SIAM Journal on Applied Mathematics, Volume 80, Issue 6, Page 2365-2387, January 2020.
A continuum model of the two dimensional low angle grain boundary motion and the dislocation structure evolution on the grain boundaries has been developed in [L. Zhang and Y. Xiang, J. Mech. Phys. Solids, 117 (2018), pp. 157--178]. The model is based on the motion and reaction of the constituent dislocations of the grain boundaries. The long-range elastic interaction between dislocations is included in the continuum model, and it maintains a stable dislocation structure described by Frank's formula for grain boundaries. In this paper, we develop a new continuum model for the coupling and sliding motions of grain boundaries that avoids the time-consuming calculation of the long-range elastic interaction. In this model, the long-range elastic interaction is replaced by a constraint of Frank's formula. The constrained evolution problem in our new continuum model is further solved by using the projection method. Effects of the coupling and sliding motions in our new continuum model and relationship with the classical motion by curvature model are discussed. The continuum model is validated by comparisons with discrete dislocation dynamics model and the early continuum model [L. Zhang and Y. Xiang, J. Mech. Phys. Solids, 117 (2018), pp. 157--178] in which the long-range dislocation interaction is explicitly calculated.

中文翻译：

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基于位错结构的晶界耦合和滑动运动的新公式

SIAM应用数学杂志，第80卷，第6期，第2365-2387页，2020年1月。
二维低角度晶界运动和晶界上位错结构演化的连续模型在[L. 张和向翔，机械学报。物理 固体，117（2018），第157--178页]。该模型基于晶界组成位错的运动和反应。位错之间的远距离弹性相互作用包含在连续模型中，它保持了由弗兰克晶界公式描述的稳定的位错结构。在本文中，我们为晶界的耦合和滑动运动开发了一个新的连续模型，该模型避免了耗时的长程弹性相互作用计算。在该模型中，远程弹性相互作用被弗兰克公式的约束所代替。我们使用投影方法进一步解决了我们新的连续体模型中的约束演化问题。讨论了耦合和滑动运动在我们新的连续体模型中的作用以及与曲率模型与经典运动的关系。通过与离散位错动力学模型和早期连续体模型的比较来验证连续体模型[L。张和向翔，机械学报。物理 Solids，117（2018），157--178页]，其中明确计算了远程位错相互作用。通过与离散位错动力学模型和早期连续体模型的比较来验证连续体模型[L。张和向翔，机械学报。物理 Solids，117（2018），157--178页]，其中明确计算了远程位错相互作用。通过与离散位错动力学模型和早期连续体模型的比较来验证连续体模型[L。张和向翔，机械学报。物理 Solids，117（2018），157--178页]，其中明确计算了远程位错相互作用。