Representation of Constitutive Equations in Creep Mechanics of Isotropic and Anisotropic Materials

Summary

In this paper constitutive equations for the secondary creep stage of isotropic and anisotropic materials are formulated. The theory is based upon the assumption of the existence of a creep potential, which can depend only on the basic or, alternatively, on the principal invariants of the stress tensor, if the material is isotropic. These invariants are the elements of the integrity basis for the orthogonal group. For anisotropic solids the representation of constitutive expressions is given by using an integrity basis under a subgroup of transformations associated with the symmetry properties of the anisotropic material considered. Instead of this representation by an integrity basis under a sub group the anisotropic behaviour is considered by a creep potential which contains constitutive tensors characterizing the anisotropy of the material. For these tensors an integrity basis is constructed. Together with the invariants of the single argument tensors a system of simultaneous or joint invariants is found. The approach by the creep potential hypothesis is compared with the response of an anisotropic material approximated by a tensor power series of arbitrary degree in connection with HAMILTON-CAYLEY’s theorem.

Furthermore, in order to arrive more workable constitutive equations, a simplified theory is developed, which employs a mapped stress tensor involving anisotropy effects.