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1

The f.c.c. Crystals of Hard Spheres with an Array of [001]-Nanochannel Inclusions Filled by the Simplest Hard Sphere Molecules

Narojczyk Jakub W.

Computational Methods in Science and Technology

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2023

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Vol. 29, No. 1-4

37--44

EN

In this work the systems composed of particles interacting with hard potential are investigated. These systems feature certain modifications to the crystal structure – selected particles are replaced with ones that differ slightly in their diameters. Such modifications, which can be thought of as “inclusions”, concern particles located in cylindrical nanochannels, oriented in [001] direction. In this study, for the first time, additional constrains have been imposed on the particles forming the inclusions. Namely, the replaced spheres have been randomly grouped into neighbouring pairs which were connected to form simple, di-atomic molecules. The results have been compared with previously investigated systems with similar inclusions but without the connections, i.e. filled only by spheres. The comparison of elastic properties between these systems is presented. It is shown that inclusions filled with dimers have different impact on the values of elastic compliances. It has been demonstrated that by introducing a small number of molecules made of spheres whose diameters differ from the rest of the particles forming the crystal, one is able to modify the hardness and shear resistance of the f.c.c. crystal without changing the Poisson’s ratio (with respect to the analogous system without additional constrains imposed on the inclusion particles).

2

Rise of the Poisson’s Ratio in f.c.c. Hard Sphere Crystals with the Narrowest Orthogonal Nanochannels Filled by Hard Spheres of Another Diameter

Narojczyk Jakub W., Tretiakov Konstantin V., Wojciechowski Krzysztof W.

Computational Methods in Science and Technology

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2022

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Vol. 28, No. 2

61--75

EN

Auxetic materials, i.e. materials exhibiting negative Poisson’s ratio, stand to answer the demand for novel materials with unique and application-tailored properties. The vast range of potential applications motivates researchers to search for new materials with such properties, or to look for ways to modify the properties of existing materials. The study of systems with structural inclusions falls into the latter category. This work reports numerical investigations of elastic properties of hard sphere f.c.c. crystal. The investigations have been focused on Monte Carlo simulations of systems with arrays of inclusions filled by hard spheres of different diameter, resulting in binary systems, i.e. systems composed of two kinds of particles that differ only in size. Two different layouts of narrow nanoinclusions have been studied in the isobaricisothermal ensemble. It has been shown that even the narrowest inclusions can significantly alter elastic properties of hard particle crystal by eliminating auxetic properties while maintaining the effective cubic symmetry.

3

Poisson’s Ratio of Yukawa Systems with Nanoinclusions: Nanochannel vs. Nanolayer

Tretiakov Konstantin V., Wojciechowski Krzysztof W., Narojczyk J. W., Pigłowski Paweł M.

Computational Methods in Science and Technology

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2022

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Vol. 28, No. 3

81--85

EN

The influence of periodically distributed inclusions on elastic properties of crystals in which particles interact through Yukawa potential is discussed briefly. The inclusions in the form of channels oriented along the [001]-direction and layers orthogonal to the [010]-direction are considered. Monte Carlo simulations have shown that, depending on the type of inclusion and the concentration of inclusion particles in Yukawa crystal, qualitative changes in elastic properties occur. In selected directions, one observes appearance of auxetic properties for systems with nanolayers and enhancement of auxeticity for systems with nanochannels.

4

Blast resistance of sandwich plate with auxetic anti-tetrachiral core

Michalski Jakub, Strek Tomasz

Vibrations in Physical Systems

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2020

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Vol. 31, nr 3

art. no. 2020317

EN

Auxetic structures exhibit unusual behavior not only when subjected to static loads but also in case of dynamic events. However, their response to transient loads still requires further research. In this article, the blast resistance of auxetic and non-auxetic sandwich plates was compared using the finite element method. The first stage of works, that consisted of the analyses of plates with homogenized core with different values of Poisson’s ratio subjected to blast load, proved that auxetic core may increase the resistance to this kind of load. In the next step, two sandwich plates were compared - one with auxetic anti-tetrachiral core and one with a non-auxetic hexagonal honeycomb core. Obtained results indicate that auxetic plate has superior blast resistance when compared with the regular sandwich panel.

