We develop a novel nonlocal model of dislocations based on the framework of peridynamics. By embedding interior discontinuities into the nonlocal constitutive law, the displacement jump in the Volterra dislocation model is reproduced, intrinsic singularities in classical elasticity are regularized, and the surface effect in previous peridynamics models is avoided. The extended embedded discontinuity peridynamics overcomes unphysical dissipation in treating discontinuity and is still easy to be solved with the particle-based meshless method. The properties of the proposed dislocation model are compared with classical elasticity solutions under the case of an edge dislocation, double edge dislocations, a screw dislocation, and a circular dislocation loop. Numerical results show a high consistency in the displacement field while no singularity appears in the peridynamics model, the interaction force is in agreement with the Peach-Koehler formula down to the core region and high accuracy can be reached in 3D with limited computational cost. The proposed model provides a feasible tool for multiscale modeling of dislocations. Though dislocation is modeled as a pre-defined displacement jump, it is straightforward to extend the method to model various fracture conditions.

我们开发了一种新的基于局部动力学框架的位错非局部模型。通过将内部不连续性嵌入到非局部本构定律中，可以再现Volterra位错模型中的位移跃变，对经典弹性中的固有奇点进行正则化，并避免了以前的周边动力学模型中的表面效应。扩展的嵌入式不连续周围动力学克服了处理不连续性时的非物理耗散，并且仍然易于使用基于粒子的无网格方法解决。在边缘错位，双边缘错位，螺钉错位和圆形错位环的情况下，将提出的位错模型的特性与经典弹性解进行了比较。数值结果表明，位移场具有很高的一致性，而在动力学模型中没有出现奇异点，相互作用力与Peach-Koehler公式相一致，直到核心区域，并且在3D中可以以有限的计算成本实现高精度。所提出的模型为位错的多尺度建模提供了一种可行的工具。尽管将位错建模为预定义的位移跃变，但可以很容易地扩展该方法以对各种裂缝条件进行建模。