The analysis of multiple necking phenomenon during dynamic stretching of a metallic plate is investigated. For that purpose, a new 1D linear stability analysis is proposed to capture the perturbation evolution. The multidimensional aspect of the stress field within the neck region is taken into account with a Bridgman correction factor. The novelty of the 1D approach is to let the time evolution of the perturbation determined by the linearized field equations. So, no predefined time dependency is assumed as in classical 1D linear stability analysis of the literature, see Zhou et al., An elastic-visco-plastic analysis of ductile expanding ring, Int. J. Impact Eng., 2006. The proposed model, named hereafter 1D-XLSA (standing for 1D-eXtended Linear Stability Analysis), can also be viewed as the restriction to 1D of the 2D-XLSA model developed in Xavier et al., Extension of linear stability analysis for the dynamic stretching of plates: Spatio-temporal evolution of the perturbation, European Journal of Mechanics-A/Solids, 2020. A comparison for a thermo-viscoplastic material with strain hardening is proposed for three possible routes : a 1D model based on the frozen coefficient theory named 1D-CLSA (standing for 1D-Classical Linear Stability Analysis), the proposed 1D-XLSA and 2D-XLSA models. It is shown that while growth rates in late deformation stage are similar, a strong difference in amplitude exists due to large discrepancies in the early deformation stage. The comparison also illustrates the importance of the modeling of multiaxiality of the stress field within the neck region and of initial defects. While differences between models are limited for perturbations with small wavenumbers, large discrepancies are observed for perturbations with large wavenumbers. Our model is also derived for the case of the extension of a cylindrical bar which is representative of the ring expansion during dynamic loading.

研究了金属板动态拉伸过程中的多颈缩现象。为此，提出了一种新的一维线性稳定性分析来捕获扰动演化。颈部区域内应力场的多维方面被考虑为Bridgman校正因子。一维方法的新颖性在于让扰动的时间演化由线性化的场方程确定。因此，没有像文献中经典的一维线性稳定性分析中那样假设预定义的时间依赖性，请参见Zhou等人的《延展性膨胀环的弹黏塑性分析》，Int。J. Impact Eng。，2006年。拟议的模型，以下称1D-XLSA（代表1D扩展线性稳定性分析），也可以看作是Xavier等人开发的2D-XLSA模型对1D的限制，扩展了用于板的动态拉伸的线性稳定性分析：扰动的时空演化，《欧洲力学杂志》 A / Solids ，2020年。针对三种可能的路径，对具有应变硬化作用的热粘塑性材料进行了比较：基于冻结系数理论的1D模型1D-CLSA（代表1D-经典线性稳定性分析），拟议的1D-XLSA和2D-XLSA型号。结果表明，尽管变形后期的增长率相似，但由于变形初期的差异较大，振幅存在很大差异。比较还说明了对颈部区域内的应力场和初始缺陷进行多轴建模的重要性。虽然对于小波数的摄动，模型之间的差异是有限的，但对于大波数的摄动，则观察到较大的差异。我们的模型也是针对圆柱杆延伸的情况而得出的，它代表了动态载荷过程中的环膨胀。