Applications of tensor functions to the formulation of constitutive equations involving damage and initial anisotropy

In this paper some results of the tensor function theory are applied to the formulation of constitutive equations of isotropic and anisotropic materials in the secondary and tertiary creep stage. The creep process, in its tertiary phase, is characterized by a damage tensor. Because of its microscopic nature, damage has, in general, an anisotropic character even in cases where the material was originally isotropic, i.e. isotropic in its virgin state. Fissure orientation and length cause anisotropic macroscopic behaviour. In the first part of the paper some possible ways of representing constitutive equations involving (initial) anisotropy of the material (e.g. from rolling) and involving anisotropic creep-damage are dealt with. The formulations of such equations are based upon theorems concerning tensor-valued functions. Furthermore, some simplified constitutive equations for more practical use are discussed. The main problem of this part is: to find an irreducible set of tensor generators. Besides the problem of finding such tensor generators it is very important to determine the scalar coefficients in constitutive equations as functions of the invariants and experimental data. The second part of the paper is concerned with the determination of the scalar functions. This can be done by using tensorial interpolation methods as pointed out in detail.