Strain softening is responsible for mesh dependence in numerical analyses concerning a vast variety of fields such as solid mechanics, dynamics, biomechanics and geomechanics. Therefore, numerical methods that regularize strain localization are paramount in the analysis and design of engineering products and systems. In this paper we revisit the elasto-viscoplastic, strain-softening, strain-rate hardening model as a means to avoid strain localization on a mathematical plane (“wave trapping”) in the case of a Cauchy continuum. Going beyond previous works (de Borst and Duretz, 2020; Needleman, 1988; Sluys and de Borst, 1992; Wang et al., 1997), we assume that both the frequency $\omega$ and the wave number $k$ belong to the complex plane. Therefore, a different expression for the dispersion relation is derived. We prove then that under these conditions strain localization on a mathematical plane is possible. The above theoretical results are corroborated by extensive numerical analyses, where the total strain and plastic strain rate profiles exhibit mesh dependent behavior.

在固体力学、动力学、生物力学和地质力学等广泛领域的数值分析中，应变软化是网格依赖性的原因。因此，规范应变局部化的数值方法在工程产品和系统的分析和设计中至关重要。在本文中，我们重新审视弹粘塑性、应变软化、应变率硬化模型，作为避免在柯西连续介质情况下数学平面上的应变局部化（“陷波”）的一种手段。超越以前的工作（de Borst 和 Duretz，2020 年；Needleman，1988 年；Sluys 和 de Borst，1992 年；Wang 等人，1997 年），我们假设$\omega$ 和波数 $克$属于复平面。因此，导出了色散关系的不同表达式。我们证明，在这些条件下，在数学平面上进行应变定位是可能的。上述理论结果通过广泛的数值分析得到证实，其中总应变和塑性应变率曲线表现出网格相关行为。