Finite element simulation of dynamic strain-localization: A multi-scale problem

A Finite Element procedure for the post-localization analysis of elasto-plastic solids is developed. To ensure unique solutions, the Duvaut-Lions visco-plastic regularization procedure [1] is implemented. A bifurcation analysis of the underlying backbone elasto-plastic material is performed to locate the shear band and to define its orientation. The width of the shear band is assumed to be much smaller than the characteristic element size h. To capture the structure of the shear band, the kinematics is enriched by incorporating additional degrees of freedom in a patch within the element and overlying the shear band. Within each localized element, compatibility is ensured between the strain fields inside and outside the patch. A Petrov-Galerkin type procedure to account for the narrow width of the patch is implemented. The results indicate formation of mesh and patch invariant shear bands. Finally, the effects of varying material parameters are studied. The results are found to be consistent with known localization characteristics.