Mechanics of elastic networks
Andrew N. Norris
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Source: Crossref
Published: Dec 8, 2014
DOI: 10.1098/rspa.2014.0522
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We consider a periodic lattice structure in d =2 or 3 dimensions with unit cell comprising Z thin elastic members emanating from a similarly situated central node. A general theoretical approach provides an algebraic formula for the effective elasticity of such frameworks. The method yields the effective cubic elastic constants for three-dimensional space-filling lattices with Z =4, 6, 8, 12 and 14, the last being the ‘stiffest’ lattice proposed by Gurtner & Durand (Gurtner & Durand 2014 Proc. R. Soc. A 470 , 20130611. ( doi:10.1098/rspa.2013.0611 )). The analytical expressions provide explicit formulae for the effective properties of pentamode materials, both isotropic and anisotropic, obtained from the general formulation in the stretch-dominated limit for Z = d +1.
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