An accelerating dislocation exhibited a logarithmic singularity in the near field (associated with the acceleration), which had been earlier derived from the full solution. Here, the existence and evaluation of the logarithmic singularity were obtained solely from the leading terms (1/r) of the near-field expansions (which were the same as those of the steady-state motion with the instantaneous velocity of the accelerating motion as the uniform velocity) by means of a conservation law involving the dynamic energy—momentum tensor. It was also shown that logarithmic terms of the near-field expansions were independent of the angular coordinate, a question that was posed in the past by David Barnett, and which was critical in this analysis. The self-force and effective mass for an accelerating dislocation depended essentially on that logarithmic singularity as shown by Eshelby and more generally by Ni and Markenscoff.

The Logarithmic Singularity of a Generally Accelerating Dislocation from the Dynamic Energy-Momentum Tensor. L.Ni, X.Markenscoff: Mathematics and Mechanics of Solids, 2009, 14[1-2], 38-51