Transitory metamaterials based on symmetrical splitting of rotating squares

Abstract Materials exhibiting a negative Poisson’s ratio, known as auxetic materials, have garnered significant interest due to their unique mechanical properties and potential applications. This paper introduces a new class of auxetic metamaterials based on modified interconnected rotating rigid squares, where each square can split into two or four isosceles right triangles. The study explores three models categorized by their order of splitting, ranging from purely rotating squares (zeroth order) to systems with sub-units exhibiting relative motion (first and second orders). Detailed analyses of the in-plane Poisson’s ratio for these models were conducted, focusing on both infinitesimal and finite deformations. The results reveal that the proposed metamaterials demonstrate a transition in Poisson’s ratio behavior, characterized either by discontinuity or continuous but non-differentiable Poisson’s ratio at the transitory state between deformation mechanisms. This transition highlights the potential of these metamaterials to exhibit tunable mechanical responses, offering insights into designing materials with customized properties for advanced engineering applications.