  The paper presents analytical or semi-analytical solutions for the formation
and evolution of localized plastic zone in a uniaxially loaded bar with
variable cross-sectional area. A variationally based formulation of explicit
gradient plasticity with linear softening is used, and the ensuing jump
conditions and boundary conditions are discussed. Three cases with different
regularity of the stress distribution are considered, and the problem is
converted to a dimensionless form. Relations linking the load level, size of
the plastic zone, distribution of plastic strain and plastic elongation of the
bar are derived and compared to another, previously analyzed gradient
formulation.
