  Precipitation of fine particles into the base material of a metal is a potent
strengthening mechanism. This is numerically analyzed within a continuum
framework based on a higher order strain gradient plasticity theory and by use
of an axi-symmetric unit cell model. The unit cell contains a spherical
particle which is resilient to inelastic deformation and embedded in a
homogeneous matrix material. An interface with special characteristics, that
separates the particle from the matrix, plays a key role for the overall
strengthening. Based on a systematic parametric study a closed form relation is
deduced and proposed for the increase in the overall yield stress. This
relation is limited to materials containing elastic particles with spacing
smaller than the material length scale and volume fractions less than 10 $\%$.
It these conditions are met, the plastic strain field in the material becomes
essentially constant on the scale of particle spacing. The character of the
solution suggests that this result is general despite the simplicity of the
unit cell employed in the parametric study. Predictions from the closed form
relation is compared with published experimental results, and good agreement is
observed in some metal matrix composites and alloys. The influence of a
mismatch in elastic modulus between particles and matrix is elucidated, and
effects on post yield strain hardening are discussed.
