TENSORIAL REPRESENTATION OF THE ORIENTATION DISTRIBUTION FUNCTION OF INTERNAL STRUCTURE ELEMENTS FOR HETEROGENEOUS SOLIDS

The paper deals with constructing the anisotropic orientation distribu tion function of internal structure elements in nonhomogeneous materia l. This function is necessary for estimating the average mechanical pr operties of the materials. For the specifying of this function, we pro pose to utilize the partial sums of Fourier series on three-dimensiona l rotation group. We show that these partial sums can be presented in coordinate free tensorial form, thereby reducing the anisotropy of dis tribution function to the anisotropy of tensors possessing some specif ic properties. By way of illustration, we consider a simple example in case of cubic symmetry.