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Micromechanics of Hierarchical Materials: Modeling and Perspectives

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Abstract

Hierarchical materials represent a new, promising direction of the materials development, inspired by biological materials and allowing the creation of multiscale materials design and multiple functionalities and achieving extraordinary material properties. In this article, a short overview of possible applications and perspectives on hierarchical materials is given. Several examples of the modeling of strength and damage in hierarchical materials are summarized. The main areas of research in micromechanics of hierarchical materials are identified, among them, the investigations of the effects of load redistribution between reinforcing elements at different scale levels, possibilities to control different material properties and to ensure synergy of strengthening effects at different scale levels and using the nanoreinforcement effects.

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References

  1. Mishnaevsky L Jr. Computational mesomechanics of composites. Wiley, Chichester, 2007. 280 pp.

    Google Scholar 

  2. Mishnaevsky L Jr, Tsapatsis M. Hierarchical materials: background and perspectives. MRS Bulletin on “Hierarchical Materials”. MRS Bull. 2016; 41: 661–4.

    Article  Google Scholar 

  3. Kanzaki S, Shimada M, Komeya K, Tsuge A. Recent progress in the synergy ceramics project. Key Eng Mater. 1999;161–163:437–42.

    Google Scholar 

  4. Lakes R. Materials with structural hierarchy. Nature. 1993;361:511–5.

    Article  Google Scholar 

  5. Fratzl P, Weinkamer R. Nature’s hierarchical materials. Prog Mater Sci. 2007;52(8):1263–334.

    Article  Google Scholar 

  6. Weinkamer R, Fratzl P. Solving conflicting functional requirements by hierarchical structuring – Examples from biological materials. MRS Bulletin on “Hierarchical Materials”. 2016; 41: 667–71.

    Article  Google Scholar 

  7. Bekyarova E, Thostenson ET, Yu A, Kim H, Gao J, Tang J, et al. Multiscale carbon nanotube-carbon fiber reinforcement for advanced epoxy composites. Langmuir. 2007;23(7):3970–4. E. Bekyarova et al., Functionalized single-walled carbon nanotubes for carbon fiber–epoxy composites, J Phys Chem C 111 (2007), pp. 17865–17871.

    Article  Google Scholar 

  8. Sidorenko D, Mishnaevsky L Jr, et al. Hierarchical machining materials and their performance. MRS Bulletin on “Hierarchical Materials”. 2016; 41: 678–82.

    Article  Google Scholar 

  9. Schmauder S, Mishnaevsky L Jr. Micromechanics and nanosimulation of metals and composites. Springer; Heidelberg, 2008. 420 pp.

    Google Scholar 

  10. Newman WI, Gabrielov AM. Failure of hierarchical distributions of fiber bundles. Int J Fract. 1991;50(1):1–15.

    Google Scholar 

  11. Daniels HE. The statistical theory of the strength of bundles of threads. Proc R Soc Lond. 1945;183(A995):405–35.

    MathSciNet  MATH  Google Scholar 

  12. Mishnaevsky L Jr. Hierarchical composites: analysis of damage evolution based on fiber bundle model. Compos Sci Technol. 2011;71(4):450–60.

    Article  Google Scholar 

  13. Yao H, Gao H. Multi-scale cohesive laws in hierarchical materials. Int J Solids Struct. 2007;44(25–26):8177–93.

    Article  MATH  Google Scholar 

  14. Wu MS. Strategies and challenges for the mechanical modeling of biological and bio-inspired materials. Mater Sci Eng C. https://doi.org/10.1016/j.msec.2010.11.012.

    Article  Google Scholar 

  15. Buehler MJ. Multiscale mechanics of biological and biologically inspired materials and structures. Acta Mech Solida Sin. 2010;23(6):471–83.

    Article  Google Scholar 

  16. Sarikaya M. Biomimetics: materials fabrication through biology. Proc Natl Acad Sci U S A. 1999;96:14183–5.

    Article  Google Scholar 

  17. Katti KS, Katti DR, Pradhan SM, Bhosle A. Platelet interlocks are the key to toughness and strength in nacre. J Mater Res. 2005;20(5):1097–100.

