Microtruss Composites

  • Khaled Abu Samk
  • Glenn D. HibbardEmail author
Part of the Springer Series in Materials Science book series (SSMATERIALS, volume 282)


This chapter provides a framework for predicting buckling instabilities (global and local) in composite struts using a discretizing approach to divide the cross-section into finite regions or blocks (elements) with distinctive composition and material properties. This framework is applied to two compositing approaches: (1) an additive process, e.g. electrodeposition of nanocrystalline nickel (n-Ni) on steel or aluminum substrates creating a discrete interface, and (2) mass transport phenomena, e.g. gas carburization of steel microtrusses creating a continuous and gradual change in composition. The individual composite struts are prone to failure through inelastic/elastic global/local buckling instabilities due to their typically high slenderness ratio (for lightweight requirements). An optimal architecture is defined as the lightest architecture in the defined architectural space that can support a given load before failing; mathematically equivalent to satisfying the Kuhn-Tucker condition. For the electrodeposition example, the optimal trajectory was found to be dependent on the substrate material as well as the level of adhesion of the sleeve to the substrate. However, in the carburizing example, optimal architectures cannot be found using the same optimization approach due to the negligible weight penalty associated with the addition of carbon atoms (i.e. no trade-off between strength and mass). Other factors such as ductility and fracture toughness need to be addressed to find the optimal architectures.


