位错的多尺度建模:将周动力学与梯度弹性相结合

Jonas Ritter, Michael Zaiser
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引用次数: 0

摘要

位错建模本质上是一个多尺度问题,因为我们需要同时描述位错核心附近的高应力场(取决于原子长度尺度)和表面边界值问题(取决于样品尺度上的边界条件)。我们提出了一种基于周动力位错模型的新方法来处理表面边界值问题。在该模型中,由于周动力学的非局部性,差排核心处应力场的奇异性被正则化。有效核心半径由周动力学水平线定义,出于计算成本的考虑,必须选择比晶格常数大得多的水平线。这意味着近核区域的位错应力被严重低估。通过利用周动力学和明德林梯度弹性之间的关系,我们证明梯度弹性可用于构建周动力学应力场的短程修正,从而正确描述从原子到样品尺度的差排应力。
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Multiscale modeling of dislocations: combining peridynamics with gradient elasticity

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.

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期刊介绍: Journal of Materials Science: Materials Theory publishes all areas of theoretical materials science and related computational methods. The scope covers mechanical, physical and chemical problems in metals and alloys, ceramics, polymers, functional and biological materials at all scales and addresses the structure, synthesis and properties of materials. Proposing novel theoretical concepts, models, and/or mathematical and computational formalisms to advance state-of-the-art technology is critical for submission to the Journal of Materials Science: Materials Theory. The journal highly encourages contributions focusing on data-driven research, materials informatics, and the integration of theory and data analysis as new ways to predict, design, and conceptualize materials behavior.
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