Uniform motion of an edge dislocation within Mindlin's first strain gradient elasticity

Motion of dislocations plays the fundamental role in plastic deformations of crystalline solids. According to the prediction of classical elasticity, the strain and stress fields due to a moving dislocation suffer from singularities. In the present paper, it is shown that the employment of Mindlin's first strain gradient theory of elasticity leads to the removal of the singularities from all the elastic fields induced by a straight edge dislocation that moves uniformly in an infinitely extended isotropic body. However, at distances far enough away from the dislocation core, the predictions of such theory and classical elasticity coincide with each other. The present analysis also shows that the corresponding plastic strain field of the moving dislocation is, likewise, free from any singularity. Moreover, explanations are provided in the current paper for the roles of the micro-inertia and the characteristic lengths of the constituent material of the body as well as the effect of the velocity of the dislocation on its induced field quantities.