A class of auxetic three-dimensional lattices

  title={A class of auxetic three-dimensional lattices},
  author={L. Cabras and Michele Brun},
  journal={Journal of The Mechanics and Physics of Solids},
  • L. Cabras, M. Brun
  • Published 16 June 2015
  • Mathematics
  • Journal of The Mechanics and Physics of Solids
A 2D microstructure with auxetic out-of-plane behavior and non-auxetic in-plane behavior
Customarily, in-plane auxeticity and synclastic bending behavior (i.e. out-of-plane auxeticity) are not independent, being the latter a manifestation of the former. Basically, this is a feature of
Periodic Auxetics: Structure and Design
It is shown that a purely geometric approach to periodic auxetics is apt to identify essential characteristics of frameworks with auxetic deformations and can generate a systematic and endless series of periodic auxetic designs.
A design method for metamaterials: 3D transversely isotropic lattice structures with tunable auxeticity
A method for designing 3D transversely isotropic auxetic lattice structures is proposed. Based on it, two new auxetic structures have been designed. Systematically, their effective elastic properties
Homogenized couple stress model of optimal auxetic microstructures computed by topology optimization
Auxetic materials and microstructures are attracting the attention of a growing community of researchers due to their unusual properties and high mechanical performances, in both the static and


Auxetic two-dimensional lattices with Poisson's ratio arbitrarily close to −1
  • L. Cabras, M. Brun
  • Mathematics
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2014
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
A three‐dimensional rotating rigid units network exhibiting negative Poisson's ratios
Materials exhibiting auxetic behaviour get fatter when stretched (i.e. possess a negative Poisson's ratio). This property has been closely related to particular geometrical features of a system and
On three-dimensional dilational elastic metamaterials
Dilational materials are stable, three-dimensional isotropic auxetics with an ultimate Poissonʼs ratio of −1. Inspired by previous theoretical work, we design a feasible blueprint for an artificial
3D Auxetic Microlattices with Independently Controllable Acoustic Band Gaps and Quasi‐Static Elastic Moduli
Mechanical metamaterials offer unique possibilities to tune their mechanical response by adjusting their geometry, without the complexity that the thermodynamics and kinetics of materials synthesis
Rotation and dilation deformation mechanisms for auxetic behaviour in the α-cristobalite tetrahedral framework structure
Abstract Analytical expressions are derived for the Poisson's ratios associated with a three-dimensional network of regular, corner-sharing tetrahedra in which: (1) the tetrahedra are assumed to be
On the properties of real finite‐sized planar and tubular stent‐like auxetic structures
Auxetics, i.e. systems with a negative Poisson's ratio, exhibit the unexpected property of becoming wider when stretched and narrower when compressed. This property arises from the manner in which
Microporous materials with negative Poisson's ratios. I. Microstructure and mechanical properties
A microporous, anisotropic form of expanded polytetrafluoroethylene has been found to have a large negative major Poisson's ratio. The value of Poisson's ratio varies with tensile strain and can
3D soft metamaterials with negative Poisson's ratio.
Buckling is exploited to design a new class of three-dimensional metamaterials with negative Poisson's ratio and the auxetic properties of these materials exhibit excellent qualitative and quantitative agreement.
Poisson's ratio in cubic materials
  • A. Norris
  • Mathematics
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2006
Expressions are given for the maximum and minimum values of Poisson's ratio ν for materials with cubic symmetry. Values less than −1 occur if and only if the maximum shear modulus is associated with
Hierarchical Auxetic Mechanical Metamaterials
Using simulations on typical hierarchical multi-level rotating squares, it is shown that, through design, one can control the extent of auxeticity, degree of aperture and size of the different pores in the system, making the system more versatile than similar non-hierarchical ones.