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14 pages, 3349 KiB

Open AccessFeature PaperArticle

Poisson’s Ratio of the f.c.c. Hard Sphere Crystals with Periodically Stacked (001)-Nanolayers of Hard Spheres of Another Diameter

by Jakub W. Narojczyk and Krzysztof W. Wojciechowski

Materials 2019, 12(5), 700; https://doi.org/10.3390/ma12050700 - 27 Feb 2019

Cited by 25 | Viewed by 3577

Abstract

The results of studies on the influence of periodically stacked nanolayer inclusions, introduced into the face-centered cubic (f.c.c.) hard sphere crystal, on Poisson’s ratio of the obtained nanocomposite system are presented. The monolayers are orthogonal to the

[001]

-direction. They are [...] Read more.

The results of studies on the influence of periodically stacked nanolayer inclusions, introduced into the face-centered cubic (f.c.c.) hard sphere crystal, on Poisson’s ratio of the obtained nanocomposite system are presented. The monolayers are orthogonal to the

[001]

-direction. They are formed by hard spheres with diameter different from the spheres forming the matrix of the system. The Monte Carlo computer simulations show that in such a case the symmetry of the system changes from the cubic to tetragonal one. When the diameter of the inclusion spheres increases at certain range, a decrease of the negative Poisson’s ratio in the

[101] [\bar{1} 01]

-directions is observed, i.e., the system enhances its partial auxeticity. The dependence of the maximal, average, and negative parts of the minimal Poisson’s ratio on the direction of the applied load are shown in a form of surfaces in spherical coordinates, plotted for selected values of nanolayer particle diameters. The most negative value of the Poisson’s ratio found among all studied systems was

- 0.11

(at pressure

p^{*} = 100

, which is about ten times higher than the melting pressure) what is almost twice more negative than in the f.c.c. crystal of identical hard spheres. The observed effect weakens along with the decrease of pressure and becomes hardly noticeable near melting. This study indicates that modifying only the size of the inclusion particles one can change Poisson’s ratio of nanocomposites at high pressures. Full article

(This article belongs to the Special Issue Auxetic Materials 2017-2018)

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11 pages, 4537 KiB

Open AccessArticle

An Anisotropic Auxetic 2D Metamaterial Based on Sliding Microstructural Mechanism

by Teik-Cheng Lim

Materials 2019, 12(3), 429; https://doi.org/10.3390/ma12030429 - 30 Jan 2019

Cited by 14 | Viewed by 3688

Abstract

A new 2D microstructure is proposed herein in the form of rigid unit cells, each taking the form of a cross with two opposing crossbars forming slots and the other two opposing crossbars forming sliders. The unit cells in the microstructure are arranged [...] Read more.

A new 2D microstructure is proposed herein in the form of rigid unit cells, each taking the form of a cross with two opposing crossbars forming slots and the other two opposing crossbars forming sliders. The unit cells in the microstructure are arranged in a rectangular array in which the nearest four neighboring cells are rotated by 90° such that a slider in each unit cell is connected to a slot from its nearest neighbor. Using a kinematics approach, the Poisson’s ratio along the axes of symmetry can be obtained, while the off-axis Poisson’s ratio is obtained using Mohr’s circle. In the special case of a square array, the results show that the Poisson’s ratio varies between 0 (for loading parallel to the axes) and −1 (for loading at 45° from the axes). For a rectangular array, the Poisson’s ratio varies from 0 (for loading along the axes) to a value more negative than −1. The obtained results suggest the proposed microstructure is useful for designing materials that permit rapid change in Poisson’s ratio for angular change. Full article

(This article belongs to the Special Issue Auxetic Materials 2017-2018)

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12 pages, 1876 KiB

Open AccessArticle

High Partial Auxeticity Induced by Nanochannels in [111]-Direction in a Simple Model with Yukawa Interactions

by Konstantin V. Tretiakov, Paweł M. Pigłowski, Jakub W. Narojczyk, Mikołaj Bilski and Krzysztof W. Wojciechowski

Materials 2018, 11(12), 2550; https://doi.org/10.3390/ma11122550 - 14 Dec 2018

Cited by 9 | Viewed by 2601

Abstract

Computer simulations using Monte Carlo method in the isobaric-isothermal ensemble were used to investigate the impact of nanoinclusions in the form of very narrow channels in the

[111]

-direction on elastic properties of crystals, whose particles interact via Yukawa potential. The [...] Read more.

