Modeling dislocations is an inherently multiscale problem as one needs to simultaneously describe the high stress fields near the dislocation cores, which depend on atomistic length scales, and a surface boundary value problem which depends on boundary conditions on the sample scale. We present a novel approach which is based on a peridynamic dislocation model to deal with the surface boundary value problem. In this model, the singularity of the stress field at the dislocation core is regularized owing to the non-local nature of peridynamics. The effective core radius is defined by the peridynamic horizon which, for reasons of computational cost, must be chosen much larger than the lattice constant. This implies that dislocation stresses in the near-core region are seriously underestimated. By exploiting relationships between peridynamics and Mindlin-type gradient elasticity, we then show that gradient elasticity can be used to construct short-range corrections to the peridynamic stress field that yield a correct description of dislocation stresses from the atomic to the sample scale.

翻译：位错建模本质上是一个多尺度问题，因为需要同时描述位错芯附近依赖于原子尺度的高应力场，以及依赖于样品尺度边界条件的表面边界值问题。我们提出了一种新方法，基于近场动力学位错模型来处理表面边界值问题。在该模型中，由于近场动力学的非局部特性，位错芯处应力场的奇异性被正则化。有效芯半径由近场动力学范围定义，出于计算成本的考虑，该范围必须远大于晶格常数。这意味着近芯区域的位错应力被严重低估。通过利用近场动力学与Mindlin型梯度弹性之间的关系，我们证明梯度弹性可用于构建近场动力学应力场的短程修正，从而能够从原子尺度到样品尺度准确描述位错应力。