Affiliation:
1. Department of Mechanical and Aerospace Engineering, Rutgers University, Piscataway, NJ 08854-8058, USA
Abstract
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.
Subject
General Physics and Astronomy,General Engineering,General Mathematics
Cited by
51 articles.
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