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The buckling instability of micro- and nanopillars can be an issue whendesigning intelligent miniaturized devices and characterizing compositematerials reinforced with beam-like particles on the small-scale. Analyticalmodeling of the buckling of miniaturized pillars is especially important due tothe difficulties in conducting experiments. Here, a well-posed stress-drivennonlocal model is developed, which allows the calculation of the critical loadsand buckling configurations of the miniaturized pillars on an elasticfoundation and with arbitrary numbers of edge cracks. The discontinuities inbending slopes and deflection at the damaged cross-sections due to the edgecracks are captured through the incorporation of both rotational andtranslational springs. A comprehensive analysis is conducted to investigate theinstability of pillars containing a range of one to four cracks. This analysisreveals interesting effects regarding the influence of crack location,nonlocality, and elastic foundation on the initial and subsequent criticalloads and associated buckling configurations. The main findings are: (i) theshielding and amplification effects related to a system of cracks become moresignificant as the dimensions of pillars reduce, (ii) the influence of theshear force at the damaged cross-section related to the translational springmust not be neglected when dealing with higher modes of buckling and longcracks, (iii) an elastic foundation decreases the effects of the cracks andsize dependency on the buckling loads, and (iv) the effects of the edge crackson the critical loads and buckling configurations of the miniaturized pillarsare highly dependent on the boundary conditions.

Effects of multiple edge cracks, shear force, elastic foundation, and boundary conditions on bucking of small-scale pillars