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

2021 
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 in the case of a Cauchy continuum. In contrast to the work of previous researchers 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 numerical analyses, where the total strain and plastic strain profiles exhibit mesh dependent behavior.
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