Hierarchical Cellular Materials
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HIERARCHICAL CELLULAR MATERIALS
L.J. GIBSON* AND M. F. ASHBY** *Department of Civil Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139 **Cambridge University Engineering Department, Cambridge, England
ABSTRACT Cellular materials are made up of an interconnecting network of strut- or plate-like members. Natural cellular materials include wood, cancellous bone, cork, palm and leaves. Engineering cellular materials are either in the form of honeycombs, with two-dimensional, prismatic cells, or foams with three-dimensional, polyhedral cells. Natural cellular materials usually have multiple phases at multiple scales while engineering cellular materials use a single phase at a single scale. In this paper, the efficiencies of various natural cellular materials are estimated by analyzing their behavior at various microstructural scales. The results of the analysis suggest microstructural design of hierarchically structured engineering cellular materials.
INTRODUCTION Cellular materials are made up of an interconnected network of struts or plates. They are widespread in nature: for instance, wood, cork and cancellous bone all have a cellular structure. In the last 50 years, engineers have made their own cellular materials in the form of honeycombs, with two-dimensional, prismatic cells, and foams, with three-dimensional, polyhedral cells. Today, both honeycombs and foams can be made from every class of material: polymers, metals, ceramics and glasses. Their cellular structure gives rise to unique properties which are exploited in engineering design. Their low density makes them ideal for buoyancy devices and for the cores of structural sandwich panels; their low strength, combined with their capacity to undergo large strains, makes them excellent energy absorbers for packaging and protective padding, and their low thermal conductivity makes them the best insulating material available. The properties of cellular solids depend on three variables: the relative density of the material, equivalent to the volume fraction of solid; the properties of the cell wall material; and the geometry of the cells (cell size, prismatic or polyhedral, open or closed, equiaxed or anisotropic). The most notable difference between natural and engineering cellular solids is that those occuring in nature tend to have composite cell walls while engineered cellular solids have cell walls made of a single material: natural cellular solids have a hierarchicalstructure. For instance, the cell wall of wood is a composite of semi- crystalline cellulose microfibrils in a matrix of lignin and hemi-cellulose and that of cancellous bone is a composite of collagen fibrils in a matrix of hydroxyapatite. In this paper a method for estimating the contributions of both the composite and the cellular microstructures to the overall material properties and the mechanical efficiency of natural cellular solids will be described. The method will be demonstrated by focussing on the Young's modulus; similar techniques can be used for other material
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