  We study the quasistatic evolution of a linear peridynamic Kelvin-Voigt
viscoelastic material. More specifically, we consider the gradient flow of a
nonlocal elastic energy with respect to a nonlocal viscous dissipation.
Following an evolutionary $\Gamma$-convergence approach, we prove that the
solutions of the nonlocal problem converge to the solution of the local
problem, when the peridynamic horizon tends to $0$, that is, in the
nonlocal-to-local limit.
