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14 pages, 7505 KiB

Open AccessEditor’s ChoiceArticle

Cancellation of Auxetic Properties in F.C.C. Hard Sphere Crystals by Hybrid Layer-Channel Nanoinclusions Filled by Hard Spheres of Another Diameter

by Jakub W. Narojczyk, Krzysztof W. Wojciechowski, Jerzy Smardzewski, Attila R. Imre, Joseph N. Grima and Mikołaj Bilski

Materials 2021, 14(11), 3008; https://0-doi-org.brum.beds.ac.uk/10.3390/ma14113008 - 01 Jun 2021

Cited by 9 | Viewed by 2693

Abstract

The elastic properties of f.c.c. hard sphere crystals with periodic arrays of nanoinclusions filled by hard spheres of another diameter are the subject of this paper. It has been shown that a simple modification of the model structure is sufficient to cause very [...] Read more.

The elastic properties of f.c.c. hard sphere crystals with periodic arrays of nanoinclusions filled by hard spheres of another diameter are the subject of this paper. It has been shown that a simple modification of the model structure is sufficient to cause very significant changes in its elastic properties. The use of inclusions in the form of joined (mutually orthogonal) layers and channels showed that the resulting tetragonal system exhibited a complete lack of auxetic properties when the inclusion spheres reached sufficiently large diameter. Moreover, it was very surprising that this hybrid inclusion, which can completely eliminate auxeticity, was composed of components that, alone, in these conditions, enhanced the auxeticity either slightly (layer) or strongly (channel). The study was performed with computer simulations using the Monte Carlo method in the isothermal-isobaric (

N p T

) ensemble with a variable box shape. Full article

(This article belongs to the Special Issue Advances in Mechanical Metamaterials)

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11 pages, 1817 KiB

Open AccessEditor’s ChoiceArticle

Comparison of Transmission Measurement Methods of Elastic Waves in Phononic Band Gap Materials

by Maximilian Wormser, Daniel A. Kiefer, Stefan J. Rupitsch and Carolin Körner

Materials 2021, 14(5), 1133; https://0-doi-org.brum.beds.ac.uk/10.3390/ma14051133 - 28 Feb 2021

Cited by 1 | Viewed by 2180

Abstract

Periodic cellular structures can exhibit metamaterial properties, such as phononic band gaps. In order to detect these frequency bands of strong wave attenuation experimentally, several devices for wave excitation and measurement can be applied. In this work, piezoelectric transducers are utilized to excite [...] Read more.

Periodic cellular structures can exhibit metamaterial properties, such as phononic band gaps. In order to detect these frequency bands of strong wave attenuation experimentally, several devices for wave excitation and measurement can be applied. In this work, piezoelectric transducers are utilized to excite two additively manufactured three-dimensional cellular structures. For the measurement of the transmission factor, we compare two methods. First, the transmitted waves are measured with the same kind of piezoelectric transducer. Second, a laser Doppler vibrometer is employed to scan the mechanical vibrations of the sample on both the emitting and receiving surfaces. The additional comparison of two different methods of spatial averaging of the vibrometer data, that is, the quadratic mean and arithmetic mean, provides insight into the way the piezoelectric transducers convert the transmitted signal. Experimental results are supported by numerical simulations of the dispersion relation and a simplified transmission simulation. Full article

(This article belongs to the Special Issue Advances in Mechanical Metamaterials)

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17 pages, 2280 KiB

Open AccessArticle

Extreme Mechanical Properties of Regular Tensegrity Unit Cells in 3D Lattice Metamaterials

by Anna Al Sabouni-Zawadzka

Materials 2020, 13(21), 4845; https://0-doi-org.brum.beds.ac.uk/10.3390/ma13214845 - 29 Oct 2020

Cited by 6 | Viewed by 2121

Abstract

The study focuses on the identification of extreme mechanical properties of 3D lattice metamaterials based on regular tensegrity modules: 4-strut simplex, 3-strut simplex, expanded octahedron, truncated tetrahedron and X-module. The basis of the analysis is a continuum model which is used to find [...] Read more.

