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Mathematics and Mechanics of Solids
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Tensorial Representation of the Orientation Distribution Function of Internal Structure Elements for Heterogeneous Solids

A. Lagzdins

V. Tamuzs

Institute of Polymer Mechanics of Latvian Academy of Sciences, Riga, LV-1006, Latvia

The paper deals with constructing the anisotropic orientation distribution function of internal structure elements in nonhomogeneous material. This function is necessary for estimating the average mechanical properties of the materials. For the specifying of this function, we propose to utilize the partial sums of Fourier series on three-dimensional rotation group. We show that these partial sums can be pre- sented in coordinate free tensorial form, thereby reducing the anisotropy of distribution function to the anisotropy of tensors possessing some specific properties. By way of illustration, we consider a simple example in case of cubic symmetry.

Mathematics and Mechanics of Solids, Vol. 1, No. 2, 193-205 (1996)
DOI: 10.1177/108128659600100203
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