  Dislocation climb plays an important role in understanding plastic
deformation of metallic materials at high temperature. In this paper, we
present a continuum formulation for dislocation climb velocity based on
densities of dislocations. The obtained continuum formulation is an accurate
approximation of the Green's function based discrete dislocation dynamics
method (Gu et al. J. Mech. Phys. Solids 83:319-337, 2015). The continuum
dislocation climb formulation has the advantage of accounting for both the
long-range effect of vacancy bulk diffusion and that of the Peach-Koehler climb
force, and the two longrange effects are canceled into a short-range effect
(integral with fast-decaying kernel) and in some special cases, a completely
local effect. This significantly simplifies the calculation in the Green's
function based discrete dislocation dynamics method, in which a linear system
has to be solved over the entire system for the long-range effect of vacancy
diffusion and the long-range Peach-Koehler climb force has to be calculated.
This obtained continuum dislocation climb velocity can be applied in any
available continuum dislocation dynamics frameworks. We also present numerical
validations for this continuum climb velocity and simulation examples for
implementation in continuum dislocation dynamics frameworks.