    Article  Google Scholar 

  18. Meyers MA, et al. Biological materials: a materials science approach. J Mech Behav Biomed Mater. 2011;4(5):626–57.

    Article  Google Scholar 

  19. Amada S, Ichikawa Y, Munekata T, Nagase Y, Shimizu H. Fiber texture and mechanical graded structure of bamboo. Compos Part B. 1997;28(1–2):13–20.

    Article  Google Scholar 

  20. Ramachamndra Rao P. Biomimetics. Sadhana. 2003;28(3–4):657–76.

    Google Scholar 

  21. Katti KS, Katti DR. Why is nacre so tough and strong? Mater Sci Eng C. 2006;26(8):1317–24.

    Article  Google Scholar 

  22. Currey JD. Mechanical properties of mother of pearl in tension. Proc R Soc Lond. 1977;196:443. Jackson AP, Vincent JFV, Turner RM. The mechanical design of nacre. Proc R Soc Lond 1988;234:415.

    Article  Google Scholar 

  23. Katti DR, Katti KS, Sopp JM, Sarikaya M. 3D finite element modeling of mechanical response in nacre-based hybrid nanocomposites. Comput Theor Polym Sci. 2001;11(5):397–404.

    Article  Google Scholar 

  24. Nukala PKVV, Simunovic S. A continuous damage random thresholds model for simulating the fracture behavior of nacre. Biomaterials. 2005;26(30):6087–98.

    Article  Google Scholar 

  25. Barthelat F, Tang H, Zavattieri PD, Li C-M, Espinosa HD. On the mechanics of mother-of-pearl: a key feature in the material hierarchical structure. J Mech Phys Solids. 2007;55(2):306–37.

    Article  Google Scholar 

  26. Bertoldi K, Bigoni D, DruganNacre WJ. An orthotropic and bimodular elastic material. Compos Sci Technol. 2008;68(6):1363–75.

    Article  Google Scholar 

  27. Rhoa J-Y. Mechanical properties of hard tissues. In: Jürgen Buschow KH, et al, editors. Encyclopedia of materials: science and technology. Elsevier; 2001. p. 3723–28.

    Google Scholar 

  28. Fritsch A, Hellmich C, Dormieux L. Ductile sliding between mineral crystals followed by rupture of collagen crosslinks: experimentally supported micromechanical explanation of bone strength. J Theor Biol. 2009;260(2):230–52.

    Article  MATH  Google Scholar 

  29. Hellmich C, Fritsch A, Dormieux L. Universal microstructural patterns in bone: micromechanics-based prediction of anisotropic material behavior. J Biomech. 2006;39(Suppl 1):S416–7.

    Article  Google Scholar 

  30. Liu XS, Bevill G, Keaveny TM, Sajda P, Guo XE. Micromechanical analyses of vertebral trabecular bone based on individual trabeculae segmentation of plates and rods. J Biomech. 2009;42(3):249–56.

    Article  Google Scholar 

  31. Niebur GL, Feldstein MJ, Yuen JC, Chen TJ, Keaveny TM. High-resolution finite element models with tissue strength asymmetry accurately predict failure of trabecular bone. J Biomech. 2000;33(12):1575–83.

    Article  Google Scholar 

  32. Qing H, Mishnaevsky Jr L. Fatigue modeling of materials with complex microstructures. Comput Mater Sci. 2011;50(5):1644–50.

    Article  Google Scholar 

  33. Hofstetter K, Hellmich C, Eberhardsteiner J. Development and experimental validation of a continuum micromechanics model for the elasticity of wood. Eur J Mech A-Solid. 2005;24:1030–53.

    Article  MATH  Google Scholar 

  34. Hofstetter K, Hellmich C, Eberhardsteiner J. Micromechanical modeling of solid-type and plate-type deformation patterns within softwood materials. A review and an improved approach. Holzforschung. 2007;61:343–51.

    Article  Google Scholar 

  35. Astley RJ, Harrington JJ, Stol KA. Mechanical modelling of wood microstructure: an engineering approach. Ipenz Trans. 1997;24:21–9.