The study focuses on the identification of extreme mechanical properties of 3D lattice metamaterials based on regular tensegrity modules: 4-strut simplex, 3-strut simplex, expanded octahedron, truncated tetrahedron and X-module. The basis of the analysis is a continuum model which is used to find the equivalent elasticity matrices of the unit cells. For each examined tensegrity module a line of extreme properties is determined, which indicates the occurrence of the soft mode of deformation. Moreover, the eigenvectors corresponding to soft and stiff deformation modes are calculated and presented graphically. The obtained results are promising from the point of view of future creation of tensegrity lattices and metamaterials with extreme mechanical properties. One of the analysed materials is identified as quasi bimode, two as quasi trimodes, another one as a trimode and one more as a unimode. Full article

(This article belongs to the Special Issue Advances in Mechanical Metamaterials)

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17 pages, 2443 KiB

Open AccessArticle

Thermoelastic Processes by a Continuous Heat Source Line in an Infinite Solid via Moore–Gibson–Thompson Thermoelasticity

by Ahmed E. Abouelregal, Ibrahim-Elkhalil Ahmed, Mohamed E. Nasr, Khalil M. Khalil, Adam Zakria and Fawzy A. Mohammed

Materials 2020, 13(19), 4463; https://0-doi-org.brum.beds.ac.uk/10.3390/ma13194463 - 08 Oct 2020

Cited by 46 | Viewed by 2248

Abstract

Many attempts have been made to investigate the classical heat transfer of Fourier, and a number of improvements have been implemented. In this work, we consider a novel thermoelasticity model based on the Moore–Gibson–Thompson equation in cases where some of these models fail [...] Read more.

Many attempts have been made to investigate the classical heat transfer of Fourier, and a number of improvements have been implemented. In this work, we consider a novel thermoelasticity model based on the Moore–Gibson–Thompson equation in cases where some of these models fail to be positive. This thermomechanical model has been constructed in combination with a hyperbolic partial differential equation for the variation of the displacement field and a parabolic differential equation for the temperature increment. The presented model is applied to investigate the wave propagation in an isotropic and infinite body subjected to a continuous thermal line source. To solve this problem, together with Laplace and Hankel transform methods, the potential function approach has been used. Laplace and Hankel inverse transformations are used to find solutions to different physical fields in the space–time domain. The problem is validated by calculating the numerical calculations of the physical fields for a given material. The numerical and theoretical results of other thermoelastic models have been compared with those described previously. Full article

(This article belongs to the Special Issue Advances in Mechanical Metamaterials)

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16 pages, 3058 KiB

Open AccessFeature PaperArticle

The Multidirectional Auxeticity and Negative Linear Compressibility of a 3D Mechanical Metamaterial

by Krzysztof K. Dudek, Daphne Attard, Ruben Gatt, James N. Grima-Cornish and Joseph N. Grima

Materials 2020, 13(9), 2193; https://0-doi-org.brum.beds.ac.uk/10.3390/ma13092193 - 10 May 2020

Cited by 26 | Viewed by 3267

Abstract

In this work, through the use of a theoretical model, we analyse the potential of a specific three-dimensional mechanical metamaterial composed of arrowhead-like structural units to exhibit a negative Poisson’s ratio for an arbitrary loading direction. Said analysis allows us to assess its [...] Read more.

In this work, through the use of a theoretical model, we analyse the potential of a specific three-dimensional mechanical metamaterial composed of arrowhead-like structural units to exhibit a negative Poisson’s ratio for an arbitrary loading direction. Said analysis allows us to assess its suitability for use in applications where materials must be able to respond in a desired manner to a stimulus applied in multiple directions. As a result of our studies, we show that the analysed system is capable of exhibiting auxetic behaviour for a broad range of loading directions, with isotropic behaviour being shown in some planes. In addition to that, we show that there are also certain loading directions in which the system manifests negative linear compressibility. This enhances its versatility and suitability for a number of applications where materials exhibiting auxetic behaviour or negative linear compressibility are normally implemented. Full article

(This article belongs to the Special Issue Advances in Mechanical Metamaterials)

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27 pages, 6557 KiB

Open AccessArticle

Hybridized Love Waves in a Guiding Layer Supporting an Array of Plates with Decorative Endings

by Kim Pham, Agnès Maurel, Simon Félix and Sébastien Guenneau

Materials 2020, 13(7), 1632; https://0-doi-org.brum.beds.ac.uk/10.3390/ma13071632 - 01 Apr 2020

Cited by 3 | Viewed by 1816

Abstract

This study follows from Maurel et al., Phys. Rev. B 98, 134311 (2018), where we reported on direct numerical observations of out-of-plane shear surface waves propagating along an array of plates atop a guiding layer, as a model for a forest of trees. [...] Read more.

