Asymptotic analysis of cold sandwich rolling
An analytical model for the cold rolling of sandwich sheets is proposed, assuming a rigid-plastic flow rule and Coulomb friction. Asymptotic analysis is used to solve the equations based on the assumptions of small aspect ratio and friction coefficient. This model relaxes the assumption, crucial to slab methods, that the stresses are uniformly distributed through the thickness of each material layer. Thus, our model is able to predict the through-thickness velocity and stress distributions. The leading-order behaviour is shown to be consistent with the slab method, and the predictions are compared with finite element simulations. Computation times are orders of magnitude smaller than finite element calculations.