    Google Scholar 

  36. Astley RJ, Stol KA, Harrington JJ. Modelling the elastic properties of softwood– part II: the cellular microstructure. Holz Roh Werkst. 1998;56:43–50.

    Article  Google Scholar 

  37. Bergander A, Salmen L. Variations in transverse fibre wall properties: relations between elastic properties and structure. Holzforschung. 2000;54:654–60.

    Article  Google Scholar 

  38. Bergander A, Salmen L. Cell wall properties and their effects on the mechanical properties of fibres. J Mater Sci. 2002;37:151–6.

    Article  Google Scholar 

  39. Perré P. Wood as a multi-scale porous medium: observation, experiment, and modelling. In: Keynote lecture, 1st international conference of European society for wood mechanics, Lausanne; 2001. p. 403–22.

    Google Scholar 

  40. Mishnaevsky L Jr, Qing H. Micromechanical modelling of mechanical behaviour and strength of wood: state-of-the-art review. Comput Mater Sci. 2008;44(2):363–70.

    Article  Google Scholar 

  41. Qing H, Mishnaevsky Jr L. 3D hierarchical computational model of wood as a cellular material with fibril reinforced, heterogeneous multiple layers. Mech Mater. 2009;41(9):1034–49.

    Article  Google Scholar 

  42. Mishnaevsky Jr L, et al. Strength and reliability of wood for the components of low-cost wind turbines: computational and experimental analysis and applications. J Wind Eng. 2009;33(2):183–96.

    Article  Google Scholar 

  43. Qing H, Mishnaevsky Jr L. 3D multiscale micromechanical model of wood: from annual rings to microfibrils. Int J Solids Struct. 2010;47(9):1253–67.

    Article  MATH  Google Scholar 

  44. Qing H, Mishnaevsky Jr L. 3D constitutive model of anisotropic damage for unidirectional ply based on physical failure mechanisms. Comput Mater Sci. 2010;50(2):479–86.

    Article  Google Scholar 

  45. Studart AR, Erb RM, Libanori R. In: Kim C-S, et al, editors. Hybrid and hierarchical composite materials, Springer; 2015. p. 287.

    Google Scholar 

  46. Bouville F, Maire E, Meille S, de Moortele VB, Stevenson AJ, Deville S. Nat Mater. 2014;13(5):508–14.

    Article  Google Scholar 

  47. Libanori R, Munch FHL, Montenegro DM, Studart AR. Compos Sci Technol. 2012;72(3):435–45.

    Article  Google Scholar 

  48. Godara A, et al. Influence of carbon nanotube reinforcement on the processing and the mechanical behaviour of carbon fiber/epoxy composites. Carbon. 2009;47(12):2914–23.

    Article  Google Scholar 

  49. Wicks SS, de Villoria RG, Wardle BL. Interlaminar and intralaminar reinforcement of composite laminates with aligned carbon nanotubes. Compos Sci Technol. 2010;70(1):20–8.

    Article  Google Scholar 

  50. Iwahori Y, Ishiwata S, Ishikawa T. Mechanical properties of CFRP using CNF (Carbon Nano-Fiber) dispersed resin. In: Proceedings ICCM-14, San Diego; 2003.

    Google Scholar 

  51. Zhu J, et al. Processing a glass fiber reinforced vinyl ester composite with nanotube enhancement of interlaminar shear strength. Compos Sci Technol. 2007;67(7–8):1509–17.

    Article  Google Scholar 

  52. Dzenis Y. Materials science: structural nanocomposites. Science. 2008;319(5862):419–20.

    Article  Google Scholar 

  53. Carpinteri A, Paggi M. A top-down approach for the prediction of hardness and toughness of hierarchical materials. Chaos, Solitons Fractals. 2009;42(4):2546–52.

    Article  MATH  Google Scholar 

  54. Pugno N, Carpinteri A. Design of micro-nanoscale bio-inspired hierarchical materials. Philos Mag Lett. 2008;88:397–405.

