Determining in-plane material properties of square core cellular materials using computational homogenization technique

Utilizing the multi-scale homogenization technique based on averaging theorems, three methodologies are proposed for determining equivalent (effective) in-plane properties of square-shaped core honeycombs. In this regard, two theoretical approaches based on strain energy density equivalency (SEDE) condition and Hook's law as well as a semi-empirical based method are employed. Purposefully two possible geometries of representative volume element (RVE) with related boundary conditions are investigated. Featuring as a fast estimation method, the constant boundary element method (CBEM) is utilized to solve the boundary integral form of equivalent stress and strain equations. The assessment of proposed methods is done for a typical material by comparing the results with the outputs of existing analytical and numerical methods. The obtained results demonstrate the capability of proposed relations in estimating the in-plane engineering constants for the wide range of elative densities where the previously published methods fail at high relative densities.

Automated summary

In this paper, three methodologies are proposed for determining the equivalent in-plane properties of square-shaped core honeycombs using the multi-scale homogenization technique. The proposed methods are compared with existing analytical and numerical methods to demonstrate their effectiveness.