Computer simulations using Monte Carlo method in the isobaric-isothermal ensemble were used to investigate the impact of nanoinclusions in the form of very narrow channels in the

[111]

-direction on elastic properties of crystals, whose particles interact via Yukawa potential. The studies were performed for several selected values of Debye screening length (

{(κ σ)}^{- 1}

). It has been observed that introduction of the nanoinclusions into the system reduces the negative value of Poisson’s ratio towards

[110] [1 \bar{1} 0]

, maintaining practically constant values of Poisson’s ratio in the directions

[100]

and

[111]

. These studies also show that concentration of particles forming the nanoinclusions in the system has a significant effect on the value of Poisson’s ratio in the

[110] [1 \bar{1} 0]

-direction. A strong (more than fourfold) decrease of Poisson’s ratio in this direction was observed, from

- 0.147 (3)

(system without inclusions) to

- 0.614 (14)

(system with nanoinclusions) at

κ σ = 10

when the inclusion particles constituted about 10 percent of all particles. The research also showed an increase in the degree of auxeticity in the system with increasing concentration of nanoinclusion particles for all the screening lengths considered. Full article

(This article belongs to the Special Issue Auxetic Materials 2017-2018)

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13 pages, 11624 KiB

Open AccessArticle

Filtration Properties of Auxetics with Rotating Rigid Units

by Daphne Attard, Aaron R. Casha and Joseph N. Grima

Materials 2018, 11(5), 725; https://doi.org/10.3390/ma11050725 - 3 May 2018

Cited by 18 | Viewed by 5203

Abstract

Auxetic structures and materials expand laterally when stretched. It has been argued that this property could be applied in the design of smart filters with tunable sieving properties. This work analyses the filtration properties of a class of auxetic structures which achieve their [...] Read more.

Auxetic structures and materials expand laterally when stretched. It has been argued that this property could be applied in the design of smart filters with tunable sieving properties. This work analyses the filtration properties of a class of auxetic structures which achieve their auxeticity through a rotating rigid unit mechanism, an archetypal mechanism known to be responsible for this behavior in a number of crystalline materials. In particular, mathematical expressions are derived for the space coverage of networks constructed from a variety of quadrilaterals, as well as the pore radius. The latter is indicative of the particle size that can pass through when the particle dimension is comparable to the pore size, whereas the space coverage is indicative of the rate of flow when the particles are of a much smaller dimension than the pore size. The expressions suggest that these systems offer a wide range of pore sizes and space coverages, both of which can be controlled through the way that the units are connected to each other, their shape and the angle between them. Full article

(This article belongs to the Special Issue Auxetic Materials 2017-2018)

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12 pages, 1433 KiB

Open AccessArticle

Auxeticity of Concentric Auxetic-Conventional Foam Rods with High Modulus Interface Adhesive

by Teik-Cheng Lim

Materials 2018, 11(2), 223; https://doi.org/10.3390/ma11020223 - 31 Jan 2018

Cited by 12 | Viewed by 4136

Abstract

While the rule of mixture is applicable for addressing the overall Poisson’s ratio of a concentrically aligned bi-layered rod under longitudinal loading, the same cannot be said for this rod under torsional loading due to the higher extent of deformation in the rod [...] Read more.

While the rule of mixture is applicable for addressing the overall Poisson’s ratio of a concentrically aligned bi-layered rod under longitudinal loading, the same cannot be said for this rod under torsional loading due to the higher extent of deformation in the rod material further away from the torsional axis. In addition, the use of adhesives for attaching the solid inner rod to the hollow outer rod introduces an intermediate layer, thereby resulting in a tri-layered concentric rod if the adhesive layer is uniformly distributed. This paper investigates the effect of the adhesive properties on the overall auxeticity of a rod consisting of two concentrically aligned cylindrical isotropic foams with Poisson’s ratio of opposite signs under torsional loads. An indirect way for obtaining Poisson’s ratio of a concentrically tri-layered rod was obtained using a mechanics of materials approach. Results show that the auxeticity of such rods is influenced by the adhesive’s stiffness, Poisson’s ratio, thickness, and radius from the torsional axis. Full article