    Article  Google Scholar 

  55. Joshi SP, Ramesh KT. An enriched continuum model for the design of a hierarchical composite. Scr Mater. 2007;57(9):877–80.

    Article  Google Scholar 

  56. Habibi MK, Joshi SP, Gupta M. Hierarchical magnesium nano-composites for enhanced mechanical response. Acta Mater. 2010;58(18):6104–14.

    Article  Google Scholar 

  57. Song M, He YH, Wu ZG, Huang BY. Multi-scale model for the ductility of multiple phase materials. Mech Mater. 2009;41(5):622–33.

    Article  Google Scholar 

  58. Niihara K, Nakahira A, Sekino T. In: Komarneni S, Parker JC, Thomas GJ, editors. Nanophase and Nanocomposite Materials Symposium. Materials Research Society; 1993.

    Google Scholar 

  59. Zhang Z, Chen DL. Prediction of fracture strength in Al2O3/SiCp ceramic matrix nanocomposites. Sci Technol Adv Mater. 2007;8(1–2):5–10.

    Article  Google Scholar 

  60. Choi SM, Awaji H. Nanocomposites – a new material design concept. Sci Technol Adv Mater. 2005;6(1):2–10.

    Article  Google Scholar 

  61. Awaji H, Choi SM, Yagi E. Mechanisms of toughening and strengthening in ceramic-based nanocomposites. Mech Mater. 2002;34(7):411–22.

    Article  Google Scholar 

  62. Sternitzke M. Structural ceramic nanocomposites. J Eur Ceram Soc. 1997;17(9):1061–82.

    Article  Google Scholar 

  63. Bekyarova E, et al. Multiscale carbon nanotube−carbon fiber reinforcement for advanced epoxy composites. Lang Des. 2007;23(7):3970–4.

    Article  Google Scholar 

  64. Mishnaevsky Jr L, Brøndsted P. Micromechanical modeling of damage and fracture of unidirectional fiber reinforced composites: a review. Comput Mater Sci. 2009;44(4):1351–9.

    Article  Google Scholar 

  65. Jiang LY, Huang Y, Jiang H, Ravichandran G, Gao H, Hwang KC, Li B. A cohesive law for carbon nanotube/polymer interfaces based on the van der Waals force. J Mech Phys Solids. 2006;54(11):2436–52.

    Article  MATH  Google Scholar 

  66. Shokrieh MM, Rafiee R. Stochastic multi-scale modeling of CNT/polymer composites. Comput Mater Sci. 2010;50(2):437–46.

    Article  Google Scholar 

  67. Odegard GM, Gates TS, Wise KE, Park C, Siochi EJ. Constitutive modeling of nanotube–reinforced polymer composites. Compos Sci Technol. 2003;63(11):1671–87.

    Article  Google Scholar 

  68. Luo JJ, Daniel IM. Characterization and modeling of mechanical behavior of polymer/clay nanocomposites. Compos Sci Technol. 2003;63:1607–16.

    Article  Google Scholar 

  69. de Villoria RG, Miravete A. Mechanical model to evaluate the effect of the dispersion in nanocomposites. Acta Mater. 2007;55(9):3025–31.

    Article  Google Scholar 

  70. Dai GM, Mishnaevsky Jr L. Carbone nanotube reinforced hybrid composites: computational modelling of environmental fatigue and their usability for wind blades. Compos Part B. 2015;78:349–60.

    Article  Google Scholar 

  71. Dai GM, Mishnaevsky L Jr. Fatigue of multiscale composites with secondary nanoplatelet reinforcement: 3D computational analysis. Compos Sci Technol. 2014;91:71–81.

    Article  Google Scholar 

  72. Zhou HW, Yi HY, Liu YQ, Hu X, Warrier A, Dai GM, Mishnaevsky L Jr. Carbon fiber/carbon nanotube based hierarchical composites: effect of CNT distribution on shearing strength. Compos Part B. 2016;88:201–11.

    Article  Google Scholar 

  73. Mishnaevsky L Jr, Dai G. Hybrid and hierarchical nanoreinforced polymer composites: computational modelling of structure-properties relationships. Compos Struct. 2014;117:156–68.

