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.
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Deshpande, V.S., Ashby, M.F. and Fleck, N.A., Foam topology bending versus stretching dominated architectures. Acta Materilia, Vol.49, 2001a, 1035–1040.
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.
Evans, A.G., Lightweight materials and structures. MRS Bulletin, Vol.26, 2001, 790–797.
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.
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.
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.
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.
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.
Wicks, N. and Hutchinson, J.W., Optimal truss plates. International Journal of Solids and Structures, Vol.38, 2001, 5165–5183.
Wicks, N. and Hutchinson, J.W., Performance of sandwich plates with truss cores. Mechanics of Materials, Vol.36, 2004, 739–751.
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.
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.
Jensen, D.W. and Weaver, T.J., Mechanical characterization of a graphite/epoxy isotruss. Journal of Aerospace Engineering, 13, 2000, 23–35.
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.
Noor, A.k., Continumm modeling of repetitive lattice structures. Applied Mechanics Review, Vol.41, 1988, 285–296
Kollar, L. and Hegedus, I., Analysis and Design of Space Frames by the Continuum Method. Amsterdam: Elsevier Science, 1985.
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.
Ziegler, E., Accorsi, M. and Bennett, M., Continuum plate model for lattice block material. Mechanics of Materials, Vol.36, 2004, 753–766.
Mohr, D., Mechanism-based multi-surface plasticity model for ideal truss lattice materials. International Journal of Solids and Structures, Vol.42, 2005, 3235–3260.
Gibson, L.J. and Ashby, M.F., Cellular Solids: Structure and Properties, 2nd ed. Cambridge/UK: Cambridge University Press, 1997.
Hill, R., A theory of the yielding and plastic flow of anisotropic metals. Proc. Roy. Soc. London, A193, 1948, 281–300.
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Project supported by the Key Project of Chinese Ministry of Education (No.106015).
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Fan, H., Yang, W. An equivalent continuum method of lattice structures. Acta Mech. Solida Sin. 19, 103–113 (2006). https://doi.org/10.1007/s10338-006-0612-x
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DOI: https://doi.org/10.1007/s10338-006-0612-x