Distributional and regularized radiation fields of non-uniformly moving straight dislocations, and elastodynamic Tamm problem

Abstract

This work introduces original explicit solutions for the elastic fields radiated by non-uniformly moving, straight, screw or edge dislocations in an isotropic medium, in the form of time-integral representations in which acceleration-dependent contributions are explicitly separated out. These solutions are obtained by applying an isotropic regularization procedure to distributional expressions of the elastodynamic fields built on the Green tensor of the Navier equation. The obtained regularized field expressions are singularity-free, and depend on the dislocation density rather than on the plastic eigenstrain. They cover non-uniform motion at arbitrary speeds, including faster-than-wave ones. A numerical method of computation is discussed, that rests on discretizing motion along an arbitrary path in the plane transverse to the dislocation, into a succession of time intervals of constant velocity vector over which time-integrated contributions can be obtained in closed form. As a simple illustration, it is applied to the elastodynamic equivalent of the Tamm problem, where fields induced by a dislocation accelerated from rest beyond the longitudinal wave speed, and thereafter put to rest again, are computed. As expected, the proposed expressions produce Mach cones, the dynamic build-up and decay of which is illustrated by means of full-field calculations.

36 pages, 6 figures. v2: metadata amended. v3: a few minor typos corrected in the text, and better-looking hyperlinks

References in corpus (7)

• On gradient field theories: gradient magnetostatics and gradient elasticity
• Equation of motion for dislocations with inertial effects
• The gauge theory of dislocations: conservation and balance laws
• Inertial and retardation effects for dislocation interactions
• On the non-uniform motion of dislocations: The retarded elastic fields, the retarded dislocation tensor potentials and the Liénard-Wiechert tensor potentials
• Reply to "Comment on 'Dynamic Peierls-Nabarro equations for elastically isotropic crystals' "
• On the gradient of the Green tensor in two-dimensional elastodynamic problems, and related integrals: Distributional approach and regularization, with application to nonuniformly moving sources

Cited by in corpus (3)

• Causal Stroh formalism for uniformly-moving dislocations in anisotropic media: Somigliana dislocations and Mach cones
• Elastic Liénard-Wiechert potentials of dynamical dislocations from tensor gauge theory in 2+1 dimensions
• Shock-driven nucleation and self-organization of dislocations in the dynamical Peierls model