Auxetics among 6-constant tetragonal crystals

Goldstein, R. V.; Городцов, В. А.; Lisovenko, D. S.; Volkov, M. A.

doi:10.22226/2410-3535-2015-4-409-413

Cited by 24 publications

(11 citation statements)

References 8 publications

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“…An analysis of average Poisson's ratio have shown that all hexagonal crystals have positive Poisson's ratio [9]. We note that more than four hundred crystals with negative Poisson's ratio (auxetics) are detected for crystals of other crystalline systems [5][6][7][8][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. The least number of auxetics is found among hexagonal crystals, and the largest amount is detected among cubic crystals (more than three hundred).…”

Section: Introductionmentioning

confidence: 72%

Variability of Young’s modulus and Poisson’s ratio of hexagonal crystals

Komarova

Городцов

Lisovenko

2018

IOP Conf. Ser.: Mater. Sci. Eng.

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Abstract. In this paper, the variability of elastic characteristics (Young's modulus and Poisson's ratio) of hexagonal crystals has been studied. Analytic expressions for Young's modulus and Poisson's ratio are obtained. Stationary values for these elastic characteristics are found. Young's modulus has three stationary values, and Poisson's ratio has eight stationary values. Numerical analysis of these elastic characteristics for hexagonal crystals is given based on the experimental data from the Landolt-Börnstein handbook. Global extrema of Young's modulus and Poisson's ratio for hexagonal crystals are found. Crystals are found in which the maximum values exceeds the upper limit for isotropic materials.

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Section: Introductionmentioning

confidence: 72%

Variability of Young’s modulus and Poisson’s ratio of hexagonal crystals

Komarova

Городцов

Lisovenko

2018

IOP Conf. Ser.: Mater. Sci. Eng.

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“…If for any choice the Poisson's ratio is negative, the material is called auxetic, and if it is negative in some cases and positive in the other cases then it is called partial auxetic (). It was already shown for anisotropic materials that negative Poisson's ratio can be found for tension along particular directions . By now about four hundred materials with negative Poisson's ratio have been found and three hundred of them are of cubic anisotropy .…”

Section: Introductionmentioning

confidence: 97%

“…A number of sources of auxeticity have been revealed, among them are (i) anisotropy of the elastic media ; (ii) re‐entrant honeycombs and re‐entrant foams ; (iii) rotating rigid units ; (iv) polydispersity of fcc crystal formed by soft spheres and dimers of soft spheres ; (v) fractality (); (vi) negative hydrostatic pressure (), and some other. Obviously, the search for new sources of auxeticity is an important theoretical problem which can have an impact on the field.…”

Section: Introductionmentioning

confidence: 99%

Auxeticity from nonlinear vibrational modes

Korznikova

Bokij²,

Zhou

2016

Physica Status Solidi (b)

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Abstractauthoren It is demonstrated that the large‐amplitude, short‐wavelength vibrational modes excited in the lattice can change its elastic properties due to physical and/or geometric nonlinearity of the lattice bonds. Depending on the symmetry of the vibrational mode the symmetry of the elastic properties of the lattice can also change. Using as an example the two‐dimensional honeycomb structure with normalβ‐FPU pairwise interparticle interactions, we demonstrate that the excitation of a large‐amplitude vibrational mode in combination with equiaxial tensile strain can change the sign of the Poisson's ratio from positive to negative, thus leading to the auxetic property of the lattice. It is shown that the considered lattice supports discrete breathers, i.e., spatially localized nonlinear vibrational modes. The excitation of the discrete breathers as a result of the modulational instability of the extended short‐wavelength modes is analyzed. Our results contribute to the understanding of the relation between the elastic properties and nonlinear dynamics of the lattices of interacting particles. Extended vibrational modes in the 2D honeycomb lattice presented by the stroboscopic pictures of the particle motion. Excitation of such modes with sufficiently large amplitude in combination with equiaxial tension changes the sign of the Poisson's ratio of the lattice from positive to negative.

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“…If for any choice Poisson's ratio is negative, the material is called auxetic, and if it is negative in some cases and positive in the other cases then it is called partial auxetic (). It was already shown that negative Poisson's ratio can be found for tension along different directions for anisotropic materials . By now about 400 materials with negative Poisson's ratio are found and 300 of them are of cubic anisotropy .…”

Section: Introductionmentioning

confidence: 97%

Equilibrium diamond‐like carbon nanostructures with cubic anisotropy: Elastic properties

Lisovenko

Baimova

Rysaeva

et al. 2016

Physica Status Solidi (b)

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Diamond‐like carbon nanostructures with cubic anisotropy made by joining fullerene‐like molecules of different types via valence bonds are studied by means of molecular dynamics simulations. The considered structures are interesting because they include both sp2‐ and sp3‐hybridized carbon atoms, which lead to their distinct properties compared to the structures with one type of hybridization. Seven diamond‐like carbon phases having different shapes of structural units and/or different ways of their connection are studied in the present work. For the relaxed equilibrium structures, the engineering elastic constants (Poisson's ratio, Young's modulus, and shear modulus) are calculated as the functions of the crystal orientation angles. Extreme values of the elastic constants are reported. It is shown that two of the considered diamond‐like structures have negative Poisson's ratio and can be regarded as the partial auxetics. According to the results of the present study, elastic properties of the bulk diamond‐like carbon structures can vary considerably depending on their structure. Diamond‐like carbon nanostructures

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Auxetics among 6-constant tetragonal crystals

Cited by 24 publications

References 8 publications

Variability of Young’s modulus and Poisson’s ratio of hexagonal crystals

Variability of Young’s modulus and Poisson’s ratio of hexagonal crystals

Auxeticity from nonlinear vibrational modes

Equilibrium diamond‐like carbon nanostructures with cubic anisotropy: Elastic properties

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