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 magnetoelastic effects. The crystalline plates are assumed to have cubic symmetry, expose either (1 0 0) or (1 1 1) surfaces, and be clamped along one edge. It is shown that the effect of clamping can be described by a dimensionless parameter, the 'dimensionality' D, which in general depends on the length-to-width ratio of the sample, the Poisson ratio ν, and the elastic anisotropy A. Using a finite element analysis we find that the dimensionality parameters for anisotropic and isotropic surface stresses are identical. The theory is applied to the bending caused by magnetoelastic stresses in deposited thin films. Expressions are derived to calculate the magnetoelastic coupling constants of films with cubic, tetragonal, or hexagonal symmetry from a measurement of the change of radius of curvature of the film-substrate composite upon an in-plane reorientation of the film magnetization