Computational Mechanics

, Volume 51, Issue 2, pp 203–216 | Cite as

Viscoplastic regularization of local damage models: revisited

  • M. S. Niazi
  • H. H. Wisselink
  • T. Meinders
Original Paper


Local damage models are known to produce pathological mesh dependent results. Regularization techniques are therefore mandatory if local damage models are used for academic research or industrial applications. The viscoplastic framework can be used for regularization of local damage models. Despite of the easy implementation of viscoplasticity, this method of regularization did not gain much popularity in comparison to the non-local or gradient damage models. This work is an effort to further explore viscoplastic regularization for quasi-static problems. The focus of this work is on ductile materials. Two different types of strain rate hardening models i.e. the Power law (with a multiplicative strain rate part) and the simplified Bergström van Liempt (with an additive strain rate part) models are used in this study. The modified Lemaitre’s anisotropic damage model with a strain rate dependency was used in this study. It was found that the primary viscoplastic length scale is a function of the hardening and softening (damage) parameters and does not depend upon the prescribed strain rate whereas the secondary length scale is a function of the strain rate. As damage grows, the effective regularization length gradually decreases. When the effective regularization length gets shorter than the element length numerical results become mesh dependent again. This loss of objectivity can not be solved but the effect can be minimized by selecting a very fine mesh or by prescribing high deformation velocities.


Viscoplastic regularization Modified Lemaitre’s damage model Mesh dependency Length scale Bergström van Liempt hardening 


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Materials innovation institute (M2i)DelftThe Netherlands
  2. 2.Faculty of Engineering TechnologyUniversity of TwenteEnschedeThe Netherlands

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