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This work studies the constitutive response of two- and three-dimensional lattice materials subject to isotropic prestress. The unit cell of the examined lattices is formed by an arbitrary number of junctions attached to a junction. Analytic formulae for second-order elastic constants and elastic stiffness coefficients of stretching-dominated lattices are provided. In addition, numerical results for the incremental elastic moduli of composite lattices equipped with hard and soft rods are presented. The given results highlight that isotropically pre-tensioned lattices may exhibit marked variations of the elastic stiffness moduli in the prestressed state, over the values competing to the stress-free configuration. This study also discloses that prestressed lattices may feature incremental auxetic response, when composite architectures suitably combining hard and soft materials are employed for their fabrication., Comment: 20 pages, 3 figures, 6 tables

This work deals with the multiscale modeling of the mechanical response of pentamode lattices, and a preliminary study on engineering applications of structural bearings formed by pentamode lattices confined between stiffening plates. Numerical and experimental results show that the confinement effect played by the stiffening plates, the geometry and mechanical properties of the junctions strongly influence the overall stiffness properties of such structures. As a result, the mechanics of confined pentamode lattices significantly differs from that of unconfined lattices, being able to accommodate compression and tension vertical loads, and featuring performance-based response under shear loading. Their application for use in anti-seismic system development and/or as shear-wave band gap systems awaits attention.

A numerical study on the elastic response of single- and multi-layer systems formed by alternating pentamode lattices and stiffening plates is presented. Finite element simulations are conducted to analyze the dependence of the effective elastic moduli of such structures upon suitable aspect ratios, which characterize the geometry of the generic pentamode layer at the micro- and macro-scale, and the lamination scheme of the layered structure. The given numerical results highlight that the examined structures exhibit bending-dominated response, and are able to achieve low values of the effective shear modulus and, contemporarily, high values of the effective compression modulus. We are lead to conclude that confined pentamode lattices can be regarded as novel metamaterials that are well suited for seismic isolation and impact protection purposes. Their elastic response can be finely tuned by playing with several geometrical and mechanical design variables.

An experimental investigation on the mechanical response of confined pentamode lattices in the elastic and post-yield regimes is presented. An Electron Beam Melting facility is employed to additively manufacture pentamode lattices confined by terminal plates in a titanium alloy. The given experimental results show that the geometry of the microstructure, and the macroscopic aspect ratio of the confined lattices strongly influence the lateral and vertical stiffness properties of the structure. The post-elastic response of the analyzed materials features acceptable energy dissipation capacity. The presented results highlight several analogies between the mechanical response of confined pentamode lattices and that of elastomeric bearings formed by soft rubber pads and stiffening steel or fiber-reinforced composite layers. They pave the way to future studies on the use of pentamode materials for the fabrication of innovative seismic isolation devices and/or shear-wave band gap systems.