Deformation of rectangular thin glass plate coated with magnetostrictive material

As magnetic smart materials (MSMs), magnetostrictive materials have great potential to be selected as coating materials for lightweight x-ray telescope mirrors due to their capability to tune the mirror profile to the desired shape under a magnetic field. To realize this potential, it is necessary to study the deformation of the mirror substrate with the MSM coating subjected to a localized magnetic field. In this paper, an analytical model is developed to calculate the deformation of rectangular coated samples locally affected by magnetostrictive strains driven by an external magnetic field. As a specific case to validate the model, a square glass sample coated with MSMs is prepared, and its deformation is measured in a designed experimental setup by applying a magnetic field. The measured deformation of the sample is compared with the results calculated from the analytical model. The comparison results demonstrate that the analytical model is effective in calculating the deformation of a coated sample with the localized mismatch strains between the film and the substrate. In the experiments, different shape patterns of surface profile changes are achieved by varying the direction of the magnetic field. The analytical model and the experimental method proposed in this paper can be utilized to further guide the application of magnetostrictive coating to deformable lightweight x-ray mirrors in the future.