# Extreme values of Young’s modulus and Poisson’s ratio of hexagonal crystals

@article{Gorodtsov2019ExtremeVO, title={Extreme values of Young’s modulus and Poisson’s ratio of hexagonal crystals}, author={Valentin A. Gorodtsov and Dmitry S. Lisovenko}, journal={Mechanics of Materials}, year={2019} }

Abstract The variability of Young’s modulus and Poisson’s ratio for hexagonal crystals was studied. Expressions for three stationary values of Young’s modulus and eight stationary values of Poisson’s ratio were obtained. Numerical analysis of the extrema of the elastic characteristics for crystals was given based on experimental data from the Landolt-Bornstein reference book. Classification schemes for extreme values of Young’s modulus and Poisson’s ratio are proposed. Data on hexagonal…

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## References

SHOWING 1-10 OF 53 REFERENCES

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

- Materials Science
- 2018

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…

Extreme values of the Poisson’s ratio of cubic crystals

- Physics
- 2016

The problem of determining the extrema of Poisson’s ratio for cubic crystals is considered, and analytical expressions are derived to calculate its extreme values. It follows from the obtained…

Auxetics among 6-constant tetragonal crystals

- Materials Science
- 2015

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…

Relation of Poisson’s ratio on average with Young’s modulus. Auxetics on average

- Physics
- 2012

A linear relation between the Poisson’s ratio averaged along the transverse directions and Young’s modulus of the tensed cubic crystal is established. It is found that the coefficients of the linear…

On the Extreme Values of Young’s Modulus, the Shear Modulus, and Poisson’s Ratio for Cubic Materials

- Mathematics
- 1998

For homogeneous cubic elastic materials with positive definite stored energy it is shown that the maximum and minimum values of Young's modulus E are related to the maximum and minimum values of the…

Poisson's ratio in cubic materials

- Materials Science, PhysicsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2006

Expressions are given for the maximum and minimum values of Poisson's ratio ν for materials with cubic symmetry. Values less than −1 occur if and only if the maximum shear modulus is associated with…

The anisotropy of Young's modulus, shear modulus and Poisson's ratio in cubic materials

- Physics
- 1971

The directional behaviour of Young's modulus, shear modulus, and Poisson's ratio are expressed for a number of crystallographic planes for cubic materials. Their behaviour as a function of direction…

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

- Materials Science
- 2015

In the paper, the elasticity theory was applied to consider the mechanical properties of rectilinearly anisotropic seven-constant tetragonal crystals and their cylindrically anisotropic…

Extrema of Young’s modulus for elastic solids with tetragonal symmetry

- Mathematics
- 2005

Abstract For a homogeneous and linearly elastic solid the general expression of Young’s modulus E(n) is given, and a constrained extremum problem is formulated for the evaluation of the directions n…

Elastic anisotropy and extreme Poisson's ratios in single crystals

- Materials Science
- 2010

Abstract The relationship between elastic anisotropy and extreme Poisson’s ratio behaviour (either positive or negative) in single-crystalline materials has been investigated using experimentally…