Combined necking & fracture model to predict ductile failure with shell finite elements

The implementation of recent progress on stress state dependent ductile fracture models is inhibited by the break-down of shell element solutions whenever through-thickness necking occurs. The concept of the Domain of Shell-to-Solid Equivalence (DSSE) is therefore introduced to capture the onset of localized necking with shell element meshes. As long as the elasto-plastic loading paths lie inside the DSSE, ductile fracture may be predicted with shell elements using exactly the same models as for solid elements. A simple criterion describing the boundary of the DSSE is proposed based on the results from Marciniak-Kuczynski type of localization analysis. It is combined with the stress triaxiality and Lode angle dependent Hosford-Coulomb (HC) fracture initiation model and implemented as a user material subroutine for explicit finite element analysis. The combined DSSE-HC model is validated for a DP780 steel for notched tension, hemispherical punch loading, stretch bending, and V-bending of strips.