  We consider load controlled quasistatic evolution. Well posedness results for
the nonlocal continuum model related to peridynamics are established. We show
local existence and uniqueness of quasistatic evolution for load paths
originating at stable critical points. These points can be associated with
local energy minima among the convex set of deformations belonging to the
strength domain of the material. The evolution of the displacements however is
not constrained to lie inside the strength domain of the material. The
load-controlled evolution is shown to exhibit energy balance.
