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) DDD-PD, 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.

在本文中，我们使用叠加 (SP) 框架提出了一种基于近场动力学 (PD) 的离散位错动力学 (DDD) 问题解决方案。通过将互补问题中的经典表面牵引替换为非局部/近场动力学问题，SP DDD-PD 方案可以模拟任意域，包括具有任意形状的预损坏、裂缝和空隙的域，而无需显式跟踪边界、界面、新的 SP DDD-PD 方案针对单个位错、多个位错、从裂纹尖端发出的位错以及位错-空洞相互作用的边值问题 (BVP) 进行了验证。数值结果与其他现有方案的结果进行了比较：离散连续 (DC) DDD-PD 和 SP DDD-FEM。新的SP DDD-PD比DC DDD-PD方案更准确，尤其是位错核心附近和缺陷（损伤或界面）附近的位错问题。新的 SP DDD-PD 近位错核心的高精度使其适合模拟基于位错的塑性和断裂，这是本工作第二部分研究的问题。