Finite Deformation of Magnetoelastic Film

A nonlinear two-dimensional theory is developed for thin magnetoelastic films capable of large deformations. This is derived directly from three-dimensional theory. Significant simplifications emerge in the descent from three dimensions to two, permitting the self field generated by the body to be computed a posteriori. The model is specialized to isotropic elastomers with two material models. First weak magnetization is investigated leading to a free energy where magnetization and deformation are un-coupled. The second closely couples the magnetization and deformation. Numerical solutions are obtained to equilibrium boundary-value problems in which the membrane is subjected to lateral pressure and an applied magnetic field. An instability is inferred and investigated for the weak magnetization material model.