Mechanics of Novel Double-Rounded-V Hierarchical Auxetic Structure: Finite Element Analysis and Experiments Using Three-Dimensional Digital Image Correlation

Auxetic design is increasingly being used in applications that demand high strength-to-weight ratio. Auxetic structures are also used for crash safety and cushioning applications. Hierarchical auxetic structures inspired by natural cellular structures show a negative Poisson ratio. This phenomenon is caused by inherent geometric constraints in these structures. Due to the advancements in additive manufacturing, high-performance computing, and shape optimization algorithms, developing high-performance auxetic structures has emerged as an active area of research. Recently, a sinusoidal design of repeating cell with smooth and curved members, referred to as double-U hierarchical (DUH) structure, has been proved to perform better than the traditional double-V hierarchical (DVH) structure. However, the possibility of improving the existing DVH design has not been explored in the literature. In the present work, we fill this research gap by conducting a systematic study wherein the extent of curviness and roundness in its unit cell is varied and evaluated using finite element analysis and experiments. We call our improved version of DVH as DRVH (double-rounded-V hierarchical) auxetic structure. Finite element analyses of DUH and DRVH structures are conducted by simulating quasi-static loading (0.16667 mm/s) and impact loading (1,00,000 mm/s) conditions. The total simulation time is 30 s for quasi-static loading, whereas it is 0.00005 s for impact loading when a 5-mm displacement is applied at one end of the DUH and DRVH auxetic structures. The comparative analyses are carried out by evaluating internal energy, plastic deformation, kinetic energy, total energy, displacements, contact forces, reaction forces, and stress values. History and field outputs are requested at every 0.5 s time increment for quasi-static loading, whereas they are requested at every 10−6 s for impact loading. Experiments are conducted on DRVH structures manufactured through fused deposition modeling (FDM), which is the most commonly used additive manufacturing technology. The filament used in this work is PLA Flax filament supplied by Nanovia®. It is a biodegradable material, which is comprised of poly lactic acid (PLA) and Flax fiber. Three-dimensional digital image correlation is performed to validate the deformation of DRVH structure. The combination of straightness and roundness of the DRVH members not only provides more room for absorbing impact energy than the DUH design but also reduces peak stress and enhances auxetic behavior and static collapse stress.