Mechanical response of a novel square dome shell with bistable behavior: Improved analytical method and empirical model

In this study, a novel square dome -shaped shell with a fascinating bistable behavior is proposed, which is able to quickly switch to a new stable configuration within its elastic range under a certain load, due to its elastic instability. Compared to most circular shells currently studied, it is easier to arrange multiple structures in threedimensional space to obtain multistable responses. Numerical and experimental methods were adopted for the study of the mechanical response of the square shell, and main influence parameters were also investigated. In addition, an improved piecewise fitting method is introduced to establish an empirical formula for predicting the mechanical response of bistable shells, which can be used to guide the design of bistable shells. Finally, two types of metamaterials, uniaxial compressible metamaterials and triaxial compressible metamaterials, are successfully designed according to the above theory, the typical behaviors of which are studied via simulations. This novel structure presented in this paper has broad application prospects in the fields of energy absorption and programmable deformation structures.