3D equivalent Cauchy model for serrated re-entrant auxetic honeycombs based on variational asymptotic method

The presence of serrated ligaments in the re-entrant auxetic honeycomb (abbreviated as serrated RAH) effectively enhances the stiffness while maintaining auxeticity in the re-entrant direction. To investigate its auxetic characteristics, a 3D equivalent Cauchy model (3D-ECM) was established using the variational asymptotic method. The unique aspect is that the engineering constants are obtained by homogenizing the representative unit-cell and then utilized in the 3D-ECM for global analysis. Subsequently, the resulting global responses are fed into the recovery relationships for localized field analysis. The accuracy of the 3D-ECM and the recovered local field distributions were confirmed by comparing them with the results obtained from the three-dimensional FE model (3D-FEM) and the experimental data collected from the 3D-printed specimen. The effects of the geometric parameters on the negative Poisson's ratio and engineering constants were in-depth discussed. Specifically, an optimal value of 0.5 for the re-entrant ratio and d-value (corresponding to the reentrant angle of 90 degree) yield maximum auxeticity and comparatively higher elastic moduli. In addition, the 3D-ECM greatly enhanced the computational efficiency without compromising the accuracy in predicting global behaviors and local field distributions. The unit-cell tailorability in the proposed model offers valuable guidance for optimizing the design of serrated RAHs.