Work

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

Year: 2025

Type: article

Abstract: This work investigates the localization of plastic strain during the dynamic expansion of metallic shells, with a focus on improving the time evolution of perturbations.We extend the 1DXLSA (One-Dimensional eXtended Linear Stability Analysis) model of Xavier et al. (2020) to better capture the onset of dynamic instabilities (multiple necking) in cylindrical (plate) and ring (round bar) geometries. A modified Bridgman correction factor is introduced to address limitations in the prediction of the neck evolution observed in former 1DXLSA of the literature.Through unit cell and multimodal studies on a plate configuration, we confirm excellent agreement between fully resolved numerical simulations and the 2DXLSA model of Xavier et al. (2021), validating its reliability as a reference.From unit cell calculations, it is shown that the primary limitation of the original 1DXLSA lies in overly rapid instability growth, especially for intermediate to long-wavenumber modes, due to an inaccurate estimation of multiaxial contribution within the neck. By identifying an optimal correction factor, mode by mode, we significantly improve the ability of 1DXLSA to track multiple necking development is significantly improved.The corrected model is validated based on both unit-cell and multimodal configurations. The proposed methodology is also shown to be applicable to dynamically stretched bars.

Source: Journal of the Mechanics and Physics of Solids

DOI: 10.1016/j.jmps.2025.106487

Authors: U. Houire, S. Mercier, C. Czarnota, M. Xavier, S. El Maï