Mechanical properties of 3D-printed hierarchical structures based on Sierpinski triangles

Abstract

Incorporating structural hierarchy in the design of engineering composites can be used to tailor or enhance the physical and mechanical properties for specific functionalities. In this study, we propose a design of hierarchical triangular composite (HTC) composed of multi-scale Sierpinski triangles and fabricated using 3D printing with thermoplastic urethanes (TPU) material. A comprehensive framework incorporating theoretical and experimental methods is developed to study the effects of hierarchy order on the quasi-static, dynamic properties and energy absorption performance. Under in-plane quasi-static compression, it is found that higher-order HTC exhibits multi-stage deformation modes due to the non-uniform distribution of substructures, resulting in exceptional compression strength and energy absorption performance, which are increased by 30% and 200% than compared to lower order structures, respectively. Based on the deformation modes, an analytical model is derived to predict the compressive strength, which is validated by numerical and experimental results. In terms of specific energy absorption, the higher-order HTC also demonstrates enhanced performance compared to other honeycomb composite of TPU materials. Under high velocity dynamic impact, it is observed that although the multi-stage deformation mode cannot be activated for higher-order HTC, the fluctuations in dynamic response curve can still be reduced as a result of layer-by-layer collapse of substructures. Moreover, an analytical model using rigid-perfectly plastic-lock (R-PP-L) is employed to explain the dynamic behavior and predict the plateau stress under various impact velocities, which is verified by numerical simulations with good agreement. This study elucidates the effect of structural hierarchy on the mechanical properties and energy absorption performance, and the results are of potential engineering use in the design of lightweight impact-protective composites.