On the complete extinction of selected imperfection wavelengths in dynamically expanded ductile rings

Abstract

In this work the inception and development of multiple necks in dynamically expanded ductile rings with ab initio geometric imperfections has been addressed. Finite element simulations and linear perturbation analysis have been applied for that task. In the numerical calculations a selected wavelength is included into the model defining along the circumference of the ring an array of periodic geometric imperfections of predefined amplitude. In the stability analysis a perturbation of a given mode is added to the background solution and the growth rate of the perturbation is evaluated. The attention has been focused on the extinction of both long and short wavelength imperfections and the appearance of a dominant necking pattern which emerges when the geometric imperfections are vanished. The role played by the loading rate on the extinction of imperfections is also addressed. Moreover, the necking strain is found to be dependent on the imperfection pattern and the loading rate. Its maximum value is registered for the loading cases in which the initial imperfections distribution is completely extinguished.