, 2003, pp. R33–R68

    Article  Google Scholar 

  18. L.E. Shilkrot, W.A. Curtin, and R.E. Miller, “A Coupled Atomistic/Continuum Model of Defects in Solids,” J. Mech. Phys. Solids, Vol. 50, 2002, pp. 2085–2106

    Article  MATH  Google Scholar 

  19. L.E. Shilkrot, R.E. Miller, and W.A. Curtin, “Multiscale Plasticity Modeling: Coupled Atomistics and Discrete Dislocation Mechanics,” J. Mech. Phys. Solids, Vol. 2004, 52, pp. 755–787

    Article  MathSciNet  MATH  Google Scholar 

  20. S.P. Xiao and Belytschko T, “A Bridging Domain Method for Coupling Continua with Molecular Dynamics,” Comput. Methods Appl. Mech. Eng., Vol. 193, 2004, pp. 1645–1669

    Article  MathSciNet  MATH  Google Scholar 

  21. G.J. Wagner and W.K. Liu, “Coupling of Atomistic and Continuum Simulations Using a Bridging Scale Decomposition,” J. Comput. Phys., Vol. 190, 2003, pp. 249–274

    Article  MATH  Google Scholar 

  22. B. Liu, H. Jiang, Y. Huang, S. Qu, and M.F. Yu, “Atomic-Scale Finite Element Method in Multiscale Computation with Appliations to Carbon Nanotubes,” Phys. Rev. B, Vol. 72, 2005, pp. 035435

    Article  Google Scholar 

  23. V. Yamakov, E. Saether, D.R. Phillips, and E.H. Glaessgen, “Molecular-Dynamics Simulation-Based Cohesive Zone Representation of Intergranular Fracture Processes in Aluminum,” J. Mech. Phys. Solids, Vol. 54, 2006, pp. 1899–1928

    Article  MATH  Google Scholar 

  24. M. Parrinello and A. Rahman, “Strain Fluctuations and Elastic Constants,” J. Chem. Phys., Vol. 76, 1982, 2662–2666

    Article  Google Scholar 

  25. A.A. Gusev, M.M. Zehnder, and U.W. Suter, Fluctuation Formula for Elastic Constants. Phys. Rev. B, Vol. 54, 1996, 1–4

    Article  Google Scholar 

  26. M.T. Meyers, J.M. Rickman, and T.J. Delph, “The Calculation of Elastic Constants from Displacement Fluctuations,” J. Appl. Phys., Vol. 98, 2005, pp. 1–3

    Article  Google Scholar 

  27. C.R. Miranda, K.V. Tretiakov, and S. Scandolo, “A Computational Study of Elastic Properties of Disordered Systems with Voids,” J. Non-Cryst. Solids, Vol. 352, 2006, pp. 4283–4286

    Article  Google Scholar 

  28. J.R. Ray and A. Rahman, “Statistical Ensembles and Molecular Dynamics Studies of Anisotropic Solids,” J. Chem. Phys., Vol. 80, 1984, pp. 4423–4428

    Article  Google Scholar 

  29. K. Van Workum and J.J. de Pablo, “Computer Simulation of the Mechanical Properties of Amorphous Polymer Nanostructures,” Nano Lett., Vol. 3, 2003, pp. 1405–1410

    Article  Google Scholar 

  30. K. Yoshimoto, G.J. Papakonstantopoulos, J.F. Lutsko, and J.J. De Pablo, “Statistical Calculation of Elastic Moduli for Atomistic Models,” Phys. Rev. B, Vol. 71, 2005, pp. 1–6

    Article  Google Scholar 

  31. Z. Zhou, “Fluctuations and Thermodynamics Properties of the Constant Shear Strain Ensemble,” J. Chem. Phys., Vol. 114, 2001, pp. 8769–8774

    Article  Google Scholar 

  32. C. Aleman and S. Munoz-Guerra, “On the Mechanical Properties of Poly(ethylene terephthalate). Force-Field Parametrization and Conformational Analysis for the Prediction of the Crystal Moduli,” J. Polym. Sci. Part B: Polym. Phys., Vol. 34, 1996, pp. 963–973