    Article  Google Scholar 

  74. Peng RD, et al. Modeling of nano-reinforced polymer composites: microstructure effect on the Young’s modulus. Comput Mater Sci. 2012;60:19–31.

    Article  Google Scholar 

  75. Dai GM, Mishnaevsky L Jr. Graphene monolayer nanocomposites: 3D simulation of damage and fracture. Comput Mater Sci. 2014;95:684–92.

    Article  Google Scholar 

  76. Zhang H, et al. Integrated damage sensing in fibre-reinforced composites with extremely low carbon nanotube loadings. J Nanomater. 2015;2015:ID785834.

    Google Scholar 

  77. Kang I, et al. A carbon nanotube strain sensor for structural health monitoring. Smart Mater Struct. 2006;15:737–48.

    Article  Google Scholar 

  78. Wood JR, et al. Carbon nanotubes: from molecular to macroscopic sensors. Phys Rev B. 2000;62:7571.

    Article  Google Scholar 

  79. Fiedler B, Gojny FH, Wichmann MHG, Bauhofer W, Schulte K. Can carbon nanotubes be used to sense damage in composites. Annal de Chim-Sci des Materiaux 2004;29(6):81–94.

    Article  Google Scholar 

  80. Smart anti-icing system for rotor blades. Research News / 1.12.2014.

    Google Scholar 

  81. U.S. Patent Application 20100134946; Carbon nanotubes used to form improved lightning strike protection for wind turbines, 36.2010, U.S. Patent Application 20100134946.

    Google Scholar 

  82. Li C, Thostenson ET, Chou TW. Sensors and actuators based on carbon nanotubes and their composites: a review. Compos Sci Technol. 2008;68(6):1227–49.

    Article  Google Scholar 

  83. Hu N, Karube Y, Yan C, Masuda Z, Fukunaga H. Tunneling effect in a polymer/carbon nanotube nanocomposite strain sensor. Acta Mater. 2008;56(13):2929–36.

    Article  Google Scholar 

  84. Grabowski K, et al. Electrical conductivity of nanocomposites based on carbon nanotubes: a 3D multiscale modeling approach. In: Proceedings SPIE 9803, Sensors and smart structures technologies for civil, mechanical, and aerospace systems 2016, 98030O (April 20, 2016); https://doi.org/10.1117/12.2219275

  85. Li C, Chou TW. Modeling of damage sensing in fiber composites using carbon nanotube networks. Compos Sci Technol. 2008;68(15–16):3373–9.

    Article  Google Scholar 

  86. Franzen M, et al. Naturfaserverstärkte Spritzgießmaterialien für den praktischen Einsatz in der Automobilindustrie. Vortrag: 4a Technologietag 2014. Schladming, 25 Feb 2014.

    Google Scholar 

  87. Akampumuza O, et al. Review of the applications of biocomposites in the automotive industry. Polym Compos. 2016. https://doi.org/10.1002/pc.23847.

    Article  Google Scholar 

  88. Löwer C. Die neue Holzklasse. PM. 2012; 12: 92–8. see also http://www.projekt-hammer.de/.

  89. Roy SB, et al. A review on biocomposites. Int J Innov Res Sci Eng Technol. 2014; 3(10):27–37.

    Google Scholar 

  90. Siró I, Plackett D. Microfibrillated cellulose and new nanocomposite materials: a review. Cellulose. 2010;17(3):459–94.

    Article  Google Scholar 

  91. Berglund LA, Pejs T. MRS Bull. 2010;35:201.

    Article  Google Scholar 

  92. Okubo K, Fujii T, Yamashita N. Improvement of interfacial adhesion in bamboo polymer composite enhanced with micro-fibrillated cellulose. JSME Int J Ser A. 2005;48(4):199–204.

    Article  Google Scholar 

  93. Pommet M, Juntaro J, Heng JYY, Mantalaris A, Lee AF, Wilson K, et al. Surface modification of natural fibers using bacteria: depositing bacterial cellulose onto natural fibers to create hierarchical fiber reinforced nanocomposites. Biomacromolecules. 2008;9:1643. J. Juntaro et al, Nanocellulose enhanced interfaces in truly green unidirectional fibre reinforced composites, Compos. Interfaces 14, 753 (2007).

