The role of viscous regularization in dynamical problems, strain localization and mesh dependency
Résumé
Strain localization 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 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 ω 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.
Fichier principal
The_role_of_viscous_regularization_23_04_2021_rev.pdf (14.4 Mo)
Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)