Multiscale Analysis of Micro/Nano Size Honeycomb Structures

Abstract

The micro/nano size honeycomb structures are effective to improve the functionality such as catalysis or electronic charge due to the very high ratio of the surface area to the volume. The homogenization for such periodic structures provides easier modeling and promotion of computational efficiency. However, size-dependency of material behavior in nano scale must be involved to apply the homogenization technique to micro/nano honeycomb structures. The present work proposes a continuum model with size-dependency and provides equivalent stiffness of micro/nano size honeycomb structures computed by the numerical homogenization method through the asymptotic expansion method and dimensional reduction based on the Kirhhoff plate theory. 1 . Such structures are useful to improve the functionality of catalyst electronic charge because of the very high ratio of the surface area to the volume. However, micro/nano size structures exhibit very different mechanical behavior compared with macro size structures. Thus, reliable analysis methods for micro/nano structures have become an important issue for design purpose. It is generally known that material property in nano scale is strongly size-dependent 2-4 . Miller and Shenoy 3 show that Young's modulus or bending stiffness in plates decreases or increases as the thickness of the plate becomes thinner due to softening or hardening phenomena. These phenomena result from the surface effect and has been investigated in the previous works with both experiments and molecular dynamics (MD) simulations. The surface effect results from the difference of atomic bonding energy between surface and bulk layers. If the thickness of film is very small, surface effect, which is negligible in the macro-sized materials, plays a dominant role and it leads to the change of material property in nano-size device. For this reason, investigation of material property in nano scale is essential for designing and predicting performances of micro/nano sized structures. In order to investigate the mechanical and thermal behavior of nano-sized structures, MD simulations have been used as a conventional method. However, although numerical technique and computing resources have been improved, large-size simulations are still prohibited because they require computational memory resources and time. Thus, researchers have taken much interest in the continuum approaches to overcome the limitation of MD simulations. In contrast to the size restraint on MD simulation, the finite element analysis based on continuum theory can be carried out in an efficient manner. However, conventional continuum models are only suitable for macro size problems because they do not consider size effect of nano scale. From this motivation, continuum-based analysis model to consider surface effect have been developed. Gurtin and Murdoch 5-7 proposed the constitutive equation for the free surface of isotropic material by introducing the surface stress concept. On the basis of this