Relation of Poisson's Ratio on Average With Young's Modulus. Auxetics on Average

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 relation in the dimensionless form depend on two dimensionless elastic parameters combined from three compliance coefficients. By virtue of this fact, the form of angular regions of the crystal orientation with negative Poisson's ratio on average varies as the magnitude of one dimensionless coefficient and the sign of the other one. We find the critical value of the dimensionless parameter at which there is the topological change in the structure of the angular regions occurs is established.