  The buckling instability of micro- and nanopillars can be an issue when
designing intelligent miniaturized devices and characterizing composite
materials reinforced with beam-like particles on the small-scale. Analytical
modeling of the buckling of miniaturized pillars is especially important due to
the difficulties in conducting experiments. Here, a well-posed stress-driven
nonlocal model is developed, which allows the calculation of the critical loads
and buckling configurations of the miniaturized pillars on an elastic
foundation and with arbitrary numbers of edge cracks. The discontinuities in
bending slopes and deflection at the damaged cross-sections due to the edge
cracks are captured through the incorporation of both rotational and
translational springs. A comprehensive analysis is conducted to investigate the
instability of pillars containing a range of one to four cracks. This analysis
reveals interesting effects regarding the influence of crack location,
nonlocality, and elastic foundation on the initial and subsequent critical
loads and associated buckling configurations. The main findings are: (i) the
shielding and amplification effects related to a system of cracks become more
significant as the dimensions of pillars reduce, (ii) the influence of the
shear force at the damaged cross-section related to the translational spring
must not be neglected when dealing with higher modes of buckling and long
cracks, (iii) an elastic foundation decreases the effects of the cracks and
size dependency on the buckling loads, and (iv) the effects of the edge cracks
on the critical loads and buckling configurations of the miniaturized pillars
are highly dependent on the boundary conditions.