5

Materiały auksetyczne – struktury, potencjalne zastosowanie

Masłowska-Lipowicz Iwona, Wyrębska Łucja, Szałek Beata, Olszewski Piotr, Gajewski Robert

Technologia i Jakość Wyrobów

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2020

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R. 65

116--128

PL

Dokonano przeglądu literatury pod kątem badań materiałów auksetycznych, które posiadają ujemny współczynnik Poisson’a (NPR) charakteryzujący odpowiedź materiału na naprężenie jednoosiowe. Struktury i materiały auksetyczne zachowują się sprzecznie z intuicją, tzn. przy jednoosiowym rozciąganiu, rozszerzają się poprzecznie, co wynika z ich skomplikowanych struktur geometrycznych. Opisano reprezentatywne modele strukturalne (re-entrant, struktury składające się z tzw. sztywnych lub półsztywnych obracających się jednostek , struktury chiralne, przędze auksetyczne i struktury włókienkowo-zgrubieniowe) oraz zastosowanie materiałów auksetycznych wynikające z ich właściwości. Właściwości materiałów auksetycznych, np. synklastyczna krzywizna zginania, zmienna przepuszczalność, zwiększona odporność na wgniecenia, wysoka odporność na pękanie oraz tłumienie i pochłanianie dźwięku stwarzają szerokie możliwości ich zastosowania, m.in. w materiałach biomedycznych, materiałach amortyzujących, urządzeniach do pozyskiwania energii, wyposażeniu sportowym, filtrach, robotyce, tekstyliach czy materiałach stosowanych w przemyśle lotniczym oraz budownictwie.

EN

The literature was reviewed in terms of research on auxetic materials with a negative Poisson's ratio (NPR) characterizing the material's response to uniaxial stress. Auxetic structures and materials behave counter-intuitively, i.e. when stretched uniaxially, they expand laterally due to their complex geometric structures. Representative structural models are described (re-entrant, structures consisting of so-called rigid or semi-rigid rotating units, chiral structures, auxetic yarns and fibril - noudle structures) and the use of auxetic materials resulting from their properties. Properties of auxetic materials, e.g. synclastic bending curvature, variable permeability, high shear stiffness, increased resistance to indentation, high resistance to cracking and sound attenuation and absorption create a wide range of applications, including in biomedical materials, shock-absorbing materials, energy generation devices, sports equipment, filters, robotics, textiles or materials used in the aerospace industry and construction.

6

Mechanical and Structural Properties of Poly(Phenylethylene) Systems: a Preliminary Study

Farrugia Zachary, Grima Joseph N.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2019

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Vol. 23, No 3

269--301

EN

The structural and mechanical properties of various types of poly(phenylacetylene) crystalline networked polymers which stack in the third direction in a graphite-like manner have been the subject of extensive research over the past few years. These studies have suggested that depending on the particular manner of substitution of the phenyls, it is possible to achieve some very interesting mechanical properties, which include, in some cases, negative Poisson's ratio (NPR) andór negative linear compressibility (NLC). The current study investigated how alternatives to these systems can be designed, and specifically tailor-made to exhibit desirable anomalous properties, such as NPR and NLC, through the replacement of the acetylene chains with ethylene chains, so as to produce the poly(phenylethylene) equivalents. Using force field-based simulations, via the use of the polymer consistent force-field (PCFF) it was noted that, to a first approximation, these systems mirror some of the analogous properties exhibited by their poly(phenylacetylene) counterparts. In particular, poly(phenylethylene) systems built from 1234- and 1245-substituted phenyls exhibited negative Poisson's ratios, with the latter also exhibiting negative linear compressibility. This anomalous behaviour, mirrors, to some extent, that exhibited by their poly(phenylacetylene) counterparts, albeit some differences were noted, such as a reduction in the degrees of auxeticity. It was also noted that the poly(phenylethylene) systems modelled here tend to stack in the third direction, in a different manner than their poly(phenylacetylene) analogues, which difference is likely to be the factor for such reduction in auxeticity.

7

Dynamic analysis of optimized two-phase auxetic structure

Idczak E., Stręk T.

Vibrations in Physical Systems

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2017

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Vol. 28

art. no. 2017003

EN

This paper presents a dynamic analysis of earlier optimized auxetic structure. This optimization based on the distribution of two materials in such way to obtain a minimal value of Poisson’s ratio (PR), which indicates the auxetic properties. The initial optimized shape was so-called star structure, which if is made from one material has the PR close to 0.188. After optimization with the goal function of PR-minimization, the obtained value was equal to -9.5043. Then the eigenfrequencies for the optimized structure were investigated. The calculations were carried out by means of Finite Element Method (FEM). For optimization of the value of Poisson’s ratio was used algorithm MMA (Method of Moving Asymptotes). The computing of single material properties (PR, Young’s modulus, density) for the whole shape was made by means of SIMP method (Solid Isotropic Method with Penalization).

8

Computational modelling of vibrations transmission loss of auxetic lattice structure

Idczak E., Stręk T.

Vibrations in Physical Systems

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2016

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Vol. 27

123--128

EN

In this article dynamical properties of auxetic lattice structures will be analysed. Auxetic structures are materials, which have negative Poisson’s ratio and some of these have got specific dynamic properties. Their dynamic behaviour in the frequency domain will be also shown in this article. The possibility of isolation of auxetics will show the factor VTL – Vibration Transmission Loss.

