  A method for solving three dimensional discrete dislocation plasticity
boundary-value problems using a monopole representation of the dislocations is
presented. At each time step, the displacement, strain and stress fields in a
finite body are obtained by superposition of infinite body dislocation fields
and an image field that enforces the boundary conditions. The three dimensional
infinite body fields are obtained by representing dislocations as being
comprised of points, termed monopoles, that carry dislocation line and Burgers
vector information. The image fields are obtained from a three dimensional
linear elastic finite element calculation. The implementation of the coupling
of the monopole representation with the finite element method, including the
interaction of curved dislocations with free surfaces, is presented in some
detail because it differs significantly from an implementation with a line
based dislocation representation. Numerical convergence and the modeling of
dislocation loop nucleation for large scale computations are investigated. The
monopole discrete dislocation plasticity framework is used to investigate the
effect of size and initial dislocation density on the torsion of wires with
diameters varying over three orders of magnitude. Depending on the initial
dislocation source density and the wire diameter, three regimes of
torsion-twist response are obtained: (i) for wires with a sufficiently small
diameter, plastic deformation is nucleation controlled and is strongly size
dependent; (ii) for wires with larger diameters dislocation plasticity is
dislocation interaction controlled, with the emergence of geometrically
necessary dislocations and dislocation pile-ups playing a key role, and is
strongly size dependent; and (iii) for wires with sufficiently large diameters
plastic deformation becomes less heterogeneous and the dependence on size is
greatly diminished.
