  In this work, a higher-order irrotational strain gradient plasticity theory
is studied in the small strain regime. A detailed numerical study is based on
the problem of simple shear of a non-homogeneous block comprising an
elastic-plastic material with a stiff? elastic inclusion. Combinations of
micro-hard and micro-free boundary conditions are used. The strengthening and
hardening behavior is explored in relation to the dissipative and energetic
length scales. There is a strong dependence on length scale with the imposition
of micro-hard boundary conditions. For micro-free conditions there is marked
dependence on dissipative length scale of initial yield, though the differences
are small in the post-yield regime. In the case of hardening behavior, the
variation with respect to energetic length scale is negligible. A further
phenomenon studied numerically relates to the global nature of the yield
function for the dissipative problem; this function is given as the least upper
bound of a function of plastic strain increment, and cannot be determined
analytically. The accuracy of an upper-bound approximation to the yield
function is explored, and found to be reasonably sharp in its prediction of
initial yield.
