Continuum-discontinuum modelling of shear bands

A methodology to model shear bands as strong discontinuities within a continuum mechanics context is presented. The loss of hyperbolicity of the IBVP is used as the criterion for switching from a classical continuum description of the constitutive behaviour to a traction-separation model acting at the discontinuity surface. The extended finite element method (XFEM) is employed for the spatial discretization of the governing equations. This enables the shear bands to be arbitrarily positioned within the mesh. Examples that study the shear band progression within a rate-independent material are presented.