Fully Coupled Electromagnetic‐Thermal‐Mechanical Model for Induction Heating of Thin Steel Sheets With the Presence of Thermal Buckling

Abstract

Large deformations can become an important issue in induction heating applications, especially for structures with low bending stiffness, such as thin sheets. In such cases, thermal expansion induces not only substantial in-plane stresses but also out-of-plane buckling, which in turn strongly influences the electromagnetic field configuration. This work presents a coupled modelling framework to analyse the post-buckling behaviour of thin sheets during induction heating. The approach combines a computationally efficient structural finite element shell formulation for the thin sheet with standard finite element continuum models for the eddy-current and thermal problems. The multi-physics interaction is resolved by an iterative coupling scheme with mesh updating, adaptive load stepping, and relaxation techniques to improve robustness near critical points. The framework is used to study the strongly nonlinear response of the system, including transcritical bifurcation behaviour, characterised by “snap-through” and “snap-back” effects. Representative application examples demonstrate the influence of geometric imperfections, electromagnetic material modelling, and electromagnetic forces on the post-buckling response. The results show that the proposed strategy provides a robust and efficient tool for analysing induction-heated thin structures with strong electromagnetic-thermal-mechanical coupling.