    Article  Google Scholar 

  94. Aitomaki Y, Oksman K. Reinforcing efficiency of nanocellulose in polymers. React Funct Polym. 2014;85(SI):151–6.

    Article  Google Scholar 

  95. Lee K-Y, Aitomäki Y, Berglund LA, Oksman K, Bismarck A. On the use of nanocellulose as reinforcement in polymer matrix composites. Compos Sci Technol. 2014;105:15–27.

    Article  Google Scholar 

  96. Jogi BF, et al. Dispersion and performance properties of carbon nanotubes (CNTs) based polymer composites: a review. J Encapsulation Adsorpt Sci. 2012;2:69–78.

    Article  Google Scholar 

  97. Aström. Elasticity of Poissonian fiber networks. Physical Review E. The American physical society. 2000;61(5):5550.

    Article  Google Scholar 

  98. Favier V, Canova GR, Shrivastava SC, Cavaille JY. Mechanical percolation in cellulose whisker nanocomposites. Polym Eng Sci. 1997;37(10):1732–9.

    Article  Google Scholar 

  99. Denoyelle Th. Mechanical properties of materials made of nano-cellulose. KTH Degree; Stockholm, 2011.

    Google Scholar 

  100. Josefsson G, et al. Stiffness contribution of cellulose nanofibrils to composite materials. Int J Solids Struct. 2014;51:945.

    Article  Google Scholar 

  101. Mishnaevsky L Jr, Madsen B, Aitomäki Y. Computational simulations of nanocellulose reinforced polymers. EU FoF.NMP.2013-10 project INCOM. Report Deliverable D6.5; 2016. 19 pp.

    Google Scholar 

  102. Sidorenko D, et al. Carbon nanotube reinforced metal binders for diamond cutting tools. Mater Des. 2015;83:536–44.

    Article  Google Scholar 

  103. Loginov P, Mishnaevsky Jr L, Levashov E, Petrzhik M. Diamond and CBN hybrid and nanomodified cutting tools with enhanced performances: development, testing and modelling. Mater Des. 2015;88:310–9.

    Article  Google Scholar 

  104. Song F, Bai YL. Effects of nanostructures on the fracture strength of the interfaces in nacre. J Mater Res. 2003;18(8):1741–4.

    Article  Google Scholar 

  105. Song F, Soh AK, Bai YL. Structural and mechanical properties of the organic matrix layers of nacre. Biomaterials. 2003;24:3623–31.

    Article  Google Scholar 

  106. Mishnaevsky L Jr, et al. Nanostructured titanium based materials for medical implants: modeling and development. Mater Sci Eng R Rep. 2014;81:1–19.

    Article  Google Scholar 

  107. Liu HS, Mishnaevsky L Jr. Gradient ultrafine-grained titanium: computational study of mechanical and damage behavior. Acta Mater. 2014;71:220–33.

    Article  Google Scholar 

  108. Mishnaevsky L Jr, Dai GM. Hybrid carbon/glass fiber composites: micromechanical analysis of structure-damage resistance relationship. Comput Mater Sci. 2014;81:630–40.

    Article  Google Scholar 

  109. Blaker J, Lee KY, Bismarck A. Hierarchical composites made entirely from renewable resources. J Biobased Mater Bioenergy. 2011;5:1–16.

    Article  Google Scholar 

  110. Mishnaevsky L Jr. Nanostructured interfaces for enhancing mechanical properties of materials: computational micromechanical studies. Compos Part B. 2015;68:75–84.

    Article  Google Scholar 

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Mishnaevsky, L. (2019). Micromechanics of Hierarchical Materials: Modeling and Perspectives. In: Schmauder, S., Chen, CS., Chawla, K., Chawla, N., Chen, W., Kagawa, Y. (eds) Handbook of Mechanics of Materials. Springer, Singapore. https://doi.org/10.1007/978-981-10-6884-3_78

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