The non-uniform motion of straight dislocations in infinite media was investigated using the theory of incompatible elastodynamics. The equations of motion were derived for non-uniformly moving screw dislocations, gliding edge and climbing edge dislocations. The exact closed-form solutions of the elastic fields were calculated. The fields of the elastic velocity and elastic distortion surrounding the arbitrarily moving dislocations were given explicitly in the form of integral representations free of non-integrable singularities. The elastic fields describe the response in the form of non-uniformly moving elastic waves caused by the motion of the dislocation.

On The Elastic Fields Produced by Non-Uniformly Moving Dislocations: a Revisit. M.Lazar: Philosophical Magazine, 2011, 91[25], 3327-42