Sequential multiscale analysis on size-dependent mechanical behavior of micro/nano-sized honeycomb structures

Abstract

The elastic properties of nano-sized structures are size-dependent. To capture this phenomenon, atomistic-level calculation is generally required. The size-dependent mechanical property is due to the reconstruction of atomic bonding at surfaces. Honeycomb structures in the nanoscale level have excellent functionality due to the very high ratio of the surface area to volume. Such structures have been manufactured in practice above submicron scale so that the atomistic simulations are not tractable to evaluate their performance because the repeated computation of micro/submicro-scale in atomistic simulations requires too much computational time and resources. In this study, to overcome the limitation in atomistic simulations, a continuum finite element analysis is carried out by introducing the surface elasticity. The surface elastic property for very simple structure is once identified by using the molecular dynamic (MD) simulations, and then the numerical homogenization method in the continuum level is applied to nano-sized periodic structures including honeycomb structures. The obtained homogenized stiffness over the representative volume element (RVE) is used to predict the global behaviors of the honeycomb structures. The present sequential multiscale analysis provides the reliable prediction of size-dependent elastic properties, and is very useful to design the patterns of the nano-sized honeycomb structures. The bending stiffness and shear stiffness of patterned honeycomb structures are highly size- and height-dependent.