  We look for an enhancement of the correspondence model of peridynamics with a
view to eliminating the zero-energy deformation modes. Since the non-local
integral definition of the deformation gradient underlies the problem, we
initially look for a remedy by introducing a class of localizing corrections to
the integral. Since the strategy is found to afford only a reduction, and not
complete elimination, of the oscillatory zero-energy deformation, we propose in
the sequel an alternative approach based on the notion of sub-horizons. A most
useful feature of the last proposal is that the setup, whilst providing the
solution with the necessary stability, deviates only marginally from the
original correspondence formulation. We also undertake a set of numerical
simulations that attest to the remarkable efficacy of the sub-horizon based
methodology.
