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The effective mass of an accelerating dislocation

Abstract

Macroscopic dynamic plastic deformation is a consequence of the motion of dislocations at the microscopic level. To determine the effective mass of an accelerating dislocation is a fundamental problem in continuum mechanics and plasticity. An equally important and closely related problem is to find the force needed to accelerate a dislocation. Both open problems have attracted a great deal of interest, however solutions are still not satisfactory. It is well-known that in Eshelby's theory, the configurational force on a static defect is defined as the negative gradient of the total energy with respect to the position of the defect. It has not been clarified whether that definition will still be adequate for the dynamic case. We propose a definition of the dynamic configurational force and self-force by using the change of the total Lagrangian of the mechanical system. And by carefully treating the discontinuities and singularities, a rigorous consistent discussion on the definition and expression of the dynamic configurational force on moving elastic defect is presented. The effective mass of an accelerating dislocation is then derived from the inertial part of the self-force divided by the acceleration. For moving screw and edge dislocations, we prove new theorems on the near field behaviors, so that the full determination of the near field expansions up to the O(1) terms are achieved. The solution and evaluation of the self-force and effective mass for moving screw and edge dislocations is obtained

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