A hybrid method for computing forces on curved surfaces

doi:10.1088/0965-0393/14/7/003

A hybrid method for computing forces on curved dislocations intersecting free surfaces in three-dimensional dislocation dynamics

Meijie Tang et al 2006 Modelling Simul. Mater. Sci. Eng. 14 1139-1151 doi: 10.1088/0965-0393/14/7/003

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Meijie Tang¹, Wei Cai², Guanshui Xu³ and Vasily V Bulatov¹
¹ Lawrence Livermore National Laboratory, Livermore, CA 94551, USA
² Mechanical Engineering Department, Stanford University, Stanford, CA 94305, USA
³ Mechanical Engineering Department, University of California, Riverside, CA 92521, USA
E-mail: tang7@llnl.gov

Abstract. 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.

Print publication: Issue 7 (October 2006)
Received 1 February 2006, in final form 21 June 2006
Published 21 August 2006

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A hybrid method for computing forces on curved dislocations intersecting free surfaces in three-dimensional dislocation dynamics

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