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

**Series:** 1999-31, Preprints

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

**Abstract:**

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.

**Keywords:**