  We develop and demonstrate the first general computational tool for finite
deformation static and dynamic dislocation mechanics. A finite element
formulation of finite deformation (Mesoscale) Field Dislocation Mechanics
theory is presented. The model is a minimal enhancement of classical
crystal/$J_2$ plasticity that fundamentally accounts for polar/excess
dislocations at the mesoscale. It has the ability to compute the static and
dynamic finite deformation stress fields of arbitrary (evolving) dislocation
distributions in finite bodies of arbitrary shape and elastic anisotropy under
general boundary conditions. This capability is used to present a comparison of
the static stress fields, at finite and small deformations, for screw and edge
dislocations, revealing heretofore unexpected differences. The computational
framework is verified against the sharply contrasting predictions of
geometrically linear and nonlinear theories for the stress field of a spatially
homogeneous dislocation distribution in the body, as well as against other
exact results of the theory. Verification tests of the time-dependent numerics
are also presented. Size effects in crystal and isotropic versions of the
theory are shown to be a natural consequence of the model and are validated
against available experimental data. With inertial effects incorporated, the
development of an (asymmetric) propagating Mach cone is demonstrated in the
finite deformation theory when a dislocation moves at speeds greater than the
linear elastic shear wave speed of the material.
