A peridynamic approach to solving general discrete dislocation dynamics problems in plasticity and fracture: Part I. Model description and verification

In this paper, we present a peridynamic (PD)-based solution for discrete dislocation dynamics (DDD) problems using the superposition (SP) framework. By replacing the classical surface traction in the complementary problem with a nonlocal/peridynamic one, the SP DDD-PD scheme can simulate arbitrary domains, including those with pre-damage, cracks, and voids of arbitrary shapes, without explicitly tracking boundaries, interfaces, cracks, etc. The new SP DDD-PD scheme is verified for the boundary value problems (BVPs) for single dislocation, multiple dislocations, dislocation emitted from a crack tip, and dislocation-void interaction. The numerical results are compared with those from other existing schemes: the discrete-continuous (DC) DDDPD, and the SP DDD-FEM. The new SP DDD-PD is more accurate than the DC DDD-PD scheme, especially near dislocation cores and in problems with dislocations near defects (damage or interfaces). The high accuracy of the new SP DDD-PD near dislocation cores makes it suitable to model dislocation-based plasticity and fracture, problems that are studied in part II of this work.