1D linear stability analysis based on an adjusted correction factor for dynamic expansion: Application to plates and rods

• Dynamic stretching of plates and rods with initial surface roughness is investigated. • 2D Linear Stability Analysis (LSA) and numerical results yield same surface evolution. • Brigdman correction factor used in 1DLSA is adjusted to reflect stress multiaxiality. • Correction factor is shown to depend on the wavenumber of the perturbation. • Revised 1DLSA mimics surface profiles predicted by simulations for plates and rods. This work investigates the onset and development of plastic strain localization during the dynamic expansion of metallic shells. The multiple necking and fragmentation scenario are here viewed as originating from the development of geometrical perturbations (i.e., surface roughness), whose time evolution plays a critical role for the late free flight of fragments. Based on the extended 1DXLSA (One-Dimensional eXtended Linear Stability Analysis) model of Xavier et al. (2021), and using the 2DXLSA of Xavier et al. (2020) and FEM calculations as references, we propose an adjustment of the stress approximation in the neck section to better capture the onset of multiple necking in cylindrical (plate) and ring (round bar) geometries. A modified Bridgman correction factor is then introduced, which highlights the limitations of the previous 1DXLSA study. A good agreement in terms of time evolution of the perturbations is obtained between Finite element simulations, two-dimensional linear stability approach and the new 1D model.