Auxetic two-dimensional lattices with Poisson's ratio arbitrarily close to −1

Abstract

In this paper, we propose a class of lattice structures with macroscopic Poisson's ratio arbitrarily close to the stability limit −1. We tested experimentally the effective Poisson's ratio of the microstructured medium; the uniaxial test was performed on a thermoplastic lattice produced with a threedimensional printing technology. A theoretical analysis of the effective properties was performed, and the expression of the macroscopic constitutive properties is given in full analytical form as a function of the constitutive properties of the elements of the lattice and on the geometry of the microstructure. The analysis was performed on three microgeometries leading to an isotropic behaviour for the cases of threeand sixfold symmetries and to a cubic behaviour for the case of fourfold symmetry.

A novel layered topology of auxetic materials based on the tetrachiral honeycomb microstructure

“…As valuable point 5 of novelty, the research outcomes have led to the theoretical conceptualization, mechanical modelization and analytical/numerical simulation of an original by-layered topology, based on tetrachiral layers. The new topology, which differs from other layered auxetic materials based on radially foldable microstructure [57] and does not require a different bi-layered multimaterial 3D printing process, is kinematically based on the independent and opposite-sign rolling up mechanisms of the component layers, reciprocally constrained at the boundaries. The theoretical predictions and the experimental behaviour have been compared in terms of global rigidity and auxeticity (Section 3).…”

New examples of three‐dimensional dilational materials

“…3) that is a simplification of an earlier model of Sigmund () (see his Fig. 4), which was recently rediscovered and generalized by Cabras and Brun (). Sigmund () obtained dilational materials with sliding surfaces built from rotatable frames in both two and three dimensions.…”

The difficult challenge of modelling the non‐linear elastic behaviour of soils within a theoretically sound framework

“…As shown in Figure , Equation indicates that the Poisson's ratio assumes values in the range . Although that is the theoretically correct range of variation for the Poisson's ratio and a number of new materials with a negative ν , named auxetic , have recently been developed (eg, Bacigalupo et al and Cabras and Brun), soils are only known to exhibit a positive value of the Poisson's ratio. This outcome implies that the choice of a constant shear modulus G is unsuitable for soils.…”