A closed-form, hierarchical, multi-interphase model for compositesDerivation, verification and application to nanocomposites

Journal of the Mechanics and Physics of Solids

Volumn 59, Issue 1, 2011, Pages 43-63

  Li, Yaning ^a   Waas, Anthony M ^a   Arruda, Ellen M ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Finite Element; Interphase; Mori Tanaka; Nanocomposites; Size effects

Indexed keywords

CLOSED FORM; DIFFERENT SCALE; ELASTIC REGIME; ELASTICITY THEORY; ELLIPSOIDAL INCLUSIONS; ELLIPSOIDAL PARTICLES; ENHANCEMENT EFFICIENCY; ENHANCEMENT MECHANISM; FINITE ELEMENT; INTERPHASE; LOWER BOUNDS; MATRIX; MORI-TANAKA; MORPHOLOGY PARAMETERS; NANO SCALE; NONUNIFORM; SHAPE EFFECT; SIZE DEPENDENCY; SIZE EFFECTS; STIFFNESS RATIOS; STRESS-STRAIN FIELD; THREE DIMENSIONAL FINITE ELEMENTS; VERIFICATION AND APPLICATION;

MORPHOLOGY; NANOCOMPOSITES; SPHERES; STIFFNESS; STIFFNESS MATRIX;

ASPECT RATIO;

EID: 78249242734     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2010.09.015     Document Type: Article

References (62)

