1. IntroductionThe self-force and effective mass of a generally accelerating

dislocation. JMacroscopic dynamic plastic deformation is a consequence of the motion of dislocations at the microscopic level, and to understand the relation of the physical processes at different scales, macro and micro, the dislocation dynamics with inertial effects needs to be investigated. The determination of the self-force and the effective mass of a generally accelerating dislocation is a fundamental problem in dynamic plasticity. When a defect is moving with respect to the material, the associated ‘‘force’ ’ on the defect is a configurational force (when the stress field is solely created by the existence of the defect itself, the configurational force on the defect is called self-force), which, in the static case, is Eshelby’s configurational force on an elastic singularity given by a path-independent integral (Eshelby, 1951), later called J-integral (Rice, 1968). The path independence of the J-integral is due to the conservation laws derived from Noether’s theory (Noether, 1918) for elastostatics (Günther, 1962). Eshelby (1951, 1970, 1975) showed that the path-independent integral is equal to minus the change of the total energy of the system under an infinitesimal translation of the singularity, and defined it as the force on the singularity. More recently, Eshelby’s theory has been developedThe self-force and effective mass of a moving dislocation in a generally accelerating motion are explicitly obtained on the basis of a surface-independent dynamic J-integral. Logarithmic singularities due to non-zero acceleration result in divergent integrals in the dynamic J-integral, which are treated by smearing out the dislocation core (ramp-core) and b