On computational procedures for modelling Strong Discontinuities in finite deformation plasticity

A numerical model to evaluate the post-critical stage of strain localization problems is presented. The procedure that we follow is based on works by Oliver [6] and Oliver et al.[9]. An adequate kinematics is introduced to characterize the finite deformations produced in the regular deformation zones as well as in the part of the body which localizes. The same concept of strong discontinuity regularization as in these reference works, is adopted. In the essence of this approach, the pre-localization continuum constitutive relation is analytically continued, inside the regularized discontinuity band, at the critical point as also through the post-localization regime The strong discontinuity regularization imposes constraints over the stress state at the onset of the strong discontinuity (Strong Discontinuity Conditions), which are added to those ones resulting from the classical bifurcation criteria. These constrains and their consequences are analyzed.