Fractal space frames and metamaterials for high mechanical efficiencyR. S. Farr1 and Y. Mao2
1 Unilever R&D - Olivier van Noortlaan 120, AT3133, Vlaardingen, The Netherlands, EU
2 School of Physics and Astronomy, University of Nottingham - Nottingham, UK, EU
received 5 July 2008; accepted in final form 19 August 2008; published October 2008
published online 16 September 2008
A solid slender beam of length L, made from a material of Young's modulus Y and subject to a gentle compressive force F, requires a volume of material proportional to L3f1/2 (where f F/(YL2) 1) in order to be stable against Euler buckling. By constructing a hierarchical space frame, we are able to systematically change the scaling of the required material with f so that it is proportional to L3f(G+1)/(G+2), through changing the number of hierarchical levels G present in the structure. Based on simple choices for the geometry of the space frames, we provide expressions specifying in detail the optimal structures (in this class) for different values of the loading parameter f. These structures may then be used to create effective materials which are elastically isotropic and have the combination of low density and high crush strength. Such a material could be used to make light-weight components of arbitrary shape.
46.32.+x - Static buckling and instability.
46.25.Cc - Static elasticity: Theoretical studies.
46.70.Hg - Membranes, rods, and strings.
© EPLA 2008