The use of classical beam theory for micro-beams composed of polycrystals

Micro-beams, where the transverse dimension of the beam is of the order of microns, are sometimes composed of polycrystals where the average crystal dimension is of the same order as the transverse beam dimension. We show in this paper that classical beam theory can be used to describe the behavior of these micro-beams if the crystals have cubic symmetry. If the symmetry is of lower-order than cubic then the behavior of the micro-beam depends on the internal arrangement of the crystals within the beam. We show, however, that for a particular class of tetragonal crystals (six independent elastic constants) the classical beam equation may still be used if a local average is introduced. (C) 1998 Elsevier Science Ltd. All rights reserved.