An FFT-based method for uncertainty quantification of Nomex honeycomb’s in-plane elastic properties

Abstract

The honeycomb manufacturing process involves complex and inter-related procedures spanning multiple physics domains and scales. The geometry heterogeneity in honeycomb cells inevitably exists and propagates to the uncertainty of the honeycomb’s mechanical performance. Quantitatively characterizing the effect of cell geometry variability on the effective mechanical properties of honeycomb hence becomes critically important. In this study, a Fast Fourier Transform (FFT) based method was developed to predict the effective in-plane elastic properties of irregular hexagonal honeycomb. The honeycomb geometry heterogeneity was identified with a digital image technology by examining a large number of cells. Correlation analysis on the resulting statistical data enables determining the interdependence of cell wall lengths and angles. Using a Representative Unit Cell (RUC) with varying cell wall lengths and angles, an analytical function for the effective in-plane elastic parameters was established by incorporating the dependencies. The statistical quantification of cell geometry and the propagation of RUC’s elastic characteristics were further integrated into the FFT-based multiscale framework for predicting the in-plane elastic moduli of irregular honeycomb. The tensile and shear tests on the irregular honeycombs, together with the corresponding finite element analysis, were used to verify the proposed method. Both experimental and numerical results confirmed that the uncertainty of elastic moduli achieved by the FFT-based method provides a reasonable estimation.