An energy-consistent model of dislocation dynamics in an elastic body
An energy-consistent model of dislocation dynamics in an elastic body
复制标题
弹性体位错动力学的能量一致模型
DOI：
10.1007/978-4-431-56104-0_3
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
V. Chalupecky and M. Kimura
中科院分区：
文献类型：
--
作者：
V. Chalupecky and M. Kimura
利用相场模型的思想，提出了弹性材料中位错曲线运动的能量一致数学模型。这揭示了位错动力学中隐藏的梯度流动结构。该模型是由滑移面上的正则Allen-Cahn型能量和弹性体中的弹性能量之和构成的梯度流。得到的模型变成了3D-2D体表系统，并且自然地包括了Peach-Koehler力项和位错核的概念。我们还推导了直螺位错的2D-1D体表面系统，并给出了一些数值例子。
We propose an energy-consistent mathematical model for motion of dislocation curves in elastic materials using the idea of phase field model. This reveals a hidden gradient flow structure in the dislocation dynamics. The model is derived as a gradient flow for the sum of a regularized Allen-Cahn type energy in the slip plane and an elastic energy in the elastic body. The obtained model becomes a 3D-2D bulk-surface system and naturally includes the Peach-Koehler force term and the notion of dislocation core. We also derive a 2D-1D bulk-surface system for a straight screw dislocation and give some numerical examples for it.