Calculation of the equivalent shear moduli of the grid beetle elytron plate core layer

To establish an equivalent model of the core layer of the grid beetle elytron plate (GBEP) and perfect the bionic system of the beetle elytron plate (BEP), the in-plane and out-of-plane equivalent shear moduli of the basic unit of the GBEP core layer are calculated by the energy method, and the accuracy of the expressions is verified by comparison with the results obtained with the finite element method and experiments. The results show that the in-plane and out-of-plane shear moduli can be expressed as functions of η\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta $$\end{document}, the ratio of trabecula radius to unit width, and the trends of the in-plane and out-of-plane shear moduli of the GBEP core unit with η\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta $$\end{document} are discussed. The concept of stiffness per unit volume (SPUV, k) is proposed, and the difference in shear performance (in-plane and out-of-plane) between the GBEP and grid plate (GP) core layer is theoretically revealed for the first time. The SPUV of the GBEP is slightly less than that of the GP for out-of-plane shearing but far better than that of the GP for in-plane shearing. According to the values of the in-plane and out-of-plane SPUVs of the GBEP and GP, a theoretical explanation is given for why the shear performance of the GBEP core is better than that of the GP, and the shear moduli of GBEP core equivalent model are obtained. From the point of view of shear properties, the theoretical basis that the in-plane stiffness of GBEP core cannot be ignored is given for the first time. This paper lays a theoretical foundation for exploring the shear properties of GBEP and its application in practical engineering.