**A nonlocal continuum model for the buckling of carbon honeycombs**

J Zhang, MECCANICA, 53, 2999-3013 (2018).

DOI: 10.1007/s11012-018-0854-y

Using molecular dynamics (MD) simulations and Eringen's nonlocal elasticity theory, in this paper we comprehensively study the small- scale effects on the buckling behaviours of carbon honeycombs (CHCs). The MD simulation results show that the small-scale effects stemming from the long-range van der Waals interaction between carbon atoms can significantly affect the buckling behaviours of CHCs. To incorporate the small-scale effects into the theoretical analysis of the buckling of CHCs, we develop a nonlocal continuum mechanics (CM) model by employing Eringen's nonlocal elasticity theory. Our nonlocal CM model is found to fit MD simulations well by setting the nonlocal parameter in the nonlocal CM model as 0.67. It is shown in our MD-based nonlocal CM model that when the cell length of CHCs is smaller than 7.93 the influence of small-scale effects on the bucking of CHCs becomes unnegligible and the small-scale effects can greatly reduce the critical buckling stress of CHCs. This reduction in critical buckling stress induced by the small- scale effects becomes more significant as the length of the cell wall decreases. Moreover, CHCs are found to display two different buckling modes when they are under different states of loading. The critical condition for the transition between these two buckling modes of CHCs can be greatly affected by the small-scale effects when the vertical cell wall and the inclined cell wall of CHCs have different lengths.

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