Changes in material symmetry associated with deformation: Uniaxial extension

Abstract

When a material which is isotropic with respect to a reference configuration is deformed, it is anisotropic with respect to the deformed configuration. The nature of the anisotropy depends on the deformation. In this paper, we consider the special case of the change of a reference configuration by uniaxial extension. We first discuss the structure of the new material symmetry group, and show that it includes non-orthogonal unimodular transformations. Then using the general representation for the response functional of an isotropic material, we show how to construct a representation of the new response functional which satisfies the restrictions of the new material symmetry group.