Stiffest elastic networks

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.

Reexamining the mechanical property space of three-dimensional lattice architectures

“…[27]. For isotropic solids, the Young's modulus limit is defined by the HashinShtrikman bound [28], and for isotropic beam-based lattices the modulus limit is defined by the tighter Gurtner-Durand bound [29]. This scaling of stiffness and strength with relative density becomes particularly conspicuous for light and ultralight materials, where poor scaling relations can have ordersof-magnitude effects on the overall mechanical properties.…”

On the Use of Mechanical Metamaterials for Innovative Seismic Isolations Systems

“…Second, physical models of pentamode isolators need to be constructed, employing, e.g., additive manufacturing techniques [8,9], and laboratory tested as seismic base-isolation devices [19], in order to experimentally asses their isolation and dissipation capabilities arising, e.g., from inelastic response and/or material fracture [20]. Another relevant generalization of the present research regards the design of dynamically tunable systems based on the insertion of prestressed cables and/or curved rods within pentamode lattices, with the aim of designing novel metamaterials and bio-inspired lattices tunable by local and global prestress [12][13][14][21][22][23][24][25][26][27][28]. Future studies will also address the experimentation of pentamode materials as components of new-generation seismic dampers.…”

Mechanical modeling of innovative metamaterials alternating pentamode lattices and confinement plates

“…It is worth noting, in particular, that in the linear elastic regime, perfectly hinged sfcc lattices exhibit an effective compression modulus equal to 2 3 ⁄ of the Young modulus of the stiffest elastic networks analyzed in Ref. [14]. We make some comparisons between the mechanical response of the pentamode materials analyzed in the present work and that of rubber bearings formed by elastomeric layers confined between stiffening plates.…”

“…When a relative rigid motion of the terminal bases is such that Eqns. (13)- (14) return ̇= 0 in each rod, i.e., ̇2 = 0 and ̇1 = , we say that such a motion represents an infinitesimal mechanism of the elementary module from the reference placement B.…”