Meijie Tang et al 2006 Modelling Simul. Mater. Sci. Eng. 14 1139 doi:10.1088/0965-0393/14/7/003
Meijie Tang1, Wei Cai2, Guanshui Xu3 and Vasily V Bulatov1
Show affiliationsDislocations 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.
61.72.Bb Theories and models of crystal defects
61.72.Lk Linear defects: dislocations, disclinations
Issue 7 (October 2006)
Received 1 February 2006, in final form 21 June 2006
Published 21 August 2006
Meijie Tang et al 2006 Modelling Simul. Mater. Sci. Eng. 14 1139
Romualdo Pastor-Satorras and Alessandro Vespignani 2000 J. Phys. A: Math. Gen. 33 L33
Masayuki Morisawa et al 2001 Meas. Sci. Technol. 12 877
A Gómez and J D Meiss 2004 Nonlinearity 17 975
Danny van Noort et al 2002 Smart Mater. Struct. 11 756
D T A Blair et al 1989 J. Phys. D: Appl. Phys. 22 755
Ntina Savvidou 2004 Class. Quantum Grav. 21 615
J P Dada et al 2006 Phys. Scr. 74 618
Robert J Berry 1983 Metrologia 19 37
H L Andrews et al 2006 New J. Phys. 8 289