(This article belongs to the Special Issue Auxetic Materials 2017-2018)

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16 pages, 15743 KiB

Open AccessArticle

Computational Modelling of Structures with Non-Intuitive Behaviour

by Tomasz Strek, Hubert Jopek, Eligiusz Idczak and Krzysztof W. Wojciechowski

Materials 2017, 10(12), 1386; https://doi.org/10.3390/ma10121386 - 4 Dec 2017

Cited by 41 | Viewed by 4766

Abstract

This paper presents a finite-element analysis of honeycomb and re-entrant honeycomb structures made of a two-phase composite material which is optimized with respect to selected parameters. It is shown that some distributions of each phase in the composite material result in the counter-intuitive [...] Read more.

This paper presents a finite-element analysis of honeycomb and re-entrant honeycomb structures made of a two-phase composite material which is optimized with respect to selected parameters. It is shown that some distributions of each phase in the composite material result in the counter-intuitive mechanical behaviour of the structures. In particular, negative values of effective Poisson’s ratio, i.e., effective auxeticity, can be obtained for a hexagonal honeycomb, whereas re-entrant geometry can be characterized by positive values. Topology optimization by means of the method of moving asymptotes (MMA) and solid isotropic material with penalization (SIMP) was used to determine the materials’ distributions. Full article

(This article belongs to the Special Issue Auxetic Materials 2017-2018)

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13 pages, 7544 KiB

Open AccessArticle

Finite Element Analysis of Tunable Composite Tubes Reinforced with Auxetic Structures

by Hubert Jopek

Materials 2017, 10(12), 1359; https://doi.org/10.3390/ma10121359 - 27 Nov 2017

Cited by 26 | Viewed by 7176

Abstract

A tubular composite structure that is built of two materials, characterized by different Young moduli, is analysed in this paper. The Young’s modulus of one of these materials can be controlled by external conditions e.g., magnetic or electric field, temperature etc. The geometry [...] Read more.

A tubular composite structure that is built of two materials, characterized by different Young moduli, is analysed in this paper. The Young’s modulus of one of these materials can be controlled by external conditions e.g., magnetic or electric field, temperature etc. The geometry of the reinforcement is based on typical auxetic re-entrant honeycomb cellular structure. The influence of this external factor on the behaviour of the stretched tube is analysed in this paper. Also, the possibility of creating a tubular composite structure whose cross-section is either shrinking or expanding, while stretching the tube is presented. Full article

(This article belongs to the Special Issue Auxetic Materials 2017-2018)

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Graphical abstract

12 pages, 5084 KiB

Open AccessArticle

Auxeticity of Yukawa Systems with Nanolayers in the (111) Crystallographic Plane

by Paweł M. Pigłowski, Jakub W. Narojczyk, Artur A. Poźniak, Krzysztof W. Wojciechowski and Konstantin V. Tretiakov

Materials 2017, 10(11), 1338; https://doi.org/10.3390/ma10111338 - 22 Nov 2017

Cited by 19 | Viewed by 5333

Abstract

Elastic properties of model crystalline systems, in which the particles interact via the hard potential (infinite when any particles overlap and zero otherwise) and the hard-core repulsive Yukawa interaction, were determined by Monte Carlo simulations. The influence of structural modifications, in the form [...] Read more.

Elastic properties of model crystalline systems, in which the particles interact via the hard potential (infinite when any particles overlap and zero otherwise) and the hard-core repulsive Yukawa interaction, were determined by Monte Carlo simulations. The influence of structural modifications, in the form of periodic nanolayers being perpendicular to the crystallographic axis [111], on auxetic properties of the crystal was investigated. It has been shown that the hard sphere nanolayers introduced into Yukawa crystals allow one to control the elastic properties of the system. It has been also found that the introduction of the Yukawa monolayers to the hard sphere crystal induces auxeticity in the

[11 \bar{1}] [112]

-direction, while maintaining the negative Poisson’s ratio in the

[110] [1 \bar{1} 0]

-direction, thus expanding the partial auxeticity of the system to an additional important crystallographic direction. Full article

(This article belongs to the Special Issue Auxetic Materials 2017-2018)

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25 pages, 11482 KiB

Open AccessArticle

The Isotropic and Cubic Material Designs. Recovery of the Underlying Microstructures Appearing in the Least Compliant Continuum Bodies

by Sławomir Czarnecki, Tomasz Łukasiak and Tomasz Lewiński

Materials 2017, 10(10), 1137; https://doi.org/10.3390/ma10101137 - 26 Sep 2017

Cited by 17 | Viewed by 6371

Abstract

The paper discusses the problem of manufacturability of the minimum compliance designs of the structural elements made of two kinds of inhomogeneous materials: the isotropic and cubic. In both the cases the unit cost of the design is assumed as equal to the [...] Read more.

