Modelling of magneto-mechanically coupled soft thin shells

A geometrically exact, dimensionally reduced model is developed to describe the nonlinear deformation of thin magnetoelastic shells. The classical Kirchhoff–Love assumptions for the mechanical fields are extended to the magnetic variables, yielding a consistent two-dimensional theory derived rigorously through a variational framework. Unlike traditional approaches that rely on mid-surface kinematics, the full deformation map is adopted as the primary variable, and the influence of the surrounding free space due to the Maxwell stress on the shell’s upper and lower surfaces is accommodated through a novel application of Green’s theorem. The governing equations are solved in closed form for the canonical case of a hyperelastic thin flat plate and for an infinite cylindrical magnetoelastic shell, to illustrate the capabilities of the model and elucidate the non-standard variables arising in the modified variational formulation.