Home            Contact us            FAQs
    
      Journal Home      |      Aim & Scope     |     Author(s) Information      |      Editorial Board      |      MSP Download Statistics

     Research Journal of Applied Sciences, Engineering and Technology


Mathematical Models for in-Plane Moduli of Honeycomb Structures-A Review

Imran Ali and Yu Jing Jun
School of Mechanical and Automation Engineering, Beihang University, 37 号 Xueyuan Rd, Haidian, Beijing, China
Research Journal of Applied Sciences, Engineering and Technology  2014  3:581-592
http://dx.doi.org/10.19026/rjaset.7.294  |  © The Author(s) 2014
Received: March 05, 2013  |  Accepted: April 02, 2013  |  Published: January 20, 2014

Abstract

Honeycomb structures are light weight cellular structures having high strength to weight ratio with enormous applications in aerospace industry, high speed automobiles, computers and other electronics equipment bodies and recently as flexible structures and mechanisms. In this paper a review of mathematical models for stress strain behaviour of two dimensional honeycomb structures is presented. As proposed by different authors, expressions for in-plane Elastic Moduli and shear Modulus are presented and compared on same scale dimensions. In addition to that, effects of number of unit cells on effective in plane and out of plane Moduli of the testing specimen for regular honeycombs and open and closed cell foams, are also reviewed.

Keywords:

Auxetic honeycombs, flexure model, honeycomb structures, hinging model, stretching model,


