Aside from the Volterra field, dislocations create a core field, which can be
modeled in linear anisotropic elasticity theory with force and dislocation
dipoles. We derive an expression of the elastic energy of a dislocation taking
full account of its core field and show that no cross term exists between the
Volterra and the core fields. We also obtain the contribution of the core field
to the dislocation interaction energy with an external stress, thus showing
that dislocation can interact with a pressure. The additional force that
derives from this core field contribution is proportional to the gradient of
the applied stress. Such a supplementary force on dislocations may be important
in high stress gradient regions, such as close to a crack tip or in a
dislocation pile-up
