Computing image stress in an elastic cylinder

We develop numerical methods that efficiently compute image stress fields of defects in an elastic cylinder. These methods facilitate dislocation dynamics simulations of the plastic deformation of micro-pillars. Analytic expressions of the image stress have been found in the Fourier space, taking advantage of the translational and rotational symmetries of the cylinder. To facilitate numerical calculation, the solution is then transformed into the stress field in an infinite elastic body produced by a distribution of body forces or image dislocations. The use of the fast Fourier transform (FFT) method makes the algorithms numerically efficient.