  1. 1.
    V.S. Deshpande, M.F. Ashby, N.A. Fleck, Acta Mater. 49, 6 (2001)Google Scholar
  2. 2.
    M.F. Ashby, Phil. Trans. R. Soc. A 364, 1838 (2006)CrossRefGoogle Scholar
  3. 3.
    O. Bouaziz, J.P. Masse, Y. Brechet, Scr. Mater. 64, 2 (2011)CrossRefGoogle Scholar
  4. 4.
    C.R. Calladine, Int. J. Solids Struct. 14, 2 (1978)CrossRefGoogle Scholar
  5. 5.
    J.C. Maxwell, Philos. Mag. Series 4(27), 182 (1864)Google Scholar
  6. 6.
    V.S. Deshpande, N.A. Fleck, M.F. Ashby, J. Mech. Phys. Solids 49, 8 (2001)CrossRefGoogle Scholar
  7. 7.
    V.S. Deshpande, N.A. Fleck, Int. J. Solids Struct. 38, 36–37 (2001)CrossRefGoogle Scholar
  8. 8.
    A.T. Lausic, C.A. Steeves, G.D. Hibbard, J. Sandw. Struct. Mater. 16, 3 (2014)CrossRefGoogle Scholar
  9. 9.
    P.M. Weaver, M.F. Ashby, Prog. Mater Sci. 41, 1 (1997)CrossRefGoogle Scholar
  10. 10.
    E. Bele, B.A. Bouwhuis, C. Codd, G.D. Hibbard, Acta Mater. 59, 15 (2011)CrossRefGoogle Scholar
  11. 11.
    Z. Hashin, S. Shtrikman, J. Appl. Phys. 33, 10 (1962)CrossRefGoogle Scholar
  12. 12.
    Z. Hashin, S. Shtrikman, J. Mech. Phys. Solids 11, 2 (1963)CrossRefGoogle Scholar
  13. 13.
    W. Voigt, Lehrbuch der Krystallphysik (B. G. Teuber, Leipzig, 1928), p. 962Google Scholar
  14. 14.
    A. Reuss, Z. Angew, Math. Mech. 9, 1 (1929)Google Scholar
  15. 15.
    M.F. Ashby, Acta Metall. Mater. 41, 5 (1993)CrossRefGoogle Scholar
  16. 16.
    H.S. Kim, S.I. Hong, an S.J. Kim, J. Mater. Process. Technol. 112, 1 (2001)Google Scholar
  17. 17.
    O. Bouaziz, P. Buessler, Adv. Eng. Mater. 6, 1–2 (2004)CrossRefGoogle Scholar
  18. 18.
    T. Gladman, I.D. McIvor, F.B. Pickering, J. Iron Steel Inst. 210, 12 (1972)Google Scholar
  19. 19.
    B. Karlsson, G. Linden, Mater. Sci. Eng. 17, 2 (1975)Google Scholar
  20. 20.
    I. Tamura, Y. Tomota, A. Akao, Y. Yamaoka, M. Ozawa, S. Kanatani, Trans. ISIJ 13, 4 (1973)Google Scholar
  21. 21.
    R.T.C. Choo, J.M. Toguri, A.M. Elsherik, U. Erb, J. Appl. Electrochem. 25, 4 (1995)CrossRefGoogle Scholar
  22. 22.
    A.W. Thompson, Acta Metall. 25, 1 (1977)CrossRefGoogle Scholar
  23. 23.
    N. Wang, Z.R. Wang, K.T. Aust, U. Erb, Mater. Sci. Eng., A 237, 2 (1997)CrossRefGoogle Scholar
  24. 24.
    B.A. Bouwhuis, T. Ronis, J.L. McCrea, G. Palumbo, G.D. Hibbard, Compos. Sci. Technol. 69, 3–4 (2009)CrossRefGoogle Scholar
  25. 25.
    W. Ramberg, W.R. Osgood, National Advisory Committee for Aeronautics Technical Note No. 902 (1943)Google Scholar
  26. 26.
    E. Voce, Metall. 51 (1955)Google Scholar
  27. 27.
    J.W. Dini, Electrodeposition: the materials science of coatings and substrates (Noyes Publications, Park Ridge, NJ, 1993)Google Scholar
  28. 28.
    Modern electroplating, 4th ed. edited by M. Schlesinger, M. Paunovic (Wiley Interscience, Toronto, ON, 2000)Google Scholar
  29. 29.
    K. Abu Samk, B. Yu, G.D. Hibbard, Composites Part A 43, 6 (2012)Google Scholar
  30. 30.
    E. Bele, B.A. Bouwhuis, G.D. Hibbard, Acta Mater. 57, 19 (2009)CrossRefGoogle Scholar
  31. 31.
    F.R. Shanley, J. Aeronaut. Sci. 14, 5 (1947)CrossRefGoogle Scholar
  32. 32.
    F.R. Shanley, Strength of Materials (McGraw-Hill, New York, 1957)Google Scholar
  33. 33.
    J.M. Gere, S.P. Timoshenko, Mechanics of Materials, 4th edn. (PWS, Boston, MA, 1997)Google Scholar
  34. 34.
    S.P. Timoshenko, J.M. Gere, Theory of Elastic Stability, 2nd edn. (Dover Publications, Mineola, NY, 2009)Google Scholar
  35. 35.
    B. Yu, K. Abu Samk, G.D. Hibbard, Metall. Mater. Trans. A 46, 5 (2015)Google Scholar
  36. 36.
    B. Chehab, H. Zurob, D. Embury, O. Bouaziz, Y. Brechet, Adv. Eng. Mater. 11, 12 (2009)CrossRefGoogle Scholar
  37. 37.
    D.R. Poirier, G.H. Geiger, Transport Phenomena in Materials Processing (TMS, Warrendale, 1994)Google Scholar
  38. 38.
    ASM Handbook—Properties and Selection: Irons, Steels, and High-Performance Alloys (Materials Park, Ohio, 1990), Vol. 1Google Scholar
  39. 39.
    J. Agren, Scr. Metall. 20, 11 (1986)CrossRefGoogle Scholar
  40. 40.
    D.A. Porter, K.E. Easterling, Phase Transformations in Metals and Alloys, 2nd edn. (Chapman & Hall, London, UK, 1992)CrossRefGoogle Scholar
  41. 41.
    S. Allain, O. Bouaziz, M. Takahashi, ISIJ Int. 52, 4 (2012)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Materials Science and EngineeringUniversity of TorontoTorontoCanada

Personalised recommendations