Analysis of the localization process leading to fragmentation of dynamically expanded rings

A novel extension of the Linear Stability Analysis (LSA) applied to the development of the instabilities in a round bar in dynamic extension is proposed. The history of development of the instabilities and the multi-modal aspect of the perturbations are now considered in this extension. A new statistical approach based on the power spectrum of the perturbation pattern is proposed to evaluate the variability of the spacing between potential sites of necking. This approach has been applied to analyze the LSA results and predictions obtained from numerical simulations of a bar in dynamic extension. It is shown that both analytical and numerical approaches provides good agreement