A hybrid method for computing forces on curved dislocations intersecting free surfaces in three-dimensional dislocation dynamics
A hybrid method for computing forces on curved dislocations intersecting free surfaces in three-dimensional dislocation dynamics
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DOI：
10.1088/0965-0393/14/7/003
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发表时间：
2006-10
影响因子：
1.8
通讯作者：
M. Tang;W. Cai;Guanshui Xu;V. Bulatov
中科院分区：
文献类型：
--
作者：
M. Tang;W. Cai;Guanshui Xu;V. Bulatov
在位错动力学模拟中，位错与自由表面相交对无摩擦边界条件的数值实现提出了挑战。当位错应力场的奇异解析表达式需要与数值方法相结合来计算由于自由表面引起的镜像应力场时，困难就出现了。本文提出了一种新的混合方法，将图像应力的奇异部分和非奇异部分分开处理。对于与弹性半空间表面相交的半无限长直位错，用解析解来处理镜像应力的奇异部分，而其余的非奇异部分则用标准有限元法处理。这种分解的数值优势与例子证明。
Dislocations intersecting free surfaces present a challenge for numerical implementation of traction-free boundary conditions in dislocation dynamics simulations. The difficulty arises when singular analytic expressions of dislocation stress fields need to be used in combination with numerical methods to calculate image stress fields due to the free surfaces. A new hybrid method is developed here in which the singular and non-singular parts of the image stress are dealt with separately. The analytic solution for a semi-infinite straight dislocation intersecting the surface of elastic half-space is used to account for the singular part of the image stress, while the remaining non-singular part is treated using the standard finite element method. The numerical advantages of this decomposition are demonstrated with examples.