9

Auxetics as entropy filters - possible application

Wojciechowski K. F., Kempinski W.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2016

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Vol. 20, No 3

271--272

EN

In this note a sketch of the idea of applying auxetics to separation of 3He from a mixture of 4He and 3He by using auxetic entropy filters is presented.

10

On Effective Young’s Modulus and Poisson’s Ratio of the Auxetic Thermoelastic Material

Maruszewski B. T., Drzewiecki A., Starosta R.

Computational Methods in Science and Technology

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2016

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Vol. 22, No. 4

233--237

EN

The paper deals with an influence of the excitation frequency and the dimensions of a free supported thermoelastic plate on the effective Poisson’s ratio and the effective Young’s modulus. Both of these parameters are not, in such a situation, the elastic material constants. The considered thermoelastic problem has been modelled within the extended thermodynamical model. Therefore, the above effective elastic coefficients are also dependent on the thermal relaxation time. The numerical analysis of those coefficients vs. excitation frequency both for normal and auxetic plates have been presented.

11

Mechanical Properties of 2D Flexyne and Reflexyne Polyphenylacetylene Networks: A Comparative Computer Studies with Various Force-Fields

Trapani L., Gatt R., Mizzi L., Grima J. N.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2015

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Vol. 19, No 3

237--296

EN

Auxetic materials exhibit the very unusual property of becoming wider when stretched and narrower when compressed, – they have a negative Poisson’s ratio. This unusual behaviour is the source of many desired effects in the materials’ properties and it is therefore, no wonder that auxetics are described as being superior to conventional materials in many practical applications. Here we make use of force-field based molecular modelling simulations in order to investigate the mechanical properties of polypehyleacetylene systems known as (n, m)-flexyne and (n, m)-reflexyne in an attempt to extend the existing knowledge there is regarding these systems. These systems have already attracted considerable consideration since negative on-axis Poisson’s ratios have been discovered for the reflexynes. We first developed a methodology for the modelling and property determination of flexyne and reflexyne network systems which we validated against existing published data. Then, extended the study to prove the simulated results were independent of the modelling methodology or the force-field used. In particular, we showed that on-axis auxeticity in the reflexynes is a force-field independent property, i.e. a property which is not an artefact of the simulations but a property which is likely to be present in the real materials if these were to be synthesised. We also studied and reported the shear behaviour of these systems were we show that the flexynes and reflexynes have very low shear moduli, a property which regrettably limits the prospects of these systems in many practical applications. Finally we examine the in-plane off-axis mechanical properties of the systems and we report that in general, these mechanical properties are highly dependent on the direction of loading. We also find that the auxeticity exhibited by the reflexynes on-axis is lost when these systems are loaded off axis since the Poisson’s ratios becomes positive very rapidly as the structure is stretched slightly off-axis (e.g. 15deg off-axis). This is once again of great practical significance as it highlights another major limitation of these systems in their use as auxetics.

12

Modelling of the static and dynamic properties of tho-type silicates

Cauchi R., Grima J. N.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2014

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Vol. 18, No 1

5--65

EN

Auxetic materials are materials exhibiting a negative Poisson’s ratio in one of their planes. This phenomenon has been studied in various materials. Zeolites are crystalline substances whose structure is characterised by the framework of linked tetrahedra, each consisting of four oxygen atoms surrounding a cation. The resulting interstitial spaces make them efficient for use as adsorbents and molecular sieves, and many studies have been focused on this aspect. Some of these zeolites may exhibit auxeticity at least in one of their planes. THO (and similar systems, such as NAT and EDI) together with the all-silica equivalent of these have been studied extensively via static simulations for their negative Poisson’s ratio in the (001) plane. In this paper a study of the all-silica equivalent of THO has been carried out via both static and dynamic simulations using the same force-field, where the system was subjected to stress along the x direction. The hypothesised semi-rigid mechanism of deformation, proposed by Grima et al. was then projected over this framework. The results obtained confirmed auxeticity along this plane by means of the COMPASS force-field, in both static and dynamic studies and compared well with the proposed mechanism of semi-rigid rotating polygons. It also showed that as the Young’s modulus of this mechanism increases other mechanisms of deformation increase in importance.

13

Auxetic materials — A review

Carneiro V. H., Meireles J., Puga H.

Materials Science Poland

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2013

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Vol. 31, No. 4

561--571

EN

Auxetic materials are endowed with a behavior that contradicts common sense, when subjected to an axial tensile load they increase their transverse dimension. In case of a compression load, they reduce their transverse dimension. Consequently, these materials have a negative Poisson’s ratio in such direction. This paper reviews research related to these materials. It presents the theories that explain their deformation behavior and reveals the important role represented by the internal structure. Their mechanical properties are explored and some potential applications for these materials are shown.

