Magnetostrictive twisting of film–substrate plates

Abstract

In this paper we propose a method to calculate the torsional deformations induced in film–substrate systems by magnetostrictive strains. The calculation scheme proposed assumes that the magnetostriction phenomenon can be modeled in terms of anisotropic expansional strains. These strains are incorporated into the classical plate theory to formulate an energy minimization problem, which is solved using a Ritz method. To illustrate the method we use a cantilever plate in which the film and the substrate are mechanically isotropic and a saturating magnetic field is applied in a direction parallel to the plane of the plate. Our calculations show that the deformation induced by an in-plane field generally includes twisting as well as bending deflection. The cases in which only one of these deflections is present are discussed. One of the advantages of the method proposed is that it can be used regardless of the relative thickness of the substrate with respect to that of the film. It also allows us to consider cases in which a film–substrate system deforms due to piezoelectric, thermal or hygroscopic expansional strains.