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Article
Multipole representation of the elastic field of dislocation ensembles
Physical Review B (2004)
  • Zhiqiang Wang, University of California, Los Angeles
  • Nsar Ghoniem, University of California, Los Angeles
  • Richard Alan Lesar, Los Alamos National Laboratory
Abstract
A multipole expansion method is developed to determine the elastic field of dislocation loop ensembles of arbitrary geometric complexity. The method results in reduction of the severe computational requirements in large-scale dislocation dynamics (DD) computer simulations without an artificial cutoff on the interaction range. Order of N, O(N), algorithms for DD simulations is immediately accessible on the basis of the developed procedure. Examples of dislocation interaction with large dislocation arrays representing a tilt boundary and a dislocation wall show that the method results in speeding up the calculation of Peach-Kohler interaction forces by a factor of 100, with an error of less than 0.4%. The multipole expansion reveals a physical connection to Kröner’s continuum theory of dislocations, with the zeroth order moment being Nye’s dislocation density tensor. Higher-order tensors in the expansion correspond to moments of a basic tensor comprised of the tangent and Burgers vectors, and can be used to characterize the spatial distribution of dislocation loop ensembles.
Publication Date
May 7, 2004
Citation Information
Zhiqiang Wang, Nsar Ghoniem and Richard Alan Lesar. "Multipole representation of the elastic field of dislocation ensembles" Physical Review B Vol. 69 Iss. 174102 (2004)
Available at: http://works.bepress.com/richard_lesar/8/