Analytic design of multi-material auxetic structures with tailored mechanical performance

Abstract Multi-material 3D printing technology has enabled the development of auxetic structures composed of distinct materials, offering enhanced tunability of certain properties and consequently improved mechanical performance. This paper presents a theoretical model based on Timoshenko beam theory to explore how six geometric and three material parameters influence the auxetic behaviour of a re-entrant structure system. The derived equations showed that Poisson’s ratio was primarily governed by geometry when all material parameters were identical (i.e. in a single-material model). In contrast, for a multi-material model, both geometric and material parameters jointly controlled its auxetic behaviour. The theoretical analysis revealed that assigning materials with a higher Young’s modulus to vertical beams enhanced auxeticity, whereas the inverse assignment resulted in the least auxetic behaviour. Furthermore, both experiments and simulations were conducted, and the results validated theoretical predictions. It was also found that appropriate combinations of material distribution and geometric configuration could induce a unique deformation mode characterised by multiple peak forces, thereby significantly improving energy absorption during the plastic deformation stage. Overall, this study establishes a systematic framework for designing multi-material re-entrant auxetic structures and highlights their advantages and complexity.