Expansions for the linear-elastic contribution to the self-interaction force of dislocation curves
Expansions for the linear-elastic contribution to the self-interaction force of dislocation curves
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DOI：
10.1017/s0956792521000322
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发表时间：
2021-03
影响因子：
1.9
通讯作者：
P. van Meurs
中科院分区：
文献类型：
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作者：
P. van Meurs
金属中位错曲线的自相互作用力取决于原子的局部排列以及位错曲线段之间的非局部相互作用。虽然当片段之间的距离超过 $\varepsilon$ 大小的原子尺度时，这些非局部片段之间的相互作用可以通过线性弹性准确描述，但当片段相距 $O(\varepsilon)$ 时，该模型就会崩溃并爆炸。为了将非局部相互作用与局部贡献分开，构建了依赖于 $\varepsilon$ 的各种模型来解释非局部项。然而，这些模型之间没有可用的定量比较。本文通过将 $\varepsilon$ 中这些模型的自相互作用力扩展到 O(1) 项之外，使这种比较成为可能。我们对这些展开式的推导依赖于渐近分析。这些展开式的实际用途是通过为它们开发数值方案以及首次限制相应的离散化误差来证明的。
The self-interaction force of dislocation curves in metals depends on the local arrangement of the atoms and on the non-local interaction between dislocation curve segments. While these non-local segment–segment interactions can be accurately described by linear elasticity when the segments are further apart than the atomic scale of size $\varepsilon$ , this model breaks down and blows up when the segments are $O(\varepsilon)$ apart. To separate the non-local interactions from the local contribution, various models depending on $\varepsilon$ have been constructed to account for the non-local term. However, there are no quantitative comparisons available between these models. This paper makes such comparisons possible by expanding the self-interaction force in these models in $\varepsilon$ beyond the O(1)-term. Our derivation of these expansions relies on asymptotic analysis. The practical use of these expansions is demonstrated by developing numerical schemes for them, and by – for the first time – bounding the corresponding discretisation error.