Auxetic anti-tetrachiral materials: Equivalent elastic properties and frequency band-gaps

Bacigalupo, Andrea; Bellis, Maria Laura De

doi:10.1016/j.compstruct.2015.05.039

Cited by 89 publications

(71 citation statements)

References 42 publications

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“…It can be also demonstrated that the wavevectors b 1 = β 1 , 0 and b 2 = 0, β 2 , as defined in the periodic cell, identify the two orthogonal directions (spanned by the wavenumbers β 1 and β 2 ) traveled by the waves propagating along the orthotropy axes of the first-order equivalent continuum model of the material [28]. The Floquet-Bloch conditions (11) can be introduced in the static equation (7) to halve the passive displacements.…”

Section: Free Wave Propagationmentioning

confidence: 98%

“…With specific reference to the mechanical system under investigation, the -order smallness attributed to the parameters in (28) has been based on physical considerations, as far as it accounts for the typical low-density distribution of the rings (small δ), which usually possess a limited rotational-totranslational mass ratio (small χ) and are interconnected by highly-slender ligaments (small ). On the contrary, the O(1)-order attributed to the aspect ratio η means that extreme geometric cases (i.e.…”

Section: Multi-parameter Perturbation Eigensolutionmentioning

confidence: 99%

“…Among the available chiral topologies, the class of antitetrachiral materials is attracting major attention for its strong auxeticity, accompanied by a marked anisotropy of the elastodynamic response [12,[28][29][30][31][32]. Nonetheless, the microstructural complexity of the anti-tetrachiral periodic cell may act as a partial barrier against fully-analytical formulations.…”

Section: Introductionmentioning

confidence: 98%

“…Furthermore, the tetra-atomic cellular configuration implies a quadruple number of Lagrangian coordinates with respect to the mono-atomic layout of the trichiral, tetrachiral or hexachiral materials. To date, the anti-tetrachiral material auxeticity has been parametrically assessed through a firstorder homogenization technique, applied by imposing the classic polynomial boundary conditions on the periodic cell [28]. As complementary issue, the wave propagation properties of the heterogeneous material, described by a first order continuum in the presence of a soft matrix, have been determined by A C C E P T E D M A N U S C R I P T employing the Floquet-Bloch theory in combination with a finite element model.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

High-frequency parametric approximation of the Floquet-Bloch spectrum for anti-tetrachiral materials

Bacigalupo

Lepidi

2016

International Journal of Solids and Structures

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The class of anti-tetrachiral cellular materials is phenomenologically characterized by a strong auxeticity of the elastic macroscopic response. The auxetic behavior is activated by rolling-up deformation mechanisms developed by the material microstructure, composed by a periodic pattern of stiff rings connected by flexible ligaments. A linear beam lattice model is formulated to describe the free dynamic response of the periodic cell, in the absence of a soft matrix. After a static condensation of the passive degrees-of-freedom, a general procedure is applied to analyze the wave propagation in the low-dimensional space of the active degrees-of-freedom. The exact dispersion functions are compared with explicit – although approximate – dispersion relations, obtained from asymptotic perturbation solutions of the eigenproblem governing the Floquet–Bloch theory. A general hierarchical scheme is outlined to formulate and solve the perturbation equations, taking into account the dimension of the perturbation vector. Original recursive formulas are presented to achieve any desired order of asymptotic approximation. For the anti-tetrachiral material, the fourth-order asymptotic solutions are found to approximate the dispersion curves with fine agreement over wide regions of the parameter space. The asymptotic eigensolutions allow an accurate sensitivity analysis of the material spectrum under variation of the key physical parameters, including the cell aspect ratio, the ligament slenderness and the spatial ring density. Finally, the explicit dependence of the dispersion functions on the mechanical parameters may facilitate the custom design of specific spectral properties, such as the wave velocities and band gap amplitudes

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Section: Free Wave Propagationmentioning

confidence: 98%

Section: Multi-parameter Perturbation Eigensolutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

High-frequency parametric approximation of the Floquet-Bloch spectrum for anti-tetrachiral materials

Bacigalupo

Lepidi

2016

International Journal of Solids and Structures

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“…Chiral honeycombs are found to exhibit auxetic properties and undergo lateral extension when stretched [2,3]. The so-called negative Poisson's ratio as well as other elastic properties can be obtained by investigating the constitutive relations [4][5][6][7]. Aimed at different applications, these chiral honeycombs can also be adopted to design new structures and materials [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

A New Chiral Beam Element for Modelling Chiral Honeycombs

Lü¹,

By²,

Vbc³

et al. 2017

J Appl Mech Eng

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Chiral honeycombs which exhibit auxetic behaviors (negative Poisson's ratios) have attracted much research interest due to their novel mechanical properties. They are broadly used in designing new functional structures, such as energy absorption and noise mitigation materials. To analyze the behaviors of these materials, finite element models are generally adopted, which may require much time and labor to construct and implement. To simplify the numerical modelling, a novel Chiral Beam Element for finite element simulation is proposed in this paper. Both static and dynamic analyses are conducted and the numerical expense, i.e., the modelling procedures and the computational time, is reduced significantly when compared to traditional finite element models.

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Three Decades of Auxetics Research − Materials with Negative Poisson's Ratio: A Review

2016

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Material properties can be tailored through modification of their geometry or architecture. With this concept, a lot of smart materials, metamaterials, and smart structures have been developed. Auxetic materials and structures are a novel class of materials which exhibit an interesting property of negative Poisson's ratio. By virtue of the auxetic behavior, mechanical properties such as fracture toughness, indentation resistance, etc., can be improved. In order to exploit the interesting properties of auxetic materials, several potential applications of auxetic materials have been explored in medical, sports, automobile, defense, etc. Design and modeling of novel auxetic materials and structures is still on the way. Here, the article focuses upon the different aspects of auxetic materials and structures. A comprehensive updated review of auxetic materials, their types and properties, and applications has been presented. This paper also discusses the design and modeling approaches of auxetic structures.

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Auxetic anti-tetrachiral materials: Equivalent elastic properties and frequency band-gaps

Cited by 89 publications

References 42 publications

High-frequency parametric approximation of the Floquet-Bloch spectrum for anti-tetrachiral materials

High-frequency parametric approximation of the Floquet-Bloch spectrum for anti-tetrachiral materials

A New Chiral Beam Element for Modelling Chiral Honeycombs

Three Decades of Auxetics Research − Materials with Negative Poisson's Ratio: A Review

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