Post-buckling modeling for strips under tension and residual stresses using asymptotic numerical method

•We present a finite element buckling shell model to predict flatness defect due to residual stresses especially in cold thin strip rolling.•The asymptotic numerical method is used to solve the non-linear problem with a post-buckling algorithm.•In this paper we show the theoretical and numerical bases of the model.•In a future paper we will deal with industrial application with multidirectional and complex residual stress fields.

In many industrial processes, geometric strip defects may be generated by buckling due to excessive residual stresses and these defects are difficult to control. Usually residual stresses have complex distributions so that defects with complex shapes appear. In strip rolling, strips are fabricated under tension, which has an impact on the shape and the amplitude of the defects. This tension can hide completely or partially the defects that increase and evolve during tension release. In this work we calculate flatness defects of strips generated by residual stresses, with and without tension, by using a shell finite element model based on the asymptotic numerical method (ANM).