14

Numerical modeling of auxetics in structure strength

Stanisławek S., Morka A., Niezgoda T.

Journal of KONES

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2010

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Vol. 17, No. 4

459-462

EN

The paper deals with computer simulations of mechanical behaviour of a no-void ideal auxetic isotropic material. Current literature offers wide range of models which resemble the manufactured or natural structures. However, it does not answer the question how a change into auxetic no-void state would affect the continuum effective mechanical properties. Auxetic with the Poisson ratio -0.3 has been compared through typical tests to a classic steel elastic material. Most of the engineering software cannot precede Poisson ratio helow zero. Therefore a unique technique was applied using equation of state to overcome this obstacle. All simulations have been done in elastic regime. For the tensile compression tests a 10 mm edge cube was modelled, the bending test used a 5x5x250 mm bar. The loading for initial tests was realized as a kinematic displacement of particular nodes. For bar bending a force was applied in the middle of the beam. The finite element method has been used with explicit time integration algorithm implemented in commercial software with one integration point brick elements. Specific properties have been observed for each test, for tensile test auxetic showed higher strength while for compression material was weaker. Logically the bending test showed no clear influence of negative Poisson to material strength. Further simulations as a shear or impact tests are planned.

15

Elastic properties of orientationally disordered crystal of mono- and polydisperse hard dumbbells in three dimensions

Kowalik M, Wojciechowski K W

Materials Science Poland

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2008

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Vol. 26, No. 4

978--982

EN

Preliminary results concerning influence of polydispersity of ‘atomic’ sizes on elastic properties of the rotator phase of a three-dimensional system of hard dumbbells have been presented. It has been shown that, in contrast to two-dimensional hard discs and three-dimensional hard spheres, for the polydispersity parameter not higher than 5%, there is no significant influence on the elastic constants and Poisson’s ratio of hard dumbbells of the anisotropy parameter 0.15 (i.e., when the discs forming dumbbells are distanced by 15% of the average disc diameter).

16

Poisson’s ratio of anisotropic systems

Wojciechowski K.

Computational Methods in Science and Technology

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2005

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Vol. 11, nr 1

73-79

EN

The Poisson’s ratio of anisotropic materials depends, in general, both on a “longitudinal” direction along which the stress is changed and on a “transverse” direction in which the transverse deformation is measured. For cubic media there exist “longitudinal” directions, parallel to the 4-fold and 3-fold axes, for which the Poisson’s ratio does not depend on the “transverse” direction. Depending on the tensor of elastic compliances (or elastic constants), crystals of cubic symmetry can exhibit negative Poisson’s ratio in both these directions (they are called strongly auxetics), in one of them (i.e. either along the 4-fold axis or along the 3-fold one; they are called partially auxetic) or in none of them. For crystals exhibiting 3-fold symmetry axis the Poisson’s ratio along this axis does not depend on the “transverse” direction. For other “longitudinal” directions the Poisson’s ratio depends, in general, on the “transverse” direction. The Poisson’s ratio averaged with respect to the “transverse” direction depends only on the “longitudinal” direction and can be conveniently presented graphically. As an example the f.c.c. hard sphere crystal is considered. It is shown that the average (with respect to “transverse” direction) Poisson’s ratio of the hard sphere crystal is positive for all “longitudinal” directions. One should add, however, that there exist directions for which the (not averaged) Poisson’s ratio of hard spheres is negative.

17

An approximation method for simulating temperature dependence of Poissonąs ratios of self - expanding auxegens

Wu H., Wei G.

Computational Methods in Science and Technology

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2004

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Vol. 10, nr 2

229-234

EN

A combined molecular dynamics and molecular mechanics method has been developed for estimating Poisson's ratios of certain types of molecular auxetics at various temperatures. The temperature dependence of the auxeticity of a special class of molecular auxetics, namely, a self-expanding supramolecular network of auxegens containing alternating phenyl and acetylene links, is studied with use of this approximation method. The simulation results show that as temperature increases from O to 300 K, the auxeticity of the resulting superlattice or van der Waals network of auxegens decreases from the initial self-expandability to two negatively small Poisson ratios on the xoy piane.

18

Negative Poisson's ratio and percolating structures

Wojciechowski K. W., Novikov V. V.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2001

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Vol. 5, No 1

5-11

EN

Elastic properties of non-uniform, two-component systems are studied in frames of a model of percolation on a simple cubic lattice. It is shown that as the ratio of the bulk moduli of the components tends to zero, kappa =K/sub s//K/sub h/ to 0 (where s,h denote the softer and harder phase, respectively), the Poisson's ratio of the system tends to 0.2 at the percolation threshold of the harder phase, no matter what the values are of the Poisson's ratios of the components. A qualitatively new, collective mechanism leading to negative Poisson's ratio is suggested.