Viscoplastic regularization of local damage models: revisited
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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.
KeywordsViscoplastic regularization Modified Lemaitre’s damage model Mesh dependency Length scale Bergström van Liempt hardening
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- 1.Atzema EH, ten Horn CHLJ, Vegter H (2004) Influence of tooling layout on sheet forming process analysis. In: Neittaanmaki P, Rossi T, Korotov S, Onate E, Periaux J, Knorzer D (eds) Proceeding of European congress on computational methods in applied sciences and engineering. Jyvskyl, FinlandGoogle Scholar
- 3.Bergström Y (1969) A dislocation model for the stress–strain behaviour of polycrystalline α-fe with special emphasis on the variation of the densities of mobile and immobile dislocations. J Mater Sci Eng 5: 193–200Google Scholar
- 6.Cowie JG, Azrin M, Olson GB (1989) Microvoid formation during shear deformation of ultrahigh strength steels. Metall Trans A 20A: 143–153Google Scholar
- 9.Engelen RAB (2005) Plasticity induced damage in metals. Non-local modeling at finite strains. PhD thesis, Technical University of Eindhoven, The NetherlandsGoogle Scholar
- 16.Lemaitre J, Desmorat R (2005) Engineering damage mechanics. Springer, BerlinGoogle Scholar
- 22.Niazi MS, Wisselink HH, Meinders T, Huétink J (2011) Failure predictions for dp steel cross-die test using anisotropic damage. Int J Damage Mech. doi:10.1177/1056789511407646
- 23.Peerlings RHJ, Brekelmans WAM, de Borst R, Geers MGD (1998) Softening, singularity and mesh sensitivity in quasi-brittle and fatigue damage, in nonlocal aspects in solid mechanics. In: Brillard A, Ganghoffer JF (eds) Proceedings of EUROMECH Colloquium 378. Mulhouse, France, pp 94–99Google Scholar
- 26.Pirali P, Liaghat GhH, Ahmadi MT (2010) Viscoplasticity coupled with nonlocalized damage for incompatibilities due to strain softening. Mechanika 6(86): 17–23Google Scholar
- 29.Tasan CC (2010) Micro-mechanical characterization of ductile damage in sheet metal. PhD thesis, Technical University of Eindhoven, The NetherlandsGoogle Scholar
- 33.Vegter H, ten Horn CHLJ, An Y, Atzema E, Pijlman HH, van den Boogaard TH, Huétink H (2003) Characterization and modelling of the plastic behaviour and its application in sheet metal forming simulation. In: Onate E, Owen DRJ (eds) COMPLAS VII, 7th international conference on computational plasticity. CIMNE, BarcelonaGoogle Scholar