Acta Mechanica Solida Sinica

, Volume 19, Issue 2, pp 103–113 | Cite as

An equivalent continuum method of lattice structures

Article

Abstract

An equivalent continuum method is developed to analyze the effective stiffness of three-dimensional stretching dominated lattice materials. The strength and three-dimensional plastic yield surfaces are calculated for the equivalent continuum. A yielding model is formulated and compared with the results of other models. The bedding-in effect is considered to include the compliance of the lattice joints. The predicted stiffness and strength are in good agreement with the experimental data, validating the present model in the prediction of the mechanical properties of stretching dominated lattice structures.

Key words

stretching dominated lattice materials equivalent continuum method effective stiffness yield surface bedding-in effect 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Deshpande, V.S., Ashby, M.F. and Fleck, N.A., Foam topology bending versus stretching dominated architectures. Acta Materilia, Vol.49, 2001a, 1035–1040.CrossRefGoogle Scholar
  2. [2]
    Ashby, M.F., Evans, A.G., Fleck, N.A., Gibson, L.J., Hutchinson, J.W. and Wadley, H.N.G., Metal Foams: A Design Guide. Boston: Butterworth-Heinemann, 2000.Google Scholar
  3. [3]
    Evans, A.G., Lightweight materials and structures. MRS Bulletin, Vol.26, 2001, 790–797.CrossRefGoogle Scholar
  4. [4]
    Evans, A.G., Hutchinson, J.W., Fleck, N.A., Ashby, M.F. and Wadley, H.N.G., The topology design of multifunctional cellular metals. Progress in Materials Science, Vol.46, 2001, 309–327.CrossRefGoogle Scholar
  5. [5]
    Deshpande, V.S., Fleck, N.A. and Ashby, M.F., Effective properties of the octet-truss lattice material. Journal of The Mechanics and Physics of Solids, Vol.49, 2001b, 1747–1769.CrossRefGoogle Scholar
  6. [6]
    Wallach, J.C. and Gibson, L.J., Mechanical behavior of a three-dimensional truss material. International Journal of Solids and Structures, Vol.38, 2001, 7181–7196.CrossRefGoogle Scholar
  7. [7]
    Deshpande, V.S., Fleck, N.A. and Ashby, M.F., Yield of truss core sandwich beams in 3-point bending. International Journal of Solids and Structures, Vol.38, 2001c, 6275–6305.CrossRefGoogle Scholar
  8. [8]
    Brittain, S.T., Sugimura, Y., Schueller, O.J.A., Evans, A.G. and Whitesides, G.M., Fabrication and mechanical performance of a mesoscale space-filling truss system. Journal of Microelectromechanical Systems, Vol.10, 2001, 113–120.CrossRefGoogle Scholar
  9. [9]
    Wicks, N. and Hutchinson, J.W., Optimal truss plates. International Journal of Solids and Structures, Vol.38, 2001, 5165–5183.CrossRefGoogle Scholar
  10. [10]
    Wicks, N. and Hutchinson, J.W., Performance of sandwich plates with truss cores. Mechanics of Materials, Vol.36, 2004, 739–751.CrossRefGoogle Scholar
  11. [11]
    Kooistra, G.W., Deshpande, V.S. and Wadley, H.N.G., Compressive behavior of age hardenable tetrahedral lattice truss structures made from aluminium. Acta Materialia, Vol.52, 2004, 4229–4237.CrossRefGoogle Scholar
  12. [12]
    Wadley, H.N.G., Fleck, N.A. and Evans, A.G., Fabrication and structural performance of periodic cellular metal sandwich structures. Composites Science and Technology, Vol.63, 2003, 2331–2343.CrossRefGoogle Scholar
  13. [13]
    Jensen, D.W. and Weaver, T.J., Mechanical characterization of a graphite/epoxy isotruss. Journal of Aerospace Engineering, 13, 2000, 23–35.CrossRefGoogle Scholar
  14. [14]
    Fan, H.L., Yang, W., Wang, B., Yan, Y., Fu, Q., Fang, D.N. and Zhuang Z., Design and manufacturing of a composite lattice structure reinforced by continuous carbon fibers. Tsinghua Science and Technology, Vol.11, No.5, 2006, 153–159.CrossRefGoogle Scholar
  15. [15]
    Noor, A.k., Continumm modeling of repetitive lattice structures. Applied Mechanics Review, Vol.41, 1988, 285–296CrossRefGoogle Scholar
  16. [16]
    Kollar, L. and Hegedus, I., Analysis and Design of Space Frames by the Continuum Method. Amsterdam: Elsevier Science, 1985.Google Scholar
  17. [17]
    Zhou, J., Shrotriya, P. and Soboyejo, W.O., On the deformation of aluminum lattice block structures: from struts to structures. Mechanics of Materials, Vol.36, 2004, 723–737.CrossRefGoogle Scholar
  18. [18]
    Ziegler, E., Accorsi, M. and Bennett, M., Continuum plate model for lattice block material. Mechanics of Materials, Vol.36, 2004, 753–766.CrossRefGoogle Scholar
  19. [19]
    Mohr, D., Mechanism-based multi-surface plasticity model for ideal truss lattice materials. International Journal of Solids and Structures, Vol.42, 2005, 3235–3260.CrossRefGoogle Scholar
  20. [20]
    Gibson, L.J. and Ashby, M.F., Cellular Solids: Structure and Properties, 2nd ed. Cambridge/UK: Cambridge University Press, 1997.CrossRefGoogle Scholar
  21. [21]
    Hill, R., A theory of the yielding and plastic flow of anisotropic metals. Proc. Roy. Soc. London, A193, 1948, 281–300.MathSciNetCrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2006

Authors and Affiliations

  1. 1.Department of Engineering MechanicsTsinghua UniversityBeijingChina

Personalised recommendations