Numerical homogenization of a linearly elastic honeycomb lattice structure and with and results

This paper presents a verification and validation analysis of Finite Element (FE) models predicting the mechanical response of linearly elastic honeycomb structures. We have studied three main models, namely: analytical models based on beam theories, explicit FE models where the cell geometry is explicitly meshed with 3D elements, and numerical homogenized FE models where a plate made of a honeycomb structure is meshed with 2D elements whose mechanical properties were predicted from numerical homogenization. We compared the predictions of these simulations against experimental uni-axial tensile tests where we mechanically tested 3D printed honeycomb specimens having a relative density of 40% and made of 13 and 37 cells, respectively. Comparison of the experimentally measured axial stiffness to the numerical predictions revealed that the numerical homogenization models can predict the apparent in-plane stiffness in structures made of 37 cells within 4%, while the discrepancy increases to 70% when 13 cells are considered. To quantify this discrepancy, we also provided a relationship between the number of represented cells and the discrepancy of the numerical homogenized model against the explicit FE models to predict the in-plane stiffness. We believe that these results could be important for the application of the homogenized models in optimization of honeycomb lattice structures whose relative density varies with space.

Automated summary

This paper presents a verification and validation analysis of Finite Element (FE) models predicting the mechanical response of linearly elastic honeycomb structures. The numerical homogenization models can predict the apparent in-plane stiffness in structures made of 37 cells within 4%, while the discrepancy increases to 70% when 13 cells are considered.