Induction heating is an important technology for many engineering applications. The main reason is that induction heating has several technical advantages over other methods, due to high power densities allowing rapid temperature increase, heat supplied directly within the target body, no contamination, etc. Designing induction heating systems requires accurate modelling of the magnetic field, temperature field and, in many cases, interaction effects: Joule losses from the induced eddy currents are source terms for the thermal problem. Another significant interaction effect is the presence of mechanical deformations caused by thermal expansion. One needs to account for this effect to accurately describe the induction heating of thin steel sheets. Thermal expansion strongly affects the magnetic configuration since thin sheets are prone to thermal buckling, leading to large deformations. We suggest a modelling strategy combining a computationally highly efficient mechanical shell description for the thin sheet with a standard continuum model for eddy current and thermal problems through an iterative coupling algorithm. We used tree models for our iterative algorithm - eddy current, heat conduction, and non-linear mechanical models. The problems are solved numerically using the finite element method. For eddy current and heat conduction models, we used open-source FEM software openCFS. For the mechanical problem, we used an in-house solver. The solver is based on a Kirchoff-Love shell model built with the energy approach and the variational principle. We used an iterative procedure with geometry updates on every step to couple all the PDEs. In order to demonstrate the importance of taking large deformations into account when considering the eddy current problem, we perform a sensitivity study for various modelling layouts and induction parameters. The accuracy of the solution of the eddy current problem increased significantly for a wide range of model layouts. The proposed algorithm is the first step in exploiting the often unavoidable bucking positively, e.g. by accounting for the predicted steel sheet shape when optimizing the inductor geometry.