A Comprehensive Investigation of the Geometric Functionally Graded Auxetic Double Arrowhead Composite Lattice Structures: Exploring Tailored Longitudinal and Lateral Young's Modulus

Lattice structures with negative Poisson's ratios (NPR) can integrate advanced functionalities in various engineering applications, including biomedical, aerospace and protective systems. This study explores the mechanical properties of auxetic double arrowhead honeycomb composites, a novel geometric functionally graded auxetic double arrowhead composite with NPR. Analytical expressions for Young's modulus in both longitudinal and lateral directions are derived and validated using finite element simulations. To this aim, the Euler-Bernoulli beam theory and the free body diagram were used to investigate the elastic response on two different types of arrowhead composite structures. Two types of structures are investigated: uniform (constant forming angle) and geometrically functionally graded (varying forming angle with height). For experimental validation, chopped carbon fiber-reinforced polylactic acid (PLA) composite lattice structures were fabricated via fused filament fabrication. Results indicate that increasing the forming angle enhances lateral stiffness (Young's modulus) while decreasing longitudinal stiffness. The rate of change of Young's modulus in the lateral direction is higher than that in the longitudinal direction based on the variations of the forming angles. It was concluded that geometric functionally graded structures could simultaneously have a better elastic response with a more significant Young's modulus for both longitudinal and lateral directions.