Residual stresses and strains in a two-dimensional model composite consisti
ng of elastic reinforcements in a crystalline matrix are analysed. The comp
osite is subject to macroscopic shear and then unloaded. Plane-strain condi
tions and single slip on slip planes parallel to the shear direction are as
sumed. The dislocations are modelled as line defects in a linear elastic me
dium. At each stage of loading, superposition is used to represent the solu
tion in terms of the infinite medium solution for the discrete dislocations
and an image solution that enforces the boundary conditions, which is non-
singular and obtained from a linear elastic finite-element solution. The la
ttice resistance to dislocation motion, dislocation nucleation and dislocat
ion annihilation are incorporated into the formulation through a set of con
stitutive rules. Obstacles leading to possible dislocation pile-ups are als
o accounted for. Considerable reverse plasticity is found when the reinforc
ement arrangement is such that all slip planes are cut by particles and whe
n the unloading rate is equal to the loading rate. When unloading takes pla
ce at a very high rate, the unloading slope is essentially elastic but rela
xation of the dislocation structure occurs in the unloaded state. Predictio
ns of the discrete dislocation formulation for residual stresses, residual
strains and the strain variance are compared with corresponding predictions
obtained using conventional continuum slip crystal plasticity. The effect
of particle size, as predicted by the discrete dislocation description, is
also addressed.