Removal of unphysical arbitrariness in constitutive equations for elastically anisotropic nonlinear elastic–viscoplastic solids

Abstract

Constitutive equations for elastically anisotropic nonlinear elastic–viscoplastic solids are often formulated assuming that the strain energy function depends on an elastic deformation gradient. Also, dependence on a triad of vectors can be introduced to characterize directions of material anisotropy. The elastic deformation gradient is usually written in terms of the total deformation gradient and a plastic deformation gradient, together with a specification of the reference configuration. Alternatively, it is possible to introduce a triad of microstructural vectors which are determined by integrating evolution equations and which characterize the elastic response and orientations of directions of anisotropy. The objective of this paper is to demonstrate that the elastic, total and plastic deformation measures and the vectors used to characterize directions of material anisotropy contain unphysical arbitrariness which prevents them from being measured. In contrast, the microstructural vectors used in the alternative formulation can be measured and remove this unphysical arbitrariness.