Two-scale shear band evolution by local partition of unity

We introduce a methodology to model shear band evolution in the quasi-static regime using the extended finite element method. We enrich the finite element polynomial displacement field with a fine scale function, which models the high displacement gradient in the shear band. For this purpose we use a local partition of unity and a parameterized displacement enrichment based on closed form solutions for one-dimensional shear bands. A stabilized consistent penalty method is used to circumvent locking in the regularized elasto-viscoplastic plane-strain regime and to guarantee element stability. The loss of stability of the boundary value problem is used as an indicator of shear band initiation point and direction. Shear band development examples are shown, illustrating the capabilities of the method to track shear band evolution and strains as high as 1000%