Affiliation:
1. Matière et Systèmes Complexes (MSC), UMR 7057 CNRS and Université Paris Diderot, 10 rue Alice Domon et Léonie Duquet, 75205 Paris Cedex 13, France
Abstract
The rigidity of a network of elastic beams is closely related to its microstructure. We show both numerically and theoretically that there is a class of isotropic networks, which are stiffer than any other isotropic network of same density. The elastic moduli of these
stiffest elastic networks
are explicitly given. They constitute upper-bounds, which compete or improve the well-known Hashin–Shtrikman bounds. We provide a convenient set of criteria (necessary and sufficient conditions) to identify these networks and show that their displacement field under uniform loading conditions is affine down to the microscopic scale. Finally, examples of such networks with periodic arrangement are presented, in both two and three dimensions. In particular, we present an
optimal
and
isotropic
three-dimensional structure which, to our knowledge, is the first one to be presented as such.
Subject
General Physics and Astronomy,General Engineering,General Mathematics
Cited by
77 articles.
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