The paper discusses the problem of manufacturability of the minimum compliance designs of the structural elements made of two kinds of inhomogeneous materials: the isotropic and cubic. In both the cases the unit cost of the design is assumed as equal to the trace of the Hooke tensor. The Isotropic Material Design (IMD) delivers the optimal distribution of the bulk and shear moduli within the design domain. The Cubic Material Design (CMD) leads to the optimal material orientation and optimal distribution of the invariant moduli in the body made of the material of cubic symmetry. The present paper proves that the varying underlying microstructures (i.e., the representative volume elements (RVE) constructed of one or two isotropic materials) corresponding to the optimal designs constructed by IMD and CMD methods can be recovered by matching the values of the optimal moduli with the values of the effective moduli of the RVE computed by the theory of homogenization. The CMD method leads to a larger set of results, i.e., the set of pairs of optimal moduli. Moreover, special attention is focused on proper recovery of the microstructures in the auxetic sub-domains of the optimal designs. Full article

(This article belongs to the Special Issue Auxetic Materials 2017-2018)

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15 pages, 10410 KiB

Open AccessArticle

Design and Additive Manufacturing of 3D Phononic Band Gap Structures Based on Gradient Based Optimization

by Maximilian Wormser, Fabian Wein, Michael Stingl and Carolin Körner

Materials 2017, 10(10), 1125; https://doi.org/10.3390/ma10101125 - 22 Sep 2017

Cited by 64 | Viewed by 8440

Abstract

We present a novel approach for gradient based maximization of phononic band gaps. The approach is a geometry projection method combining parametric shape optimization with density based topology optimization. By this approach, we obtain, in a two dimension setting, cellular structures exhibiting relative [...] Read more.

We present a novel approach for gradient based maximization of phononic band gaps. The approach is a geometry projection method combining parametric shape optimization with density based topology optimization. By this approach, we obtain, in a two dimension setting, cellular structures exhibiting relative and normalized band gaps of more than 8 and 1.6, respectively. The controlling parameter is the minimal strut size, which also corresponds with the obtained stiffness of the structure. The resulting design principle is manually interpreted into a three dimensional structure from which cellular metal samples are fabricated by selective electron beam melting. Frequency response diagrams experimentally verify the numerically determined phononic band gaps of the structures. The resulting structures have band gaps down to the audible frequency range, qualifying the structures for an application in noise isolation. Full article

(This article belongs to the Special Issue Auxetic Materials 2017-2018)

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18 pages, 8110 KiB

Open AccessArticle

Finite Element Modeling of Multilayer Orthogonal Auxetic Composites under Low-Velocity Impact

by Lili Jiang and Hong Hu

Materials 2017, 10(8), 908; https://doi.org/10.3390/ma10080908 - 5 Aug 2017

Cited by 24 | Viewed by 7570

Abstract

The multilayer orthogonal auxetic composites have been previously developed and tested to prove that they own excellent energy absorption and impact protection characteristics in a specific strain range under low-velocity impact. In this study, a three dimensional finite element (FE) model in ANSYS [...] Read more.

The multilayer orthogonal auxetic composites have been previously developed and tested to prove that they own excellent energy absorption and impact protection characteristics in a specific strain range under low-velocity impact. In this study, a three dimensional finite element (FE) model in ANSYS LS-DYNA was established to simulate the mechanical behavior of auxetic composites under low-velocity drop-weight impact. The simulation results including the Poisson’s ratio versus compressive strain curves and the contact stress versus compressive strain curves were compared with those in the experiments. The clear deformation pictures of the FE models have provided a simple and effective way for investigating the damage mechanism and optimizing the material, as well as structure design. Full article

(This article belongs to the Special Issue Auxetic Materials 2017-2018)

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