Negative Poisson’s ratio for cubic crystals and nano/microtubes

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

doi:10.1134/s1029959914020027

Cited by 52 publications

(37 citation statements)

References 11 publications

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“…Their number is small because the number of the initial sevenconstant tetragonal crystals is small (fourteen crystals, according to [8]). At the same time, as was shown [7], all cubic crystals (several hundreds, according to [8]) rolled up into nano/microtubes with a non-zero chiral angle are also seven-constant tetragonal tubes with curvilinear anisotropy. All these nano/microtubes, according to [7], are partial auxetics.…”

Section: Resultsmentioning

confidence: 75%

“…At the same time, as was shown [7], all cubic crystals (several hundreds, according to [8]) rolled up into nano/microtubes with a non-zero chiral angle are also seven-constant tetragonal tubes with curvilinear anisotropy. All these nano/microtubes, according to [7], are partial auxetics. The so wide variety of auxetic nano/microtubes with curvilinear anisotropy allows one to expect their wide application.…”

Section: Resultsmentioning

confidence: 75%

“…Such anisotropic materials are considered as partial auxetics. It is demonstrated that when cubic crystal plates are rolled up into nano/microtubes with a nonzero chiral angle, curvilinearly anisotropic tubes with seven-constant tetragonal elasticity are formed and most of the nano/microtubes are found to be partial auxetics [7]. In the present paper, most attention is focused on Poissons ratios of rectilinearly anisotropic seven-constant tetragonal crystals and their nano/microtubes.…”

Section: Introductionmentioning

confidence: 92%

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Young’s modulus and Poisson’s ratio for seven-constant tetragonal crystals and nano/microtubes

2015

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In the paper, the elasticity theory was applied to consider the mechanical properties of rectilinearly anisotropic seven-constant tetragonal crystals and their cylindrically anisotropic nano/microtubes with and with no chiral angle, being the angle between the crystallographic symmetry axis and elongated tube axis. It is found that the number of crystals with negative Poissons ratio is the least for rectilinear anisotropy and is much larger for curvilinear anisotropy. With a nonzero chiral angle, all nano/microtubes can have negative Poissons ratio. The elastic problem on axial tension of cylindrical nano/microtubes is solved for radially inhomogeneous stresses: three normal stresses and one shear stress.

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Section: Resultsmentioning

confidence: 75%

Section: Resultsmentioning

confidence: 75%

Section: Introductionmentioning

confidence: 92%

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Young’s modulus and Poisson’s ratio for seven-constant tetragonal crystals and nano/microtubes

2015

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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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“…Auxetics among 6-constant tetragonal crystals, considered below, are studied in the case of rectilinear anisotropy. Previously, similar studies have been performed for all (auxetics and non-auxetics) crystals of cubic and 7-constant tetragonal systems [1][2][3][4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Auxetics among 6-constant tetragonal crystals

Goldstein¹,

Городцов²,

Lisovenko³

et al. 2015

LoM

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Analytical and numerical features of the elastic properties of the stretched rectilinearly anisotropic 6-constant tetragonal crystals are considered. Analytical formulas for Young's modulus and Poisson's ratio are obtained. They are expressed in terms of the elastic compliance coefficients in Voight notation and the parameters of crystal orientation. Numerical calculations are performed using these formulas and data on the elastic constants from the Landolt-Börnstein Handbook. Possible types of Young's modulus and Poisson's ratio are analyzed. More than eighty tetragonal crystals were studied. About 60% of them are characterized by negative Poisson's ratio for certain particular orientations of the crystals. Such auxetics are listed in the Tables. Ten crystals can have Poisson's ratio greater than unity, and Poisson's ratio for six crystals is less than -0.5. The same six crystals are characterized by high variability of Young's modulus. Young's modulus for more than ten crystals exceeds 300 GPa.

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Negative Poisson’s ratio for cubic crystals and nano/microtubes

Cited by 52 publications

References 11 publications

Young’s modulus and Poisson’s ratio for seven-constant tetragonal crystals and nano/microtubes

Young’s modulus and Poisson’s ratio for seven-constant tetragonal crystals and nano/microtubes

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

Auxetics among 6-constant tetragonal crystals

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