On directional average of the local anisotropic damage

The derivation of thermodynamical damage state potentials and the formulation of damage constitutive laws always require averaging actual directional damage distribution. The analysis of anisotropic damage state is developed here by the hidden variable technique and presented in the two canonical variants – the energy and the entropy. Thermodynamic damage state potentials in their canonical forms are obtained. A variant of the canonical description of damage and the canonical definition of the directional damage variable consistent with the irreversible thermodynamics are discussed. These involve averages of the directional damage variable. A general algorithm of derivation of symmetric even rank damage tensors from the directional damage distribution is developed. Directional damage averaging procedures are considered. Various integral and series representations of the averaged damage are obtained. It is shown that damage averaging requires rapid computations of the canonical Legendre elliptic integrals. Numerical results are presented for two-, three- and five-parametric average damages in order to determine an availability for the averaged damage values range.