Continuum Mechanics in a Space of Any Dimension : II. Isotropic Elastic Materials

Abstract

The behavior of isotropic elastic materials in a space of any dimension is investigated. The linear approximations of the constitutive equation with respect to the strain and to the principal stretches are presented, and the Hookean solid is defined. In the case of space having more than one dimension, the material has two elastic constants. In one-dimensional space the material has an elastic constant. Young's modulus, Poisson's ratio and the bulk modulus of the Hookean solid depend not only on the elastic constants but also on the dimension of space. The wave propagation is analyzed and there are a longitudinal wave and (n-l) transverse waves in n-dimensional space. Simple shear deformation is investigated and there occurs a normal stress effect. It is proved that simple shear deformation is equivalent to a pure shear deformation and the principal stretches are determined by the total amount of shear.