Uniformly moving non-singular dislocations with elliptical core shape in anisotropic media

Abstract

To allow for “relativistic”-like core contraction effects, an anisotropic regularization of steadily moving straight dislocations of arbitrary orientation is introduced, with two scale parameters [Formula: see text] and [Formula: see text] along the direction of motion and transverse to it, respectively. The dislocation core shape is an ellipse. When [Formula: see text], the model reduces to the Peierls–Eshelby dislocation, the fields of which are non-differentiable on the slip plane. For finite [Formula: see text] and [Formula: see text], fields are everywhere differentiable. Applying the author’s so-called “causal” Stroh formalism to the model, explicit expressions for the regularized fields in anisotropic elasticity are derived for any velocity. For faster-than-wave velocities, Mach-cone angles are found insensitive to the ratio [Formula: see text], as must be. However, the larger [Formula: see text], the weaker the intensity of the cone branches. An expression is given for the radiative dissipative force opposed to motion. From this expression, it is inferred that the concept of a “radiation-free” intersonic velocity can, when not applicable, be replaced by that of a “least-radiation” velocity.