By means of atomistic simulations, we demonstrate that a dislocation core exhibits intermittent quasistatic restructuring during incremental shear within the same Peierls valley. This can be regarded as a stick-slip transition, which is also reproduced for a one-dimensional Frenkel-Kontorova chain under rigid boundary conditions. This occurs due to a discontinuous jump in an order parameter of the system, which signifies the extent of region forbidden for the presence of particles in the chain. The stick-slip phenomenon observed in the dislocation core is also shown to be reflected after dimensionality reduction of the multidimensional atomic coordinates, which provides a basis for comparison with the simple one-dimensional chain.