1. A.S. Barnard, and L.A. Curtiss Computational nano-morphology: modeling shape as well as size Reviews on Advanced Materials Science 10 2005 105 109
2. J. Baschnagel, and K. Binder On the influence of hard walls on structural properties in polymer glass simulation Macromolecules 28 1995 6808 6818
3. Y. Benveniste On a new approach to the application of MoriTanaka's theory in composite materials Mechanics of Materials 6 2 1987 147 157
4. Y. Benveniste, G.J. Dvorak, and T. Chen Stress fields in composites with coated inclusions Mechanics of Materials 7 1989 305 317
5. Y. Benveniste, G.J. Dvorak, and T. Chen On diagonal and elastic symmetry of the approximate effective stiffness tensor of heterogeneous media Journal of Mechanics and Physics of Solids 39 1991 927 946
6. Y. Benveniste, G.J. Dvorak, and T. Chen On effective properties of composites with coated cylindrically orthotropic fibres Mechanics of Materials 12 1991 289 297
7. J.G. Berryman, and P.A. Berge Critique of two explicit schemes for estimating elastic properties of multiphase composites Mechanics of Materials 22 2 1996 149 164
8. R.D. Bradshaw, F.T. Fisher, and L.C. Brison Fiber waviness in nanotube-reinforced polymer compositesII: modeling via numerical approximation of the dilute strain concentration tensor Composites Science and Technology 63 2003 1705 1722
9. B. Budiansky On the elastic moduli of some heterogeneous materials Journal of Mechanics and Physics of Solids 13 1965 223 227
10. P. Castaneda, and J.R. Willis The effect of spatial distribution on the effective behavior of composite materials and cracked media Journal of the Mechanics and Physics of Solids 43 1995 1919 1951
11. T. Chen, G.J. Dvorak, and Y. Benveniste Stress fields in composites reinforced with cylindrically orthotropic fibres Mechanics of Materials 9 1990 17 32
12. R.M. Christensen, and K.H. Lo Solution for effective shear properties in three phase sphere and cylinder models Journal of Mechanics and Physics of Solids 27 4 1979 315 330
13. L.H. Dai, Z.P. Huang, and R. Wang A Generalize self-consistent MoriTanaka Scheme for prediction of the effective elastic moduli of hybrid multiphase particulate composites Polymer Composite 19 5 1998 506 513
14. J.D. Eshelby The determination of the elastic field of an ellipsoidal inclusion and related problems Proceedings of the Royal Society London, Series A A241 1957 376 396
15. J.D. Eshelby The elastic field outside an ellipsoidal inclusion Proceedings of the Royal Society London, Series A A252 1959 561 569
16. J.D. Eshelby Elastic inclusions and inhomogeneities I.N. Sneddon, R. Hill, Progress in Solid Mechanics 2 1961 North Holland Amsterdam 89 140
17. R.S. Fertig III, and M.R. Garnich Influence of constituent properties and microstructural parameters on the tensile modulus of a polymer/clay nanocomposite Composites Science and Technology 64 2004 2577 2588
18. Fossey,S., 2002. Atomistic modeling of polymer matrices in nanocomposites. Nanocomposites 2002: delivering new value to polymers conference proceedings. Executive Conference Management, San Diego, CA.
19. V.V. Ginzburg, and A.C. Balazs Calculating phase diagrams of polymer-platelet mixtures using density functional theory: implications for polymer/clay composites Macromolecules 32 1999 5681 5688
20. K. Hbaieb, Q.X. Wang, Y.H.J. Chia, and B. Cotterell Modelling stiffness of polymer/clay nanocomposite Polymer 48 2007 901 909
21. E. Helfand, and Y. Tagami Theory of the interface between immiscible polymers. II Journal of Chemistry and Physics 56 1972 3592 3601
22. R. Hill A self-consistent mechanics of composite materials Journal of Mechanics and Physics of Solids 13 1965 213 222
23. Y. Huang, K.X. Hu, X. Wei, and A. Chandra A Generalized self-consistent mechanics method for composite materials with multiphase inclusions Journal of Mechanics and Physics of Solids 42 1994 491
24. X.L. Ji Tensile modulus of polymer nanocomposites Polymer Engineering and Science 42 5 2002 983 993
25. L.Y. Jiang, Y. Huang, H. Jiang, G. Ravichandran, H. Gao, K.C. Hwang, and B. Liu A cohesive law for carbon nanotube/polymer interfaces based on the van der Waals force Journal of the Mechanics and Physics of Solids 54 2006 2436 2452
26. A.K. Kaushik, P. Podsiadlo, M. Qin, C.M. Shaw, A.M. Waas, N.A. Kotov, and E.M. Arruda The role of nanoparticle separation in the finite deformation response of polyurethaneclay nanocomposites Macromolecules 42 17 2009 6588 6955
27. J.Y. Li On micromechanics approximation for the effective thermoelastic moduli of multiphase composite materials Mechanics of Materials 31 1999 149 159
28. Li, Y., Waas, A.M., Arruda, E.M., 2008a. A particle size-shape-dependent three-phase two-step MoriTanaka method for studying of the interphase and particle size and shape effects of polymer/clay nanocomposites. In: Proceeding of the 2008 ASME International Mechanical Engineering Congress & Exposition (IMECE), vol. 13, pp. 225232.
29. Li, Y., Waas, A.M., Arruda, E.M., 2008b. A non-local visco-plastic model with strain gradient effects and interphase effects for simulating the stiffness and yield strength of a class of polymer nanocomposites. In: Proceeding of the 2008 ASME International Mechanical Engineering Congress & Exposition (IMECE), vol. 13, pp. 11191126.
30. Li, Y., Waas, A.M., Arruda, E.M., 2010. The effects of the interphase and strain gradients on the elasticity of layer by layer (LBL) polymer/clay nanocomposites. International Journal of Solids and Structures, in review.
