The elastic fields of complex-shaped ensembles of dislocation loops were treated as being an essential ingredient of the dislocation-dynamics method for the computer simulation of mesoscopic plastic deformation. Such dislocation ensembles were sorted into individual loops which were then divided into segments that were represented by parametrized space curves. The solutions were presented as fast numerical sums for relevant field variables such as displacement, strain, stress, force, self-energy and interaction energy. Gaussian numerical quadratures were used to solve the field equations of linear elasticity in an infinite isotropic elastic medium. The accuracy of the method was verified by comparing the numerical results with analytical solutions for typical prismatic and slip dislocation loops. The method was highly accurate, computationally efficient and converged as the numbers of segments and quadrature points were increased on each loop. The effect of crystal surfaces on the redistribution of the elastic field was demonstrated by superposing a finite-element image-force field on the calculated results.

Fast-Sum Method for the Elastic Field of Three-Dimensional Dislocation Ensembles. N.M.Ghoniem, L.Z.Sun: Physical Review B, 1999, 60[1], 128-40