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

• Published in: Thin-walled structures 2024-07, Vol.200, p.111883, Article 111883
• Main Authors: Zhou, Yujie, Zhong, Yifeng, Zhu, Yilin, Liu, Rong
• Format: Article
• Language: English
• Subjects: Auxetic effect; Cauchy model; Engineering constants; Serrated re-entrant honeycomb; Variational asymptotic method
• ISSN: 0263-8231; 1879-3223
• DOI: 10.1016/j.tws.2024.111883

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 re-entrant 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. •The presence of serrated ligaments enhance stiffness while maintaining auxeticity.•Engineering constants are obtained by homogenizing the unit-cell within 3D-ECM.•Auxeticity of the serrated RAH is investigated using a VAM-based 3D-ECM.•The accuracy of the 3D-ECM is validated against 3D-FEM and experimental data.•A re-entrant angle of 90-degree yield maximum auxeticity and higher elastic moduli.