Quadratic and cubic monocrystalline and polycrystalline materials: their stability and mechanical properties

Abstract

We consider 2-and 3-dimensional cubic monocrystalline and polycrystalline materials. Expressions for Young's and shear moduli and Poisson's ratio are expressed in terms of eigenvalues of the stiffness tensor. Such a form is well suited for studying properties of these mechanical characteristics on sides of the stability triangles. For crystalline highsymmetry directions lines of vanishing Poisson's ratio are found. These lines demarcate regions of the stability triangle into areas of various auxeticity properties. The simplest model of polycrystalline 2D and 3D cubic materials is considered. In polycrystalline phases the region of complete auxetics is larger than for monocrystalline materials.

Classification of cubic auxetics

“…The analysis in this paper is mainly focused on the classification of cubic partial auxetics using their parameterization by the dimensionless elastic coefficient P. We have shown that the auxetic boundary (surface) type in the space of angular variables separating the regions with positive and negative Poisson's ratio is essentially varied with the change in the value of the dimensionless parameter (a brief discussion of Poisson's ratio vanishing lines was given in Ref. [15] for a different elastic parameterization). It was found that there exists a critical value of the parameter P c % 0:745 at which a topological rearrangement of the auxetic surface from "open" to "closed" type occurs.…”

“…A lot of publications [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] are devoted to the analysis of the cubic auxetics (cubic crystals with negative Poisson's ratio). The first attempt to formulate an auxeticity criterion was made, apparently, in Ref.…”

Auxetic properties of polycrystals

“…Regions of stability for symmetry systems other than cubic and isotropic as well as for the oblique symmetry system are defined in spaces of dimensions higher than 3. In the case of rectangular symmetry system the space of parameters can be effectively reduced to a 3D space 15.…”