Mechanics

1999, No. 2

Y.N. Radayev

ON THE EXACT DIRECTIONAL DAMAGE AVERAGING

An approach to accurate description of a damage state at an average is proposed. The exact averaging procedures for the three-dimensional directional damage are considered. Various integral representations of the averaged damage and the results of the second and the fourth order averaging three-dimensional damage are discussed. Averaging directional damage requires rapid computations of the elliptic integrals to be implemented. A script of rapidly convergent series needed for numerical analysis of the averaged damage is given. A primary classification of damage induced anisotropy is advanced by introducing the amplitude damage spectrum and inversed amplitude damage spectrum. The damage, characterizing by narrow band and confluent inversed spectra, is then discriminated. It is shown that the axial symmetric damage is attributed to a confluent inversed amplitude damage spectrum. The results reported in this paper can be applied to analysis of any continuous directional variable.