  In this paper, we present a dual-horizon peridynamics formulation which
allows for simulations with dual-horizon with minimal spurious wave reflection.
We prove the general dual property for dual-horizon peridynamics, based on
which the balance of momentum and angular momentum in PD are naturally
satisfied. We also analyze the crack pattern of random point distribution and
the multiple materials issue in peridynamics. For selected benchmark problems,
we show that DH-PD is less sensitive to the spatial than the original PD
formulation.
