The Logarithmic Singularity of a Generally Accelerating Dislocation from the Dynamic Energy—Momentum Tensor

Abstract

An accelerating dislocation exhibits 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 are obtained solely from the leading terms (1/r) of the near-field expansions (which are 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 is also shown that logarithmic terms of the near-field expansions are independent of the angular coordinate, a question that was posed in the past by David Barnett, and which is critical in this analysis. The self-force and effective mass for an accelerating dislocation depends essentially on that logarithmic singularity as shown by Eshelby and more generally by Ni and Markenscoff.