The role of viscous regularization in dynamical problems, strain localization and mesh dependency

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, methods that regularize strain localization are paramount the analysis design engineering products systems. In this paper we revisit elasto-viscoplastic, strain-softening, strain-rate hardening model means to avoid on mathematical plane (“wave trapping”) case Cauchy continuum. Going beyond previous works (de Borst Duretz, 2020; Needleman, 1988; Sluys de Borst, 1992; Wang et al., 1997), assume both frequency ω wave number k belong complex plane. different expression dispersion relation derived. We prove then under these conditions possible. The above theoretical results corroborated by extensive analyses, where total plastic rate profiles exhibit dependent behavior.