Isogeometric analysis of shear bands

Numerical modeling of shear bands present several challenges, primarily due to strain softening, strong nonlinear multiphysics coupling, and steep solution gradients with fine solution features. In general it is not known a priori where a shear band will form or propagate, thus adaptive refinement is sometimes necessary to increase the resolution near the band. In this work we explore the use of isogeometric analysis for shear band problems by constructing and testing several combinations of NURBS elements for a mixed finite element shear band formulation. Owing to the higher order continuity of the NURBS basis, fine solution features such as shear bands can be resolved accurately and efficiently without adaptive refinement. The results are compared to a mixed element formulation with linear functions for displacement and temperature and Pian-Sumihara shape functions for stress. We find that an element based on high order NURBS functions for displacement, temperature and stress, combined with gauss point sampling of the plastic strain leads to attractive results in terms of rate of convergence, accuracy and cpu time. This element is implemented with a -bar strain projection method and is shown to be nearly locking free.