Uniaxial compression performance of anti-tetrachiral structures considering the effects of cell size and boundary conditions

Anti-tetrachiral structures (AS) are typical metamaterials known for their negative Poisson's ratio, and have great potential application in reducting the damage of the ship caused by collisions. The existing analysis of the mechanical properties of AS is conducted by applying the energy method to a unit cell with periodic boundary conditions (PBC). In available works, the shear force at the structure's boundaries is neglected. But is it permissible to disregard the impact of shear forces at the boundaries on the structure's equivalent mechanical properties? By examining the deformation relationship between the ribs and the nodal rings, we developed a uniaxial compression model for AS under both free and constrained boundary conditions, which accurately predicts the mechanical properties of the AS structure. This model was validated through numerical simulations and experiments. The findings reveal that the equivalent mechanical properties of AS exhibit a size dependence related to the cell size. For example, for AS with equivalent density and identical overall dimensions, the equivalent Young's modulus of an AS with 2×2 cells will be twice that of an AS with 4×4 cells. Furthermore, the size effect of the structure can be neglected when the number of cells larger than 8×8. Moreover, it is found that the present model considering boundary conditions exhibits an equivalent Young's modulus 25 % higher than the model neglecting boundary conditions. The study's findings indicate that the presence of boundary conditions can disrupt PBC, leading to significant discrepancies between theoretical derivations and practical applications.