Dual-horizon Peridynamics

TL;DR

This paper introduces a dual-horizon peridynamics approach that handles varying horizon sizes, eliminates ghost forces, and improves simulation of wave propagation and fracture with minimal implementation effort.

Contribution

The paper presents a novel dual-horizon formulation that naturally addresses ghost forces and unbalanced interactions in peridynamics, compatible with existing codes and adaptable for complex problems.

Findings

Successfully applied to 2D and 3D examples including fracture and wave propagation.

Eliminates ghost force issues without partial stress tensor or slice techniques.

Enables adaptive refinement with minimal computational overhead.

Abstract

In this paper we develop a new Peridynamic approach that naturally includes varying horizon sizes and completely solves the "ghost force" issue. Therefore, the concept of dual-horizon is introduced to consider the unbalanced interactions between the particles with different horizon sizes. The present formulation is proved to fulfill both the balances of linear momentum and angular momentum. Neither the "partial stress tensor" nor the "`slice" technique are needed to ameliorate the ghost force issue in \cite{Silling2014}. The consistency of reaction forces is naturally fulfilled by a unified simple formulation. The method can be easily implemented to any existing peridynamics code with minimal changes. A simple adaptive refinement procedure is proposed minimizing the computational cost. The method is applied here to the three Peridynamic formulations, namely bond based, ordinary state based and non-ordinary state based Peridynamics. Both two- and three- dimensional examples including the Kalthof-Winkler experiment and plate with branching cracks are tested to demonstrate the capability of the method in solving wave propagation, fracture and adaptive analysis .