Chapter 2 - Dual-horizon peridynamics (DH-PD)

Abstract

One of the essential limitations of the conventional peridynamics formulations is that the horizon radii must be the same, otherwise spurious wave reflection will appear and the effect will be pronounced with ghost forces between the particles. However, in many applications in engineering analysis, it is important to be able to vary the horizon sizes with respect to the spatial distribution of material points, e.g., for adaptive refinement and multiscale modeling, interface, heterogenous material, multibody analysis, to name but a few, in order to achieve the balance between computational efficiency and accuracy. To overcome these issues, dual-horizon peridynamics (DH-PD) was proposed, which can elegantly remove the spurious wave issues and can be simply implemented in existing peridynamics code with minimal changes, i.e., bond-based, non-ordinary or ordinary state-based peridynamics. DH-PD was proven theoretically to fulfill the balance of momentum. It can easily handle the weak discontinuity along the interfaces of different materials and the interactive dual-horizon forces make the implementation simple. Finally, the crack paths predicted by DH-PD are insensitive to the placement of particles or to the non-uniformity in the particles sizes. Examples in both 2D and 3D show the robustness and validity of DH-PD, which practically enhance the usability of the peridynamics.