Abstract
A general expression for the Poisson's ratio (PR) of square or 2D cubic materials is discussed in terms of the elastic moduli ratios, and , where G and W are the shear moduli, and K is the bulk modulus. The entire ‐plane is partitioned into nonauxetic, partially auxetic, and auxetic regions by two straight lines. A representation of the ‐plane with the elastic constant ratio is exploited to investigate 2D square materials under nonzero hydrostatic pressure. It is demonstrated that 2D square materials with 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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