On strong discontinuities in anelastic solids. A finite element approach taking a frame indifferent gradient of the discontinuous displacements

This paper presents a two-dimensional (2D) large deformation analysis of strong discontinuities in anelastic solids and its numerical implementation. We assume associative and ideal plasticity until localization occurs. In the post-localization phase discontinuous displacements develop and their material gradient is set up in a proper way | one `legʹ in the current con guration, the other `legʹ in the reference con guration | to provide a frame indi erent (= objective) description. The numerical implementation via displacement-based six-node triangular nite elements enriched by a single displacement-jump parameter (t2= 0) in the postlocalization phase (te>locte) is described in detail. The solution procedure is similar to that using assumed enhanced displacement-gradient elements, with the only but crucial di erence, that on the discontinuity surface the traction is linked to the displacement jump via a proper constitutive law. Finally, numerical results of the shear test and of the tension test are presented