Transfiguration of Random Auxeticity of Programmable Metamaterial: A Kirigami Inspired Approach

This paper presents a comprehensive investigation into the auxetic behavior of a mechanical metamaterial inspired by a Kiri-gami structure. Through an integrated approach involving finite element analysis (FEA), and Monte Carlo (MC) simulations, the study explores the mechanical response of the metamaterial unit cell and its tessellated configurations. The study confirms the manifestation of a negative Poisson’s ratio (NPR) through detailed deformation and stress analyses under compressive loading. The auxetic response is further validated by modeling 2D tessellations in rigid dynamics, demonstrating directional expansion during axial compression and a calculated Poisson's ratio of -0.5386. Analytical models are developed to evaluate angular de-formations and Poisson’s ratio based on geometric parameters. These models are statistically validated using MC simulation, generating probability distributions of NPR under varied geometric configurations. Sensitivity analyses reveal that the side length is the most influential parameter governing both in-plane and out-of-plane auxetic responses, followed by deformation and extrusion length. Connector length has minimal impact. These findings not only reveal the auxetic nature of the design but also offer critical insights for optimizing structural performance through parameter tuning. The study provides a robust design and analysis of auxetic metamaterials with potential applications in energy ab-sorption, flexible mechanics, and impact-resistant structures.