This study follows from Maurel et al., Phys. Rev. B 98, 134311 (2018), where we reported on direct numerical observations of out-of-plane shear surface waves propagating along an array of plates atop a guiding layer, as a model for a forest of trees. We derived closed form dispersion relations using the homogenization procedure and investigated the effect of heterogeneities at the top of the plates (the foliage of trees). Here, we extend the study to the derivation of a homogenized model accounting for heterogeneities at both endings of the plates. The derivation is presented in the time domain, which allows for an energetic analysis of the effective problem. The effect of these heterogeneous endings on the properties of the surface waves is inspected for hard heterogeneities. It is shown that top heterogeneities affect the resonances of the plates, hence modifying the cut-off frequencies of a wave mathematically similar to the so-called Spoof Plasmon Polariton (SPP) wave, while the bottom heterogeneities affect the behavior of the layer, hence modifying the dispersion relation of the Love waves. The complete system simply mixes these two ingredients, resulting in hybrid surface waves accurately described by our model. Full article

(This article belongs to the Special Issue Advances in Mechanical Metamaterials)

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12 pages, 2374 KiB

Open AccessArticle

Planar Mechanical Metamaterials with Embedded Permanent Magnets

by Viacheslav Slesarenko

Materials 2020, 13(6), 1313; https://0-doi-org.brum.beds.ac.uk/10.3390/ma13061313 - 13 Mar 2020

Cited by 20 | Viewed by 3504

Abstract

The design space of mechanical metamaterials can be drastically enriched by the employment of non-mechanical interactions between unit cells. Here, the mechanical behavior of planar metamaterials consisting of rotating squares is controlled through the periodic embedment of modified elementary cells with attractive and [...] Read more.

The design space of mechanical metamaterials can be drastically enriched by the employment of non-mechanical interactions between unit cells. Here, the mechanical behavior of planar metamaterials consisting of rotating squares is controlled through the periodic embedment of modified elementary cells with attractive and repulsive configurations of the magnets. The proposed design of mechanical metamaterials produced by three-dimensional printing enables the efficient and quick reprogramming of their mechanical properties through the insertion of the magnets into various locations within the metamaterial. Experimental and numerical studies reveal that under equibiaxial compression various mechanical characteristics, such as buckling strain and post-buckling stiffness, can be finely tuned through the rational placement of the magnets. Moreover, this strategy is shown to be efficient in introducing bistability into the metamaterial with an initially single equilibrium state. Full article

(This article belongs to the Special Issue Advances in Mechanical Metamaterials)

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Graphical abstract

10 pages, 5571 KiB

Open AccessFeature PaperArticle

Cloaking In-Plane Elastic Waves with Swiss Rolls

by Younes Achaoui, André Diatta, Muamer Kadic and Sébastien Guenneau

Materials 2020, 13(2), 449; https://0-doi-org.brum.beds.ac.uk/10.3390/ma13020449 - 17 Jan 2020

Cited by 7 | Viewed by 2713

Abstract

We propose a design of cylindrical cloak for coupled in-plane shear waves consisting of concentric layers of sub-wavelength resonant stress-free inclusions shaped as Swiss rolls. The scaling factor between inclusions’ sizes is according to Pendry’s transform. Unlike the hitherto known situations, the present [...] Read more.

We propose a design of cylindrical cloak for coupled in-plane shear waves consisting of concentric layers of sub-wavelength resonant stress-free inclusions shaped as Swiss rolls. The scaling factor between inclusions’ sizes is according to Pendry’s transform. Unlike the hitherto known situations, the present geometric transform starts from a Willis medium and further assumes that displacement fields

u

in original medium and

u^{'}

in transformed medium remain unaffected (

u^{'} = u

). This breaks the minor symmetries of the rank-4 and rank-3 tensors in the Willis equation that describe the transformed effective medium. We achieve some cloaking for a shear polarized source at specific, resonant sub-wavelength, frequencies, when it is located in close proximity to a clamped obstacle surrounded by the structured cloak. The structured medium approximating the effective medium allows for strong Willis coupling, notwithstanding potential chiral elastic effects, and thus mitigates roles of Willis and Cosserat media in the achieved elastodynamic cloaking. Full article

