Random cellular structures can be represented using a Voronoi construction. In two dimensions, perpendicular bisectors constructed between random points in the plane correspond to cell edges. We have calculated the mechanical response of Voronoi honeycombs generated in this way using the finite element method. We first compared the elastic moduli and compressive collapse stresses of Voronoi honeycombs with those of honeycombs with periodic hexagonal cells. We then investigated the effect of defects, in the form of missing cell edges, on the elastic moduli and compressive strength of both Voronoi and periodic honeycombs. This is of particular relevance to the study of osteoporosis in trabecular bone: as the bone density is reduced, individual trabeculae or struts initially thin and then disappear by resorption into the body, reducing the connectivity of the trabecular bone structure. The elastic moduli of random Voronoi Honeycombs are within about 5% of those of honeycombs with periodic hexagonal cells. Both the elastic and plastic collapse stresses of the Voronoi honeycomb are about 30% lower than those of honeycombs with periodic hexagonal cells. This reduction in strength resulted from a higher distribution of strains in the random Voronoi honeycombs than in the periodic hexagonal honeycombs. Defects, in the form of missing cell edges at random locations, reduce the effective mechanical properties of both Voronoi and periodic honeycombs. For example, a 10% reduction in density due to missing cell edges caused a 60% reduction in the strength of both the Voronoi and the periodic hexagonal honeycombs. The properties degraded to zero when 35% of the cell edges were removed, consistent with the percolation limit for a two-dimensional network of hexagonal cells. When four or more adjacent cell edges were removed, the localized band of cell collapse passed through the defect site.
|Number of pages||2|
|Journal||American Society of Mechanical Engineers, Applied Mechanics Division, AMD|
|State||Published - Dec 1 1997|