Buckling of cracked micro- and nanocantilevers

Abstract

The size-dependent buckling problem of cracked micro- and nanocantilevers, which have many applications as sensors and actuators, is studied by the stress-driven nonlocal theory of elasticity and Bernoulli–Euler beam model. The presence of the crack is modeled by assuming that the sections at the left and right sides of the crack are connected by a rotational spring. The compliance of the spring, which relates the slope discontinuity and the bending moment at the cracked cross section, is related to the crack length using the method of energy consideration and the theory of fracture mechanics. The buckling equations of the left and right sections are solved separately, and the variationally consistent and constitutive boundary and continuity conditions are imposed to close the problem. Novel insightful results are presented about the effects of the crack length and location, and the nonlocality on the critical loads and mode shapes, also for higher modes of buckling. The results of the present model converge to those of the intact nanocantilevers when the crack length goes to zero and to those of the large-scale cracked cantilever beams when the nonlocal parameter vanishes.

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

“…1 h a   , the buckling loads determined by the present formulation tend to those obtained in 7 for the cantilevers with one damaged cross-section located at the middle of the structure. For all the cases, the existence of a longer crack reduces the stiffness of the pillars and therefore, the buckling loads decrease.…”

“…where the elastic compliance is   The constitutive equation ( 2) is defined over the entire length of the pillar, and therefore, can be used to solve only the buckling problem of the intact pillar 21,22 . Following 7,27,28 and for the pillar with n edge cracks, the constitutive equation ( 2) can be expressed as:…”

“…The formulation presented in 7 for buckling of the Bernoulli-Euler micro-and nanocantilevers with single edge cracks is extended here to miniaturized pillars supported by an elastic foundation and with any number of edge cracks and different kinematic constraints. Unlike the work in 7 , the formulation takes into account the effect related to the shear force acting on the cracked cross-sections. All the improvements in the present formulation compared to that in 7 are important, as explained in the following.…”

“…Such analytical knowledge is also important for material science applications since the buckling of beam-like reinforcements during the manufacturing process may significantly compromise the structural integrity and mechanical properties of composite materials such as carbon nanotube-reinforced polymer composites 5 . Using molecular dynamics simulations in 6 and a nonlocal analytical formulation in 7 , it is shown that the buckling behavior of the micro-and nanopillars is highly affected by the presence of the edge cracks due to, for example, manufacturing process 8 , in-service loadings, and environmental effects. Hence, the paper is aimed at developing an efficient beam formulation to model size-dependent buckling of miniaturized cracked pillars.…”

Novel rod‐like carbon nanomaterials as near infrared‐responsive drug delivery system for potential anticancer applications

“…In recent years, many carbon nanomaterials such as carbon dots [17], single-walled carbon nanotubes [18], and graphene oxide [19] have been developed to load anti-cancer drugs for efficient treatment of tumours. And it is worth mentioning that nanoparticles below 200 nm could cause endocytosis more easily, which made them more suitable in cancer therapy applications [20,21]. However, it is still a great challenge to prepare well-dispersed carbon nanoparticles (<200 nm) with novel structures.…”