The General Relationships Between the Elastic Constants of Isotropic Materials in n Dimensions

Abstract

The relationships between the elastic constants of homogeneous isotropic materials in n dimension are derived and are shown to depend on n. The maximal value of the generalized Poisson's ratio is 1/(n?1). The n-dimensional formulae reproduce the well-known three-dimensional relations for n=3, while n=2 produces the relations, appropriate for monomolecular films. The correct degeneration is shown for n= 1.