  Small-scale mechanical behaviour shows significant departures from classical
elastic-plastic theory. In a remarkable number of instances, the strength of a
material appears to scale as the reciprocal square root of the smallest length
scale. There are several recent experimental and modeling results in the
literature that show an interaction between dimensional (extrinsic) size and
microstructural (intrinsic) size effects. In this paper, we present a
mechanical model that naturally produces the inverse square root strengthening
and derive an expression for the effective length when both the extrinsic and
intrinsic size effects are significant. The theory fits well to data from a
wide range of deformation geometries and includes the interaction between the
microstructural and dimensional size effects. Furthermore, this approach is
able to predict the size effect under uniform deformation without strain
gradient.
