An algorithm based on incompatible modes for the global tracking of strong discontinuities in shear localization analyses

Numerical methods for predicting localized shear failure in elasto-plastic solids have experienced considerable advancements in the last decades. Among these approaches, the so-called “Embedded Strong Discontinuity (ESD)” method is often successfully used to accurately simulate the post-localization response with negligible dependence on the finite element discretization. However, it was observed that the employed discontinuity tracking strategy plays a crucial role in the successful localization analysis. In this contribution, we propose a novel strategy for the global tracking of discontinuity surfaces. It is based on exploiting information obtained from the enhanced parameters employed in Enhanced Assumed Strain (EAS) formulations. It is well known, that enhanced strain element formulations are able to better capture localized shear deformations as compared to standard finite elements. This can be explained as a consequence of the improved performance in bending. We observed, that the approximation of the strain jumps delimiting the shear band is connected with a deformation field characterized by opposite bending curvatures across these two discontinuities. Hence, in view of the relations existing between the kinematics of strong and weak discontinuities, we formulate a proper scalar function of the enhanced parameters to identify potential strong discontinuity surfaces, which are evaluated in each step of the analysis with negligible computational cost. This proposed approach has a global character, as it is based upon evaluating discontinuity surfaces defined in the complete analysis domain that are, by construction, continuous across elements. We demonstrate that the tracking algorithm correctly identifies the potential strong discontinuity surface already in early loading stages, even before a localization condition is fulfilled. In those elements which are crossed by the potential failure surface and which also satisfy the localization condition, the kinematics of embedded strong discontinuities is activated to capture the shear failure surface. The performance of the new tracking algorithm is demonstrated by means of several numerical shear localization analyses using associative and non-associative Drucker–Prager elastoplastic models to simulate 2-D and 3-D benchmark analyses.