Another Look at Auxeticity of 2D Square Media,Physica Status Solidi (B) - Basic Solid State Physics

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Another Look at Auxeticity of 2D Square Media
Physica Status Solidi (B) - Basic Solid State Physics ( IF 1.5 ) Pub Date : 2020-09-09 , DOI: 10.1002/pssb.202000485
Natalia Bielejewska ₁ , Arkadiusz C. Brańka ₁ , Sławomir Pieprzyk ₁ , Tetiana Yevchenko ₁

Affiliation

A general expression for the Poisson's ratio (PR) of square or 2D cubic materials is discussed in terms of the elastic moduli ratios,

X = G / K

and

Y = G / W

, where G and W are the shear moduli, and K is the bulk modulus. The entire

X Y

‐plane is partitioned into nonauxetic, partially auxetic, and auxetic regions by two straight lines. A representation of the

X Y

‐plane with the elastic constant ratio

λ = C_{12} / C_{44}

is exploited to investigate 2D square materials under nonzero hydrostatic pressure. It is demonstrated that 2D square materials with

λ > 0

can be auxetic only under negative pressure. Similarities and differences between the corresponding descriptions of auxetic behavior of cubic 3D materials are pointed out.

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