It was noted that analytical solutions for the displacement and stress fields, due to a misfit particle in a host matrix, could be difficult to obtain; especially for complex particle geometries. A numerical method was presented here for finding such fields in the case of infinitely long particles. The method was based upon discretizing the continuous misfit region between the particle and matrix into local misfit regions which consisted of interstitial dislocation loops. The results indicated a very good agreement with analytical solutions, and better convergence with increasing loop density.

The Elastic Fields of Misfit Cylindrical Particles - a Dislocation-Based Numerical Approach. J.Lerma, T.Khraishi, Y.L.Shen, B.D.Wirth: Mechanics Research Communications, 2003, 30[4], 325-34