Strona 2_redak - Instytut Agrofizyki im. Bohdana Dobrzańskiego ...

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where:
A = ∫ E( β) sin βdβ ,
B = ∫ E( β) cosβdβ ,
E( β ) – distribution of probability density.
With progressing deformation, some of the contacts disappear and new ones
come into existence. The distribution of contact normal directions changes. The
main axes of the ellipses that describe the distribution rotate so that more contact
normals assume a direction close to that of the maximum compressive stress. This
tendency is more pronounced for spherical particles than for flatter particles.
Kanatani [80] proposed the characterization of the spatial distribution of particles
by means of the packing tensor. He performed a quantitative estimation of the
distributions of contact normal directions obtained by Konishi et al. [83]. Figure
3.3 presents the experimental distributions and Kanatani’s approximations [81] up
to the fourth order, for material prior to loading and subjected to a load.
y
0th approx.
2nd approx.
4th approx.
x
Fig. 3.3. Probability density distribution of angle of inclination of contact normals and their
approximations [81]
3.2. Anisotropy of seed layer
The literature results described above induced us to undertake studies, at the
Institute of Agrophysics, PAS, Lublin, on the effect of the anisotropy of a seed
sample on the angle of internal friction [107]. Selected for the studies were seeds
of wheat, barley, rye, as well as rapeseeds. The seed of the species chosen
represent shapes varying from the spherical (rape seeds) to a strongly elongated