(This article belongs to the Special Issue Advances in Mechanical Metamaterials)

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16 pages, 1449 KiB

Open AccessArticle

A Novel Mechanical Metamaterial Exhibiting Auxetic Behavior and Negative Compressibility

by James N. Grima-Cornish, Joseph N. Grima and Daphne Attard

Materials 2020, 13(1), 79; https://0-doi-org.brum.beds.ac.uk/10.3390/ma13010079 - 22 Dec 2019

Cited by 30 | Viewed by 4111

Abstract

Auxetics (negative Poisson’s ratio) and materials with negative linear compressibility (NLC) exhibit the anomalous mechanical properties of getting wider rather than thinner when stretched and expanding in at least one direction under hydrostatic pressure, respectively. A novel mechanism—termed the ‘triangular elongation mechanism’—leading to [...] Read more.

Auxetics (negative Poisson’s ratio) and materials with negative linear compressibility (NLC) exhibit the anomalous mechanical properties of getting wider rather than thinner when stretched and expanding in at least one direction under hydrostatic pressure, respectively. A novel mechanism—termed the ‘triangular elongation mechanism’—leading to such anomalous behavior is presented and discussed through an analytical model. Amongst other things, it is shown that this novel mechanism, when combined with the well-known ‘rotating squares’ model, can generate giant negative Poisson’s ratios when the system is stretched. Full article

(This article belongs to the Special Issue Advances in Mechanical Metamaterials)

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10 pages, 3626 KiB

Open AccessArticle

The Rise of (Chiral) 3D Mechanical Metamaterials

by Janet Reinbold, Tobias Frenzel, Alexander Münchinger and Martin Wegener

Materials 2019, 12(21), 3527; https://0-doi-org.brum.beds.ac.uk/10.3390/ma12213527 - 28 Oct 2019

Cited by 16 | Viewed by 4372

Abstract

On the occasion of this special issue, we start by briefly outlining some of the history and future perspectives of the field of 3D metamaterials in general and 3D mechanical metamaterials in particular. Next, in the spirit of a specific example, we present [...] Read more.

On the occasion of this special issue, we start by briefly outlining some of the history and future perspectives of the field of 3D metamaterials in general and 3D mechanical metamaterials in particular. Next, in the spirit of a specific example, we present our original numerical as well as experimental results on the phenomenon of acoustical activity, the mechanical counterpart of optical activity. We consider a three-dimensional chiral cubic mechanical metamaterial architecture that is different from the one that we have investigated in recent early experiments. We find even larger linear-polarization rotation angles per metamaterial crystal lattice constant than previously and a slower decrease of the effects towards the bulk limit. Full article

(This article belongs to the Special Issue Advances in Mechanical Metamaterials)

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8 pages, 1429 KiB

Open AccessArticle

Stiffer, Stronger and Centrosymmetrical Class of Pentamodal Mechanical Metamaterials

by Yan Huang, Xiaozhe Zhang, Muamer Kadic and Gongying Liang

Materials 2019, 12(21), 3470; https://0-doi-org.brum.beds.ac.uk/10.3390/ma12213470 - 23 Oct 2019

Cited by 11 | Viewed by 2462

Abstract

Pentamode metamaterials have been used as a crucial element to achieve elastical unfeelability cloaking devices. They are seen as potentially fragile and not simple for integration in anisotropic structures due to a non-centrosymmetric crystalline structure. Here, we introduce a new class of pentamode [...] Read more.

Pentamode metamaterials have been used as a crucial element to achieve elastical unfeelability cloaking devices. They are seen as potentially fragile and not simple for integration in anisotropic structures due to a non-centrosymmetric crystalline structure. Here, we introduce a new class of pentamode metamaterial with centrosymmetry, which shows better performances regarding stiffness, toughness, stability and size dependence. The phonon band structure is calculated based on the finite element method, and the pentamodal properties are evaluated by analyzing the single band gap and the ratio of bulk and shear modulus. The Poisson’s ratio becomes isotropic and close to 0.5 in the limit of small double-cone connections. Stability and scalability analysis results show that the critical load factor of this structure is obviously higher than the classical pentamode structure under the same static elastic properties, and the Young’s modulus gradually converges to a stable value (the infinite case) with an increasing number of unit cells. Full article

(This article belongs to the Special Issue Advances in Mechanical Metamaterials)

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