Abstract
Several studies have focused on the linear and non linear behavior of elastic random honeycombs. In this paper, some numerical tests are presented to explore the existence of a Representative Volume Element (RVE) for elastic buckling of these microstructures. The Voronoi tessellation technique and the finite element method are used to estimate the load plateau of two-dimensional cellular solids having irregular shapes. Elastic buckling and finite deformation calculations are conducted and compared. For a given size of specimen and a given precision, the Monte-Carlo method is used to determine the number of simulated specimens. The existence of a RVE for elastic buckling is numerically established when the microstructure is not “too” irregular and all the cells are hexagonal. In this case, it is found that the elastic buckling analysis gives a good estimation for the beginning of the load plateau regime.
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References
Chuang CH, Huang JS (2002) Effects of solid distribution on the elastic buckling of honey-combs. International Journal of Mechanical Sciences, 44:1429–1443.
Fazekas A, Dendievel R, Salvo L, Brechet Y (2002) Effect of microstructural topology upon the stiffness and strength of 2d cellular structures. International Journal of Mechanical Sciences, 44:2047–2066.
Gibson LJ, Ashby MF (1997) Cellular Solids: Stucture and properties. Second ed. Cambridge University Press, Cambridge, UK.
Laroussi M, Sab K, Alaoui A (2002) Foam mechanics: nonlinear response of an elastic 3d-periodic microstructure. International Journal of Solids and Structures, 39:3599–3623.
Li K, Gao XL, Subhash G (2005) Effects of cell shape and cell wall thickness variations on the elastic properties of two-dimensional cellular solids. International Journal of Solids and Structures, 42:1777–1795.
Ohno N, Okumura D, Noguchi H (2002) Microscopic symmetric bifurcation condition of cellular solids based on a homogenization theory of finite deformation. Journal of the Mechanics and Physics of Solids, 50:1125–1153.
Okumura D, Ohno N, Noguchi H (2002) Post-buckling analysis of elastic honeycombs subject to in-plane biaxial compression. International Journal of Solids and Structures, 39:3487–3503.
Saiki I, Terada K, Ikeda K, Hori M (2002) Appropriate number of unit cells in a representative volume element for micro-structural bifurcation encountered in a multi-scale modeling. Computer Methods in Applied Mechanics and Engineering, 191:2561–2585.
Silva MJ, Gibson LJ (1997) The effects of non-periodic microstructure and defects on the compressive strength of two-dimensional cellular solids. International Journal of Mechanical Sciences, 39:549–563.
Yang MY, Huang JS (2005) Elastic buckling of regular hexagonal honeycombs with plateau borders under biaxial compression. Composite Structures, 71:229–237.
Zhang J, Ashby MF (1992) Buckling of honeycombs under in-plane biaxial stresses. International Journal of Mechanical Sciences, 34:491–509.
Zhu H, Thorpe S, Windle A (2006) The effect of cell irregularity on the high strain compression of 2d voronoi honeycombs. International Journal of Solids and Structures, 43:1061–1078.
Zhu HX, Hobdell JR, Windle AH (2001) Effects of cell irregularity on the elastic properties of 2d voronoi honeycombs. Journal of the Mechanics and Physics of Solids, 49:857–870.
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Jouneid, F., Sab, K. (2009). Elastic Buckling of 2-D Random Honeycombs: Does a Representative Volume Element Exists?. In: Zhao, H., Fleck, N.A. (eds) IUTAM Symposium on Mechanical Properties of Cellular Materials. IUTAM Bookseries, vol 12. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9404-0_9
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DOI: https://doi.org/10.1007/978-1-4020-9404-0_9
Publisher Name: Springer, Dordrecht
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