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On the generation of discrete isotropic orientation distributions for linear elastic crystals

by Bertram, A., Böhlke, T., Gaffke, N., Heiligers, B., Offinger, R..

Series: 1999-31, Preprints

62K99 None of the above, but in this section
62N99 None of the above, but in this section

We consider a model for the elastic behaviour of a
polycrystalline material based of volume averages. In this
case the effective elastic properties depend only on the
distribution of the orientations over the grains. The
aggregate is assumed to consist of a finite number of grains
each of which behaves elastically like a cubic single
crystal. The material parameters are fixed over the grains.
An important problem is to find discrete orientation
distributions (DODs) which are isotropic, i.e., whose
VOIGT and REUSS averages of the grain stiffness tensors
coincide with those one would obtain under a continous and
homogeneous distribution of orientations. We succeed in
finding isotropic DODs for any even number of grains
$N \geq 4$ and uniform volume fractions of the grains. Also,
$N = 4$ is shown to be the minimum number of grains for an
isotropic DOD.