    Article  Google Scholar 

  33. C.F. Fan, T. Cagin, Z.M. Chen, and K.A. Smith, “Molecular Modeling of Polycarbonate. 1. Force Field, Static Structure, and Mechanical Properties,” Macromolecules, Vol. 27, 1994, pp. 2383–2391

    Article  Google Scholar 

  34. C.F. Fan and S.L. Hsu, “Application of the Molecular Simulation Technique to Characterize the Structure and Properties of an Aromatic Polysulfone System. 2. Mechanical and Thermal Properties,” Macromolecules, Vol. 25, 1992, 266–270

    Article  Google Scholar 

  35. M. Hutnik, A.S. Argon, and U.W. Suter, “Simulation of Elastic and Plastic Response in the Glassy Polycarbonate of 4,4'-Isopropylidenediphenol,” Macromolecules, Vol. 26, 1993, pp. 1097–1108

    Article  Google Scholar 

  36. S.S. Jang and W.H. Jo, “Analysis of the Mechanical Behavior of Amorphous Atactic Poly(oxypropylene) by Atomistic Modeling,” Macromol. Theory Simul., Vol. 8, 1999, 1–9

    Article  Google Scholar 

  37. S.S. Jang and W.H. Jo, “Analysis of the Mechanical Behavior of Poly(trimethylene terephthalate) in an Amorphous State under Uniaxial Extension-Compression Condition through Atomistic Modeling,” J. Chem. Phys., Vol. 110, 1999, 7524–7532

    Article  Google Scholar 

  38. J.W. Kang, K. Choi, W.H. Jo, and S.L. Hsu, “Structure-Property Relationships of Polyimides: A Molecular Simulation Approach,” Polymer, Vol. 39, 1998, pp. 7079–7078

    Article  Google Scholar 

  39. C.Y. Li and T.W. Chou, “Multiscale Modeling of Compressive Behavior of Carbon Nanotube/Polymer Composites,” Compos. Sci. Technol., Vol. 66, 2006, pp. 2409–2414

    Article  Google Scholar 

  40. G.M. Odegard, T.C. Clancy, T.S. Gates, “Modeling of the Mechanical Properites of Nanoparticle/Polymer Composites,” Polymer, Vol. 46, 2005, pp. 533–562

    Article  Google Scholar 

  41. G.M. Odegard, S.J.V. Frankland, T.S. Gates, “Effect of Nanotube Functionalization on the Elastic Properties of Polyethylene Nanotube Composites,” AIAA J., Vol. 43, 2005, pp. 1828–1835

    Article  Google Scholar 

  42. G.M. Odegard, T.S. Gates, K.E. Wise, C. Park, E. Siochi, “Constitutive Modeling of Nanotube-Reinforced Polymer Composites,” Compos. Sci. Technol., Vol. 63, 2003, pp. 1671–1687

    Article  Google Scholar 

  43. G.M. Odegard, R.B. Pipes, and P. Hubert, “Comparison of Two Models of SWCN Polymer Composites,” Compos. Sci. Technol., Vol. 64, 2004, pp. 1011–1020

    Article  Google Scholar 

  44. G.J. Papakonstantopoulos, M. Doxastakis, P.F. Nealey, J.L. Barrat, and J.J. De Pablo, “Calculation of Local Mechanical Properties of Filled Polymers,” Phys. Rev. E, Vol. 75, 2007, pp. 1–13

    Article  Google Scholar 

  45. T. Raaska, S. Niemela, and F. Sundholm, “Atom-Based Modeling of Elastic Constants in Amorphous Polystyrene,” Macromolecules, Vol. 27, 1994, 5751–5757

    Article  Google Scholar 

  46. G. Raffaini, S. Elli, and F. Ganazzoli, “Computer Simulation of Bulk Mechanical Properties and Surface Hydration of Biomaterials, “ J. Biomed. Mater. Res. A, Vol. 77, 2006, pp. 618–626

    Google Scholar 

  47. E. Saether, S.J.V. Frankland, and R.B. Pipes, “Transverse Mechanical Properties of Single-Walled Carbon Nanotube Crystals. Part I: Determination of Elastic Moduli,” Compos. Sci. Technol., Vol. 63, 2003, pp. 1543–1550