References

  1. Abd El-Sayed, F.K., R. Jones and I.W. Burgess, 1979. A theoretical approach to the deformation of honeycomb based composite materials. Composites, 10: 209-214.
    CrossRef    
  2. Akasaka, T. and T. Takagishi, 1959. The shear modulus of foil honey-comb sandwich structures. Trans. Japan Soc. Aerospace Sci., 2: 83-90.
  3. Balawi, S. and J.L. Abot, 2007b. A re?ned model for the e?ective in-plane elastic moduli of hexagonal honeycombs. Compos. Struct., 84(2): 147-158.
    CrossRef    
  4. Balawi, S. and J.L. Abot, 2008. The e?ect of honeycomb relative density on its e?ective in-plane elastic moduli: An experimental study. Compos. Struct., 84(4): 293-299.
    CrossRef    
  5. Brezny, R. and D.J. Green, 1990. Characterization of edge effects in cellular materials. J. Mater. Sci., 25(11): 4571-1578.
    CrossRef    
  6. Bubert, E., K.S. Woods, C.S. Kothera and N.M. Wereley, 2008. Design and fabrication of a passive 1-D morphing aircraft skin. Proceeding of the 49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference. AIAA2008-2045, Schaumburg, IL.
  7. Charles, L. and K.H. Ralph, 1951. Elastic Constants for Corrugated-Core Sandwich Plates. National Advisory Committee for Aeronautics, Washington DC, pp: 105.
  8. Choon, C.F., B.G. Gin and K.S. Leong, 2007. Mechanical properties of nomax material and nomax honeycomb structures. Compos. Struct., 80: 588-594.
    CrossRef    
  9. Cook, R.D. and W.C. Young, 1999. Advanced Mechanics of Materials. Prentice Hall, Upper Sadle River, NJ.
  10. Frostig, Y., 1998. Inaccuracies and validity of simpli?ed models in the theory of sandwich structures. Proceeding of 4th Int Conference Sandwich Construction. Stockholm, Sweden, Ohlsson, K.A. (Ed.), EMAS Publishing, London, pp: 167-189.
  11. Garrard, A., 1949. Theory of sandwich construction II. Br. Plast., 18: 451-458.
  12. Gaspar, N., X.J. Ren, C.W. Smith, J.N. Grima and K.E. Evans, 2005. Novel honeycombs with auxetic behaviour. Acta. Mater., 53: 2439-2445.
  13. Gibson, L.J. and F.A. Michael, 1988. Cellular Solids, Structure and Properties. Cambridge University Press, Cambridge.
  14. Grima, J.N., G. Ruben and P.S. Farrugia, 2008b. The properties of auxetic meta-tetrachiral structures. Phys. Stat. Sol., 245: 511-520.
    CrossRef    
  15. Habip, L.M., 1964. A review of recent Russian work on sandwich structures. Int. J. Mech. Sci., 6: 483-487.
    CrossRef    
  16. Hoffman, G.A., 1958. Poisson's ratio for honeycomb sandwich cores. J. Aerosp. Sci., 25: 534-535.
    CrossRef    
  17. Hohe, J. and W. Becker, 2002. Sandwich cores: Homogenization, material models, and properties. App. Mech. Rev., 55: 61-87.
    CrossRef    
  18. Horvay, H., 1952. Bending of honeycombs and of perforated plates. ASME J. Appl. Mech., 19: 122-123.
  19. Jaehyung, J., D.S. Joshua, Z. John and F. George, 2010. Complaint hexagonal periodic lattice structures having both high shear strength and and high shear strain. J. Mater. Design.
  20. Kelsey, S., R.A. Gellatly and B.W. Clark, 1958. The shear modulus of foil honeycomb cores. Aircraft Eng., 30: 294-302.
    CrossRef    
  21. Khan, M.K., 2006. Compressive and lamination strength of honeycomb sandwich panels with strain energy calculation from ASTM standards. J. Aerospace Eng., 220: 375-386.
    CrossRef    
  22. Kwangwon Kim, J.J., K. Doo-Man and Y. Hyun-Seung, 2012. Modulus and high strain flexure design with auxetic honeycomb structures. IDETC/CIE 2012, DETC2012-70552.
  23. Larsen, U.D., O. Signund and S. Bouwstra, 1997. Design and fabrication of compliant mechanisms and material structures with negative Poisson's ratio. J. Microelectromech. Syst., 6: 99-106.
    CrossRef    
  24. Lui, M. and P. Habip, 1965. A survey of modern developments in the analysis of sandwich structures. Appl. Mech. Rev., 18: 93-98.
  25. Masters, I.G. and K.E. Evans, 1993. Auxetic honeycombs for composite sandwich panels. Proceeding of the 2nd Canudian Conference on Composite Materials, Wallace, W., R. Gauvin and S.V. Hoa, (Eds.).
  26. Masters, I.G. and K.E. Evans, 1996. Models for the elastic deformation of honeycombs. Compos. Struct., 35(4): 403-422.
    CrossRef    
  27. Mellquist, E. and A. Waas, 2002. Size Effects in the Compressive Crushing of Honeycombs. AIAA SDM 2002.
  28. Mellquist, E.C. and A.M. Waas, 2004. Size Effects in the Compressive Crushing of Honeycombs. AIAA 2004-1640.
  29. Nkansah, M.A., K.E. Evans and I.J. Hutchinson, 1994. Modelling the mechanical properties of an auxetic-molecular network. Model. Simrd. Mater Sci. Engtzg., 2: 337.
    CrossRef    
  30. Olympio, K. and F. Gandhi, 2007. Zero-? cellular honeycomb flexible skins for one-dimensional wing morphing. Proceeding of the 48th AIAA/ASME/ ASCE/AHS/ASC Structures, Structural Dynamics and Materials sConference. AIAA2007-1735, Honolulu, Hawaii.
    CrossRef    
  31. Onck, P.R., A.E. Andrewsb and L.J. Gibson, 2001a. Size effects in ductile cellular solids Part I: Modelling. Int. J. Mech. Sci., 43: 681-99.
    CrossRef    
  32. Onck, P.R., A.E. Andrewsb and L.J. Gibson, 2001b. Size effects in ductile cellular solids. Part II: Experimental results. Int. J. Mech. Sci., 43: 701-713.
    CrossRef    
  33. Smith, C.W., J.N. Grima and K.E. Evans, 2000. A novel mechanism for generating auxetic behaviour in reticulated foams: missing rib foam model. Acta. Mater., 48: 4349-4356.
    CrossRef    
  34. Theocaris, P.S. and G.E. Panagiotopoulos, 1997. Negative Poisson's ratio in materials with a star-shaped microstructure. A numerical homogenization approach. Arch. Appl. Mech., 67: 274-286.
    CrossRef    
  35. Tom, B., 1997. Honeycomb Technology. Chapman and Hall, London.
  36. Vinson, J.R., 1999. The Behavior of Sandwich Structures of Isotropic and Composite Materials. Technomic Publ., Lancaster PA.
  37. Yanping, L. and H. Hong, 2010. A review on auxetic structures and polymeric materials. Sci. Res. Essays, 5(10): 1052-1063.
  38. Zhao, H. and G. Grrard, 1998. Crushing behavior of aluminum honeycombs under impact loading. Int. J. Impact Eng., 2(10): 827-836.
    CrossRef    

Competing interests

The authors have no competing interests.

Open Access Policy

This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Copyright

The authors have no competing interests.

ISSN (Online):  2040-7467
ISSN (Print):   2040-7459
Submit Manuscript
   Information
   Sales & Services
Home   |  Contact us   |  About us   |  Privacy Policy
Copyright © 2024. MAXWELL Scientific Publication Corp., All rights reserved