  Peridynamics is a nonlocal continuum-mechanical theory based on minimal
regularity on the deformations. Its key trait is that of replacing local
constitutive relations featuring spacial differential operators with integrals
over differences of displacement fields over a suitable positive interaction
range. The advantage of such perspective is that of directly including
nonregular situations, in which discontinuities in the displacement field may
occur. In the linearized elastic setting, the mechanical foundation of the
theory and its mathematical amenability have been thoroughly analyzed in the
last years.
  We present here the extension of Peridynamics to linearized elastoplasticity.
This calls for considering the time evolution of elastic and plastic variables,
as the effect of a combination of elastic energy storage and plastic energy
dissipation mechanisms. The quasistatic evolution problem is variationally
reformulated and solved by time discretization. In addition, by a rigorous
evolutive $\Gamma$-convergence argument we prove that the nonlocal peridynamic
model converges to classic local elastoplasticity as the interaction range goes
to zero.