    Article  Google Scholar 

  48. D.N. Theodorou and U.W. Suter, “Atomistic Modeling of Mechanical Properties of Polymeric Glasses,” Macromolecules, Vol. 19, 1986, pp. 139–154

    Article  Google Scholar 

  49. P.K. Valavala, T.C. Clancy, G.M. Odegard, and T.S. Gates, “Nonlinear Multiscale Modeling of Polymer Materials,” Int. J. Solids Struct., Vol. 44, 2007, pp. 1161–1179

    Article  MATH  Google Scholar 

  50. Y. Wang, C. Sun, X. Sun, J. Hinkley, G.M. Odegard, and T.S. Gates, “2-D Nano-Scale Finite Element Analysis of a Polymer Field,” Compos. Sci. Technol., Vol. 63, 2003, pp. 1581–1590

    Google Scholar 

  51. Y. Wang, C. Zhang, E. Zhou, C. Sun, J. Hinkley, T.S. Gates, and J. Su, “Atomistic Finite Elements Applicable to Solid Polymers,” Comput. Mater. Sci., Vol. 36, 2006, pp. 292–302

    Article  Google Scholar 

  52. C. Wu and W. Xu, “Atomistic Molecular Modelling of Crosslinked Epoxy Resin,” Polymer, Vol. 47, 2006, pp. 6004–6009

    Article  MathSciNet  Google Scholar 

  53. J.S. Yang and W.H. Jo, “Analysis of the Elastic Deformation of Semicrystalline Poly(trimethylene terephthalate) by the Atomistic-Continuum Model,” J. Chem. Phys., Vol. 114, 2001; pp. 8159–8164

    Article  Google Scholar 

  54. D. Brown, P. Mele, S. Marceau, and N.D. Alberola, “A Molecular Dynamics Study of a Model Nanoparticle Embedded in a Polymer Matrix,” Macromolecules, Vol. 36, 2003, 1395–1406

    Article  Google Scholar 

  55. S.J.V. Frankland, A. Caglar, D.W. Brenner, and M. Griebel, “Molecular Simulation of the Influence of Chemical Cross-Links on the Shear Strength of Carbon Nanotube-Polymer Interfaces,” J. Phys. Chem. B, Vol. 106, 2002, pp. 3046–3048

    Article  Google Scholar 

  56. S.J.V. Frankland, V.M. Harik, G.M. Odegard, D.W. Brenner, and T.S. Gates, “The Stress-Strain Behavior of Polymer-Nanotube Composites from Molecular Dynamics Simulation,” Compos. Sci. Technol., Vol. 63, 2003, pp. 1655–1661

    Article  Google Scholar 

  57. M. Griebel and J. Hamaekers, “Molecular Dynamics Simulations of the Elastic Moduli of Polymer-Carbon Nanotube Composites,” Comput. Methods Appl. Mech. Eng., Vol. 193, 2004, pp. 1773–1788

    Article  MathSciNet  MATH  Google Scholar 

  58. Y. Jin and F.G. Yuan, “Simulation of Elastic Properties of Single-Walled Carbon Nanotubes,” Compos. Sci. Technol., Vol. 63, 2003, pp. 1507–1515

    Article  Google Scholar 

  59. D. Qi, J. Hinkley, and G. He, “Molecular Dynamics Simulation of Thermal and Mechanical Properties of Polyimide-Carbon Nanotube Composites,” Model. Simul. Mater. Sci. Eng., Vol. 13, 2005, pp. 493–507

    Article  Google Scholar 

  60. N. Sheng, M.C. Boyce, D.M. Parks, G.C. Rutledge, J.I. Abes, and R.E. Cohen, “Multiscale Micromechanical Modeling of Polymer/Clay Nanocomposites and the Effective Clay Particle,” Polymer, Vol. 45, 2004, pp. 487–506

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering – Engineering Mechanics, Michigan Technological University, Houghton, MI 49931, USA

    Gregory M. Odegard

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Correspondence to Gregory M. Odegard .

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Bahram Farahmand

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Odegard, G.M. (2009). Multiscale Modeling of Nanocomposite Materials. In: Farahmand, B. (eds) Virtual Testing and Predictive Modeling. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-95924-5_8

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  • DOI: https://doi.org/10.1007/978-0-387-95924-5_8

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