Thermal post-buckling of induction-heated thin sheets

Abstract

Induction heating of thin sheets is widely used in industrial applications such as metal forming, heat treatment, and manufacturing processes. During induction heating, strong and non-uniform temperature gradients can develop in the heated parts. These gradients generate thermal stresses that can cause thin structures to buckle. Once buckling occurs, the geometry of the structure changes significantly. This geometric change alters the electromagnetic field distribution around the sheet and, as a result, modifies the induced currents and heat generation. The altered temperature field further affects the mechanical response of the structure. Therefore, the problem involves a strong two-way coupling between electromagnetic, thermal, and mechanical fields. Analytical studies indicate that this coupled system can exhibit not only classical thermal buckling but also post-buckling behavior characterized by transcritical bifurcation (“snap-through” and “snap-back” phenomena). Such effects may lead to sudden changes in deformation and temperature, which are important for the safe and reliable design of induction heating systems. We study an application-oriented example both computationally and experimentally, and relate our findings to analytical modeling. The analytical models provide insight into the governing mechanisms and stability behavior. Numerical simulations capture the fully coupled nonlinear response, while experimental observations are used to validate the models. The results improve the understanding of coupled thermal–electromagnetic–mechanical interactions and provide guidance for the design and control of induction heating processes involving thin structures.