31. T.C. Lim Simplified model for the influence of inclusion aspect ratio on the stiffness of aligned reinforced composites Journal of Reinforced Plastics and Composites 22 4 2003 301 325
32. T.C. Lim Size-dependency of nano-scale inclusions Journal of Materials Science 40 2005 3841 3842
33. Y.S. Lipatov, and A.E. Nesterov Thermodynamics of polymer blends Polymer Thermodynamics Library vol1 1997
34. H. Liu, and L.C. Brinson A hybrid numericalanalytical method for modeling the viscoelastic properties of polymer nanocomposites Transactions of the ASME Vol. 73 2006 758 768
35. H. Liu, and L.C. Brinson Reinforcing efficiency of nanoparticles: a simple comparison for polymer nanocomposites Composite Science and Technology 68 2008 1502 1512
36. R.Y.F. Liu, and T.E. Bernal-Lara Interphase materials by forced assembly of glassy polymers Macromolecules 37 2004 6972 6979
37. X. Liu, and G. Hu Contimuum micromechanical theory of overall plasticity for particulate composites including particle size effect International Journal of Plasticity 21 2005 777 799
38. S. Lyu, T. Grailera, A. Belua, J. Schleya, T. Bartletta, C. Hobota, R. Sparera, and D. Unterekera Nano-adsorbents control surface properties of polyurethane Polymer 48 20 2007 6049 6055
39. X. Markenscoff On the shape of the Eshelby inclusions Journal of Elasticity 49 1998 163 166
40. T. Mori, and K. Tanaka Average stress in matrix and average elastic energy of materials with misfitting inclusions Acta Metallurgica et Materialia 21 1973 571 574
41. Y. Miwa, A.R. Drews, and S. Schlick Detection of the direct effect of clay on polymer dynamics: the case of spin-labeled poly (methyl acrylate)/clay nanocomposites studied by ESR, XRD, and DSC Macromolecules 39 2006 3304 3311
42. T. Mura, H.M. Shodja, T.Y. Lin, A. Safadi, and A. Makkawy The determination of the elastic field of a pentagonal star shaped inclusion Bulletin of the Technical University of Istanbul 47 1994 267 280
43. H. Nozaki, and M. Taya Elastic fields in a polygon-shaped inclusion with uniform eigenstrains Journal of Applied Mechanics 64 1997 495 502
44. H. Nozaki, and M. Taya Elastic fields in a polyhedral inclusion with uniform eigenstrains and related problems Journal of Applied Mechanics 68 2001 441 452
45. P. Podsiadlo, A.K. Kaushik, E.M. Arruda, A.M. Waas, B.S. Shim, J. Xu, H. Nandivada, B.G. Pumplin, J. Lahann, A. Ramamoorthy, and N.A. Kotov Ultrastrong and stiff layered polymer nanocomposites Science 318 2007 80 83
46. P. Podsiadlo, A.K. Kaushik, B.B. Shim, A. Agarwal, Z. Tang, A.M. Waas, E.M. Arruda, and N.A. Kotov Can nature's design be improved upon high strength nacre-like nanocomposites Journal of Physical Chemistry C 2008
47. G.J. Rodin Eshelby's inclusion problem for polygons and polyhedral Journal of the Mechanics and Physics of Solids 44 12 1996 1977 1995
48. G.J. Rodin Discussion of "Elastic fields in a polygon-shaped inclusion with uniform eigenstrains," by N. Nozaki and M. Taya Journal of Applied Mechanics 6 5 1998 278
49. A.S. Sarvestani On the overall elastic moduli of composites with spherical coated fillers International Journal of Solids and Structures 40 26 2003 7553 7566
50. J. Schjodt-Thomsen, and R. Pyrz The MoriTanaka stiffness tensor: diagonal symmetry, complex fibre orientations and non-dilute volume fractions Mechanics of Materials 33 2001 531 544
51. P. Sharma, and S. Ganti Size-dependent Eshelby's tensor for embedded nano-inclusions incorporating surface/interface energies Journal of Applied Mechanics 71 2004 663 671
52. 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 45 2004 487 506
53. H.M. Shodja, and A.S. Sarvestani Elastic fields in double inhomogeneity by the equivalent inclusion method ASME Journal of Applied Mechanics 68 1 2001 3 10
54. G.D. Smith A molecular dynamics simulation study of the viscoelastic properties of polymer nanocomposites Journal of Chemistry and Physics 117 20 2002 9478 9489
55. H. Tan, Y. Huang, C. Liu, and P.H. Geubelle The MoriTanaka method for composite materials with nonlinear interface debonding International Journal of Plasticity 21 2005 1890 1918
56. G.P. Tandon, and G.J. Weng The effect of aspect ratio of inclusions on the elastic properties of unidirectionally aligned composites Polymer Composites 5 4 1984 327 333
57. G.P. Tandon, and G.J. Weng Average stress in the matrix and effective moduli of randomly orientated composites Composite Science and Technology 27 1986 111 132
58. M. Taya, and T.-W. Chou On two kinds of ellipsoidal inhomogeneities in an infinite elastic body: an application to a hybrid composite International Journal of Solids and Structures 17 1981 553 563
59. M. Taya, and T. Mura International Journal of Applied Mechanics 48 1981 361
60. F.J. Vernerey, W.K. Liu, B. Moran, and G. Olson A micromorphic model for the multiple scale failure of heterogeneous materials Journal of the Mechanics and Physics of Solids 56 2008 1320 1347
61. Y. Wu, Z. Ling, and Z. Dong Stressstrain fields and the effectiveness shear properties for three-phase composites with imperfect interface International Journal of Solids and Structures 37 1999 1275 1292
62. K.C. Yung, J. Wang, and T.M. Yue Modeling Young's modulus of polymer-layered silicate nanocomposites using a modified HalpinTsai micromechanical model Journal of Reinforced Plastics and Composites 25 2006 847 860