Structural properties of stiff elastic networks

Abstract

Abstract. -Networks of elastic beams can deform either by stretching or bending of their members. The primary mode of deformation (bending or stretching) crucially depends on the specific details of the network architecture. In order to shed light on the relationship between microscopic geometry and macroscopic mechanics, we characterize the structural features of networks which deform uniformly, through the stretching of the beams only. We provide a convenient set of geometrical criteria to identify such networks, and derive the values of their effective elastic moduli. The analysis of these criteria elucidates the variability of mechanical response of elastic networks. In particular, our study rationalizes the difference in mechanical behavior of cellular and fiber networks.

Stiffest elastic networks

“…In §3, we propose a theoretical framework to rationalize these observations: we derive bounds on the elastic moduli of isotropic networks using a variational approach and establish simple rules on the geometrical and topological arrangement of beams in a network to make it stiffer for the same amount of material. This theoretical part is an extension of our previous study [22], which was originally restricted to networks made of straight beams with uniform cross sections. In §4, we analyse the restrictions imposed by these structural conditions and show that they rationalize our numerical findings.…”

“…In a previous study [22], we have derived bounds on the elastic moduli of a specific class of networks: those made of straight and uniform beams. In this paper, we extend this study and reveal both numerically and theoretically the existence of a class of elastic networks, which are stiffer than any other ones having the same symmetry, same density and same elastic phase.…”

Mechanics of elastic networks

“…Recent fabrication of micro-architectured materials have used the octet truss tetrahedral cell design to achieve ultralight and ultrastiff structures [3]. An even stiffer structure comprising tetrakaidecahedral unit cells was proposed by [4,1], see Fig. 1.…”

Experimental investigation of the mechanical stiffness of periodic framework-patterned elastomers

“…Porous network materials can be considered as collections of elastic beams (centred by net edges) meeting at nodes (net vertices). Durand and Gurtner's analysis [11,17] led to a suite of equations that a network should satisfy to exhibit affine stretch-dominated strain assuming no vertex contribution to the elasticity and standard beam elasticity theory. (This assumption holds in practice if the edge radii are much smaller than their lengths.)…”