  The influence on macroscopic work hardening of small, spherical, elastic
particles dispersed within a matrix is studied using an isotropic strain
gradient plasticity framework. An analytical solution, based on a recently
developed yield strength model is proposed. The model accounts for random
variations in particle size and elastic properties, and is numerically
validated against FE solutions in 2D/3D material cell models. Excellent
agreement is found as long as the typical particle radius is much smaller than
the material length scale, given that the particle volume fraction is not too
large ($<10\%$) and that the particle/matrix elastic mismatch is within a
realistic range. Finally, the model is augmented to account for strengthening
contribution from shearable particles using classic line tension models and
successfully calibrated against experimental tensile data on an
$Al-2.8wt\%Mg-0.16wt\%Sc$ alloy.
