A finite element analysis of the bending of crystalline plates due to anisotropic surface and film stress applied to magnetoelasticity

The bending of crystalline plates in response to a non-isotropic stress on one of the two surfaces is investigated with special attention to magnetoel astic effects. The crystalline plates are assumed to have cubic symmetry, e xpose either (1 0 0) or (1 I I) surfaces, and be clamped along one edge. It is shown that the effect of clamping can be described by a dimensionless p arameter, the "dimensionality" D, which in general depends on the length-to -width ratio of the sample, the Poisson ratio v, and the elastic anisotropy A. Using a finite element analysis we find that the dimensionality paramet ers for anisotropic and isotropic surface stresses are identical. The theor y is applied to the bending caused by magnetoelastic stresses in deposited thin films. Expressions are derived to calculate the magnetoelastic couplin g constants of films with cubic, tetragonal, or hexagonal symmetry from a m easurement of the change of radius of curvature of the film-substrate compo site upon an in-plane reorientation of the film magnetization. (C) 2001 Els evier Science B.V. All rights reserved.