Nonlocality is one of the features that allows Peridynamic (PD) to incorporate discontinuities in the displacement field of structural materials. However, it is one of the substantial reasons of the anomalous wave dispersion properties of Bond-Based Peridynamics (BB-PD) models. Deficiencies of 2-D BB-PD models in studying of wave propagation are investigated and an improved BB-PD formulation based on an optimization approach is proposed.

The optimization problem, developed through inverse analysis, is carried out by comparing exact and numerical dispersion and by minimizing the error. A weighted residual technique, point collocation, is introduced and error minimization in 2-D PD is carried out through integration over the contour of the irreducible Brillouin zones. Consequently, a set of stiffness scaling coefficients is obtained to be applied in the original BB-PD formulation to improve the simulation of pressure and shear wave propagation. It is found that this approach substantially extends the frequency range of potential applications. Dispersion properties of the original and modified BB-PD are compared in Figure 1. The figure shows that the introduction of the scaling stiffness coefficients has effectively improved the pressure and shear wave dispersion curves.